Chapter 8 EXERGY A MEASURE OF WORK POTENTIAL

Transcription

1 8- Chaptr 8 EXERGY A MEASURE OF WORK POENIAL Exrgy, Irrvribility, Rvribl Work, and Scond-Law Efficincy 8-C Rvribl work diffr from th uful work by irrvribiliti. For rvribl proc both ar idntical. W u W rv I. 8-C Rvribl work and irrvribility ar idntical for proc that volv no actual uful work. 8-C h dad tat. 8-4C Y; xrgy i a function of th tat of th urroundg a wll a th tat of th ytm. 8-5C Uful work diffr from th actual work by th urroundg work. hy ar idntical for ytm that volv no urroundg work uch a tady-flow ytm. 8-6C Y. 8-7C No, not ncarily. h wll with th highr tmpratur will hav a highr xrgy. 8-8C h ytm that i at th tmpratur of th urroundg ha zro xrgy. But th ytm that i at a lowr tmpratur than th urroundg ha om xrgy c w can run a hat ng btwn th two tmpratur lvl. 8-9C hy would b idntical. 8-C h cond-law fficincy i a maur of th prformanc of a dvic rlativ to it prformanc undr rvribl condition. It diffr from th firt law fficincy that it i not a convrion fficincy. 8-C No. h powr plant that ha a lowr thrmal fficincy may hav a highr cond-law fficincy. 8-C No. h rfrigrator that ha a lowr COP may hav a highr cond-law fficincy. 8-C A proc with W rv i rvribl if it volv no actual uful work. Othrwi it i irrvribl.

2 8-8-4C Y. 8-5 Wdmill ar to b talld at a location with tady wd to rat powr. h mimum numbr of wdmill that nd to b talld i to b dtrmd. Aumption Air i at tandard condition of atm and 5 C Proprti h ga contant of air i.87 kpa.m /kg.k (abl A-. Analyi h xrgy or work potntial of th blowg air i th ktic nrgy it po, Exrgy k V (8 m/ kj/kg m /. kj/kg At tandard atmophric condition (5 C, kpa, th dnity and th ma flow rat of air ar P kpa ρ 8. m / kg R (.87 kpa m / kg K(98 K and hu, m& ρav π D ρ 4 Availabl Powr m& k (74 kg/(. kj/kg.74 kw V (.8 kg/m ( π / 4( m (8 m/ 74 kg/ h mimum numbr of wdmill that nd to b talld i W& total 6 kw N 5. 6 wdmill W&.74 kw

3 8-8-6E Saturatd tam i ratd a boilr by tranfrrg hat from th combution ga. h watd work potntial aociatd with thi hat tranfr proc i to b dtrmd. Alo, th ffct of crag th tmpratur of combution ga on th irrvribility i to b dicud. Aumption Stady opratg condition xit. Ktic and potntial nrgy chang ar ngligibl. Analyi h proprti of watr at th lt and lt of th boilr and at th dad tat ar (abl A-4E through A-6E P pia h h f Btu/lbm x (at.liq. f.5479 Btu/lbm R P pia h hg 98.8 Btu/lbm x (at. vap. g.546 Btu/lbm R 8 F h h F 48.7 Btu/lbm P 4.7 pia F.98 Btu/lbm R h hat tranfr durg th proc i q h h Btu/lbm h ntropy ration aociatd with thi proc i q Δw ΔR ( R 84. Btu/lbm ( Btu/lbm R (5 46R.77 Btu/lbm R h watd work potntial (xrgy dtruction i x dt (8 46 R(.77 Btu/lbm R 66.8 Btu/lbm h work potntial (xrgy of th tam tram i Δ ψ w h h ( ( Btu/lbm (54 R( Btu/lbm R. Btu/lbm Incrag th tmpratur of combution ga do not ffct th work potntial of tam tram c it i dtrmd by th tat at which watr ntr and lav th boilr. Dicuion hi problm may alo b olvd a follow: Exrgy tranfr by hat tranfr: x 54 ( hat q R Exrgy cra of tam: Δψ w.btu/lbm h nt xrgy dtruction: 68.9 Btu/lbm x x Δψ Btu/lbm dt hat w Watr pia at. liq. q pia at. vap.

4 Watr i to b pumpd to a high lvation lak at tim of low lctric dmand for u a hydrolctric turb at tim of high dmand. For a pcifid nrgy torag capacity, th mimum amount of watr that nd to b tord th lak i to b dtrmd. Aumption h vaporation of watr from th lak i ngligibl. Analyi h xrgy or work potntial of th watr i th potntial nrgy it po, 75 m Exrgy PE mgh hu, m PE gh 6 5 (9.8 m/ kwh 6 m / (75 m h kw /kg.45 kg 8-8 A hat rrvoir at a pcifid tmpratur can upply hat at a pcifid rat. h xrgy of thi hat upplid i to b dtrmd. Analyi h xrgy of th upplid hat, th rat form, i th amount of powr that would b producd by a rvribl hat ng, 5 K η th,max η Exrgy W& th,rv max, (.8(5, / 6 kj/.4 kw W& H rv, 98 K 5 K η & th,rv.8 HE 98 K &W rv 8-9 [Alo olvd by EES on nclod CD] A hat ng rciv hat from a ourc at a pcifid tmpratur at a pcifid rat, and rjct th wat hat to a k. For a givn powr put, th rvribl powr, th rat of irrvribility, and th nd law fficincy ar to b dtrmd. Analyi (a h rvribl powr i th powr producd by a rvribl hat ng opratg btwn th pcifid tmpratur limit, η W& th,max rv, η η th,rv th,rv L K.787 H 5 K & (.787(7 kj/ 55.7 kw (b h irrvribility rat i th diffrnc btwn th rvribl powr and th actual powr put: I & W& rv, W& kw u, (c h cond law fficincy i dtrmd from it dfition, Wu, kw η II 58.% W 55.7 kw rv, 5 K HE K 7 kj/ kw

5 EES Problm 8-9 i rconidrd. h ffct of rducg th tmpratur at which th wat hat i rjctd on th rvribl powr, th rat of irrvribility, and th cond law fficincy i to b tudid and th rult ar to b plottd. Analyi h problm i olvd ug EES, and th olution i givn blow. "Input Data" _H 5 [K] _dot_h 7 [kj/] {_L [K]} W_dot_ [kw] _Lurr 5 [C] "h rvribl work i th maximum work don by th Carnot Eng btwn _H and _L:" Eta_Carnot - _L/_H W_dot_rv_dot_H*Eta_Carnot "h irrvribility i givn a:" I_dot W_dot_rv-W_dot_ "h thrmal fficincy i, prcnt:" Eta_th Eta_Carnot*Convrt(, % "h cond law fficincy i, prcnt:" Eta_II W_dot_/W_dot_rv*Convrt(, % η II [%] I [kj/] W rv [kj/] L [K]

6 W rv [kj/] L [K] ηii [%] L [K] 8 I [kj/] L [K]

7 8-7 8-E h thrmal fficincy and th cond-law fficincy of a hat ng ar givn. h ourc tmpratur i to b dtrmd. Analyi From th dfition of th cond law fficincy, hu, η η th η II η th,rv th,rv L H η th,rv H η th η L II /( η th,rv (5 R/.4 5 R H HE 5 R η th 6% η II 6% 8- A body conta a pcifid amount of thrmal nrgy at a pcifid tmpratur. h amount that can b convrtd to work i to b dtrmd. Analyi h amount of hat that can b convrtd to work i imply th amount that a rvribl hat ng can convrt to work, 8 K W η th,rv max, W H rv, (.675( kj 6.75 kj 98 K K η th,rv HE 98 K kj 8- h thrmal fficincy of a hat ng opratg btwn pcifid tmpratur limit i givn. h cond-law fficincy of a ng i to b dtrmd. Analyi h thrmal fficincy of a rvribl hat ng opratg btwn th am tmpratur rrvoir i C hu, η th,rv η th η II η H th,rv 9 K.8 7 K % HE η th.4 C

8 A hou i matad at a pcifid tmpratur by lctric ritanc hatr. h rvribl work for thi hatg proc and irrvribility ar to b dtrmd. Analyi h rvribl work i th mimum work rquird to accomplih thi proc, and th irrvribility i th diffrnc btwn th rvribl work and th actual lctrical work conumd. h actual powr put i W & & & 8, kj/h. kw H h COP of a rvribl hat pump opratg btwn th pcifid tmpratur limit i COP HP, rv 4.4 L / H 88 / 95 hu, and W& rv, I& W& & COP u, W& H HP,rv rv,. kw.5 kw kw Hou C W 8, kj/h 5 C 8-5E A frzr i matad at a pcifid tmpratur by rmovg hat from it at a pcifid rat. h powr conumption of th frzr i givn. h rvribl powr, irrvribility, and th cond-law fficincy ar to b dtrmd. Analyi (a h rvribl work i th mimum work rquird to accomplih thi tak, which i th work that a rvribl rfrigrator opratg btwn th pcifid tmpratur limit would conum, H / L 55 / 48 COP R, rv W& rv, & COP L R,rv 75 Btu/m hp 4.4 Btu/m (b h irrvribility i th diffrnc btwn th rvribl work and th actual lctrical work conumd, I & W& u, W&.7..5 hp rv, (c h cond law fficincy i dtrmd from it dfition, W& η II & rv W u. hp.7 hp 8.9%. hp 75 F R 75 Btu/m Frzr F.7 hp

9 It i to b hown that th powr producd by a wd turb i proportional to th cub of th wd vlocity and th quar of th blad pan diamtr. Analyi h powr producd by a wd turb i proportional to th ktic nrgy of th wd, which i qual to th product of th ktic nrgy of air pr unit ma and th ma flow rat of air through th blad pan ara. hrfor, Wd powr (Efficincy(Ktic nrgy(ma flow rat of air η η wd wd V ( ρav η πv D ρ 8 wd V (Contant V π D ρ 4 which complt th proof that wd powr i proportional to th cub of th wd vlocity and to th quar of th blad pan diamtr. D V 8-7 A gothrmal powr produc 4 MW powr whil th xrgy dtruction th plant i 8.5 MW. h xrgy of th gothrmal watr ntrg to th plant, th cond-law fficincy of th plant, and th xrgy of th hat rjctd from th plant ar to b dtrmd. Aumption Stady opratg condition xit. Ktic and potntial nrgy chang ar ngligibl. Watr proprti ar ud for gothrmal watr. Analyi (a h proprti of gothrmal watr at th lt of th plant and at th dad tat ar (abl A- 4 through A-6 6 C h kj/kg x.946 kj/kg.k 5 C h 4.8 kj/kg x.67 kj/kg.k h xrgy of gothrmal watr ntrg th plant i X & m& h [ h ( ] [( kj/kg (5 7 K( kJ/kg.K] (44 kg/ 44,55 kw 44.5 MW (b h cond-law fficincy of th plant i th ratio of powr producd to th xrgy put to th plant W& η II X& 4, kw 44,55 kw.4 (c h xrgy of th hat rjctd from th plant may b dtrmd from an xrgy balanc on th plant X & hat, X& W& X& 44,55 4, 8,5,5 kw. MW dt

10 8- Scond-Law Analyi of Clod Sytm 8-8C Y. 8-9C Y, it can. For xampl, th t law fficincy of a rvribl hat ng opratg btwn th tmpratur limit of K and K i 7%. Howvr, th cond law fficincy of thi ng, lik all rvribl dvic, i %.

11 8-8-E Air i xpandd an adiabatic clod ytm with an intropic fficincy of 95%. h cond law fficincy of th proc i to b dtrmd. Aumption Ktic and potntial nrgy chang ar ngligibl. h proc i adiabatic, and thu thr i no hat tranfr. Air i an idal ga with contant pcific hat. Proprti h proprti of air at room tmpratur ar c p.4 Btu/lbm R, c v.7 Btu/lbm R, k.4, and R.6855 Btu/lbm R (abl A-Ea. Analyi W tak th air a th ytm. hi i a clod ytm c no ma cro th boundari of th ytm. h nrgy balanc for thi ytm can b xprd a E E ΔE 44 ytm 44 Nt nrgy tranfr by hat, work, and ma W b, Chang trnal, ktic, potntial, tc.nrgi ΔU mc ( h fal tmpratur for th intropic ca i ( k / k.4 /.4 P P v 5 pia (56 R 5 pia h actual xit tmpratur from th intropic rlation i η η ( 9. R 56 (.95( R h boundary work put i c ( (.7 Btu/lbm R(56.6R w b, v h ntropy chang of air i Δ air c p ln P R ln P (.4 Btu/lbm Rln.6 R 56 R.9 Btu/lbm R h xrgy diffrnc btwn tat and i φ φ u u P ( v v ( cv ( P R ( P P 4.84 Btu/lbm (4.7 pia(.6855 Btu/lbm R.7 Btu/lbm h uful work i dtrmd from w w u b, w urr c v ( P ( v v c (.6855 Btu/lbm Rln 56 R 5 pia.6 R 4.84 Btu/lbm (4.7 pia(.6855 Btu/lbm R 5 pia 7. Btu/lbm h cond law fficincy i thn w 7. Btu/lbm η u II.8 Δφ.7 Btu/lbm v 4.84 Btu/lbm 5 pia 5 pia.6 R (57 R(.9Btu/lbm R 5 pia ( P R P P 56 R 5 pia Air 5 pia F 5 pia 5 pia

12 8-8-E Air and hlium at pcifid tat ar conidrd. h ga with th highr xrgy contnt i to b idntifid. Aumption Ktic and potntial nrgy chang ar ngligibl. Air and hlium ar idal ga with contant pcific hat. Proprti h proprti of air at room tmpratur ar c p.4 Btu/lbm R, c v.7 Btu/lbm R, k.4, and R.6855 Btu/lbm R.74 pia ft /lbm R. For hlium, c p.5 Btu/lbm R, c v.75 Btu/lbm R, k.667, and R.496 Btu/lbm R.689 pia ft /lbm R. (abl A-E. Analyi h ma of air th ytm i PV ( pia( ft m.55 lbm R (.74 pia ft /lbm R(76 R h ntropy chang of air btwn th givn tat and th dad tat i c p ln R ln P P (.4 Btu/lbm Rln.488 Btu/lbm R 76 R 57 R (.6855 Btu/lbm Rln h air pcific volum at th givn tat and dad tat ar pia 4.7 pia Air ft pia F R v P v (.74 pia ft /lbm R(76 R.85 ft /lbm pia R P (.74 pia ft /lbm R(57 R.5 ft /lbm 4.7 pia h pcific clod ytm xrgy of th air i thn φ u u c v ( P ( v v 4.8 Btu/lbm ( P ( v v ( Btu (.7 Btu/lbm R( 77R (4.7 pia(.85.5ft /lbm 5.44 pia ft (57 R(.488 Btu/lbm R h total xrgy availabl th air for th production of work i thn Φ m φ (.55 lbm(4.8 Btu/lbm.6 Btu W now rpat th calculation for hlium: PV (8 pia( ft m.94 lbm R (.689 pia ft /lbm R(66 R c p ln R ln P P 66 R 8 pia (.5 Btu/lbm Rln (.496 Btu/lbm Rln 57 R 4.7 pia.587 Btu/lbm R Hlium ft 8 pia F

13 8- R v P v (.689 pia ft /lbm R(66 R. ft /lbm 8 pia R P φ u u c v ( 99. Btu/lbm (.689 pia ft /lbm R(57 R 97.9 ft /lbm 4.7 pia P ( v v ( P ( v v ( Btu (.75 Btu/lbm R( 77R (4.7 pia(. 97.9ft /lbm 5.44 pia ft (57 R(.587 Btu/lbm R Φ m φ (.94 lbm(99.btu/lbm 8. Btu Comparion of two rult how that th hlium ytm ha a gratr potntial for th production of work.

14 Stam and R-4a at th am tat ar conidrd. h fluid with th highr xrgy contnt i to b idntifid. Aumption Ktic and potntial nrgy chang ar ngligibl. Analyi h proprti of watr at th givn tat and at th dad tat ar P 8 kpa 8 C u kj/kg v.47 m u u f 5 C v v f P kpa h xrgy of tam i For R-4a; Φ m /kg kj/kg 5 5 C 5 C 4.8 kj/kg. m (abl A - 6 /kg.67 kj/kg K [ u u P ( v v ( ] (abl A - 4 ( kJ/kg ( kpa(.47.m (kg (98 K( kJ/kg K 6.7 kj P 8 kpa 8 C u kj/kg v m u u f 5 C v v f P kpa Φ m /kg.7 kj/kg 5 5 C 5 C kj/kg (abl A m /kg.4 kj/kg K [ u u P ( v v ( ] (abl A - ( kJ/kg ( kpa( m (kg (98 K(.7.4kJ/kg K 5. kj h tam can thrfor ha mor work potntial than th R-4a. kj /kg kpa m Stam kg 8 kpa 8 C R-4a kg 8 kpa 8 C kj /kg kpa m

15 A cyldr itially conta air at atmophric condition. Air i comprd to a pcifid tat and th uful work put i maurd. h xrgy of th air at th itial and fal tat, and th mimum work put to accomplih thi comprion proc, and th cond-law fficincy ar to b dtrmd Aumption Air i an idal ga with contant pcific hat. h ktic and potntial nrgi ar ngligibl. Proprti h ga contant of air i R.87 kpa.m /kg.k (abl A-. h pcific hat of air at th avrag tmpratur of (984/6 K ar c p.9 kj/kg K and c v.7 kj/kg K (abl A-. Analyi (a W raliz that X Φ c air itially i at th dad tat. h ma of air i P V m R ( kpa(. m.4 kg (.87 kpa m / kg K(98 K Alo, and PV P V P ( kpa(4 K V V ( L.47 L P (6 kpa(98 K c p,avg ln P R ln P 4 K (.9 kj/kg K ln (.87 kj/kg K 98 K.68 kj/kg K 6 kpa ln kpa AIR V L P kpa 5 C hu, th xrgy of air at th fal tat i (.4 kg.7 kj [ ( ( ] X Φ m cv,avg P ( V V [(.7 kj/kg K(4-98K - (98 K(-.68 kj/kg K ] ( kpa(.47-.m [kj/m kpa] (b h mimum work put i th rvribl work put, which can b dtrmd from th xrgy balanc by ttg th xrgy dtruction qual to zro, X X 44 Nt xrgy tranfr by hat,work,andma Xdtroyd ΔX ytm Exrgy dtruction (rvribl W rv, (c h cond-law fficincy of thi proc i W η II W rv, u,.7 kj. kj 4.% X Chang xrgy X.7.7kJ

16 A cyldr i itially filld with R-4a at a pcifid tat. h rfrigrant i coold and condnd at contant prur. h xrgy of th rfrigrant at th itial and fal tat, and th xrgy dtroyd durg thi proc ar to b dtrmd. Aumption h ktic and potntial nrgi ar ngligibl. Proprti From th rfrigrant tabl (abl A- through A-, v.4875 m / kg P.7 MPa u 74. kj/kg 6 C.56 kj/kg K v v f P.7 MPa u u f 4 C v P. MPa u C 4 C.78 m. kj/kg K 5.84 kj/kg.86m kj/kg / kg.958 kj/kg K / kg Analyi (a From th clod ytm xrgy rlation, {( u u ( P ( v } X Φ m v (5 kg{( kj/kg (97 K(.56. kj/kg K R-4a.7 MPa P cont. and, ( kpa( m 5. kj kj /kg kpa m {( u u ( P ( v } X Φ m v (5 kg{( kj/kg - (97 K(.958. kj/kg K } ( kpa(.86.78m 8.6 kj kj /kg kpa m (b h rvribl work put, which rprnt th mimum work put W rv, thi ca can b dtrmd from th xrgy balanc by ttg th xrgy dtruction qual to zro, X X 44 Nt xrgy tranfr by hat,work,andma dtroyd Exrgy dtruction (rvribl X ΔXytm W rv, X Chang xrgy X } kj Notg that th proc volv only boundary work, th uful work put durg thi proc i imply th boundary work xc of th work don by th urroundg air, W u, W W urr, m( P P ( v v W P ( V V P( V V P m( v v (5 kg(7 - kpa( m kj / kg kpa m. kj Knowg both th actual uful and rvribl work put, th xrgy dtruction or irrvribility that i th diffrnc btwn th two i dtrmd from it dfition to b X dtroyd I W W kj u, rv,

17 E An ulatd rigid tank conta aturatd liquid-vapor mixtur of watr at a pcifid prur. An lctric hatr id i turnd on and kpt on until all th liquid i vaporizd. h xrgy dtruction and th cond-law fficincy ar to b dtrmd. Aumption Ktic and potntial nrgi ar ngligibl. Proprti From th tam tabl (abl A-4 through A-6 v v f xv fg P 5 pia u u f xu fg x.5 x f fg.78.5 ( ft / lbm Btu / lbm Btu / lbm R v v u at. vapor u v.988 ft /lbm g v.988 ft /lbm g.9 Btu/lbm.569 Btu/lbm R Analyi (a h irrvribility can b dtrmd from it dfition X dtroyd S whr th ntropy ration i dtrmd from an ntropy balanc on th tank, which i an ulatd clod ytm, S S 44 Nt ntropy tranfr by hat and ma S { Entropy ration S ΔSytm 44 Chang ntropy ΔS ytm m( H O 5 pia W Subtitutg, X dtroyd S m ( (6 lbm(55 R( Btu/lbm R 766 Btu (b Notg that V contant durg thi proc, th W and W u ar idntical and ar dtrmd from th nrgy balanc on th clod ytm nrgy quation, E E ΔE 44 ytm 44 Nt nrgy tranfr by hat, work, and ma W, Chang trnal, ktic, potntial, tc.nrgi ΔU m( u u or, W, (6 lbm( btu/lbm 45 Btu hn th rvribl work durg thi proc and th cond-law fficincy bcom W rv, Wu, X dtroyd Btu hu, W η II rv W u 9 Btu 45 Btu.9%

18 A rigid tank i dividd to two qual part by a partition. On part i filld with comprd liquid whil th othr id i vacuatd. h partition i rmovd and watr xpand to th ntir tank. h xrgy dtroyd durg thi proc i to b dtrmd. Aumption Ktic and potntial nrgi ar ngligibl. Analyi h proprti of th watr ar (abl A-4 through A-6 v v f P kpa u u f C 6 C.7 m / kg 5.6 kj/kg.8 kj/kg K Notg that v v.7.4 m / kg,.5 kg kpa 6 C WAER Vacuum P v 5 kpa.4 x u v v f v fg..4 u x u kj/kg f f x fg fg kj/kg K akg th dirction of hat tranfr to b to th tank, th nrgy balanc on thi clod ytm bcom or, E E 44 Nt nrgy tranfr by hat, work, and ma ΔEytm 44 Chang trnal, ktic, potntial, tc.nrgi ΔU m( u u (.5 kg( kj/kg -7.5kJ 7.5 kj h irrvribility can b dtrmd from it dfition X dtroyd S whr th ntropy ration i dtrmd from an ntropy balanc on an xtndd ytm that clud th tank and it immdiat urroundg o that th boundary tmpratur of th xtndd ytm i th tmpratur of th urroundg at all tim, S Subtitutg, S 44 Nt ntropy tranfr by hat and ma X dtroyd b, S { Entropy ration S S ΔSytm 44 Chang ntropy ΔS m( ytm m( urr S m( urr 7.5 kj (98 K (.5 kg( kJ/kg K 98 K.67 kj

19 EES Problm 8-6 i rconidrd. h ffct of fal prur th tank on th xrgy dtroyd durg th proc i to b vtigatd. Analyi h problm i olvd ug EES, and th olution i givn blow. _6 [C] P_ [kpa] m.5 [kg] P_5 [kpa] _o5 [C] P_o [kpa] _urr _o "Conrvation of nrgy for clod ytm i:" E_ - E_ DELAE DELAE m*(u_ - u_ E_ E u_ tnrgy(tam_iapw,pp_,_ v_ volum(tam_iapw,pp_, ntropy(tam_iapw,pp_,_ v_ *v_ u_ tnrgy(tam_iapw, vv_,pp ntropy(tam_iapw, vv_,pp_ S_ -S_S_DELAS_y S_ [kj/k] S /(_urr7 DELAS_ym*(_ - _ X_dtroyd (_o7*s_ P [kpa] X dtroyd [kj] [kj] X dtroyd [kj] P [kpa]

20 8-8-8 An ulatd cyldr i itially filld with aturatd liquid watr at a pcifid prur. h watr i hatd lctrically at contant prur. h mimum work by which thi proc can b accomplihd and th xrgy dtroyd ar to b dtrmd. Aumption h ktic and potntial nrgy chang ar ngligibl. h cyldr i wll-ulatd and thu hat tranfr i ngligibl. h thrmal nrgy tord th cyldr itlf i ngligibl. 4 h comprion or xpanion proc i quai-quilibrium. Analyi (a From th tam tabl (abl A-4 through A-6, u P 5 kpa v v f at. liquid h h f h ma of th tam i u V. m m v.5 m kpa kpa / kg kj / kg.5 m 467. kj/kg /kg.47 kj/kg K.899 kg W tak th contnt of th cyldr a th ytm. hi i a clod ytm c no ma ntr or lav. h nrgy balanc for thi tationary clod ytm can b xprd a E E ΔE 44 ytm 44 Nt nrgy tranfr by hat, work, and ma W, W W b,, Chang trnal, ktic, potntial, tc.nrgi ΔU m( h h c ΔU W b ΔH durg a contant prur quai-quilibrium proc. Solvg for h, W, kj h h kj/kg m.899 kg hu, P 5 kpa h 65. kj/kg f fg h h f x.5 h fg 6. f x fg kj/kg K u u f xu fg kj/kg v v x v.5.5 ( m /kg h rvribl work put, which rprnt th mimum work put W rv, thi ca can b dtrmd from th xrgy balanc by ttg th xrgy dtruction qual to zro, (rvribl X Xdtroyd ΔXytm Wrv, X X X 44 Nt xrgy tranfr by hat,work,andma Exrgy dtruction 44 Chang xrgy Saturatd Liquid Subtitutg th clod ytm xrgy rlation, th rvribl work put durg thi proc i dtrmd to b H O P 5 kpa W

21 8- W rv, m [( u u ( P ( v v ] (.899 kg{( kj/kg (98 K( kj/kg K ( kpa(.5.67m 47.7 kj / kg[ kj/ kpa m ]} (b h xrgy dtruction (or irrvribility aociatd with thi proc can b dtrmd from it dfition X dtroyd S whr th ntropy ration i dtrmd from an ntropy balanc on th cyldr, which i an ulatd clod ytm, S Subtitutg, S 44 Nt ntropy tranfr by hat and ma X dtroyd S { Entropy ration S ΔSytm 44 Chang ntropy ΔS ytm m( S m ( (98 K(.899 kg( kj/kg K 75 kj

22 8-8-9 EES Problm 8-8 i rconidrd. h ffct of th amount of lctrical work on th mimum work and th xrgy dtroyd i to b vtigatd. Analyi h problm i olvd ug EES, and th olution i givn blow. x_ P_5 [kpa] V [L] P_P_ {W_El [kj]} _o5 [C] P_o [kpa] "Conrvation of nrgy for clod ytm i:" E_ - E_ DELAE DELAE m*(u_ - u_ E_W_El E_ W_b W_b m*p_*(v_-v_ u_ tnrgy(tam_iapw,pp_,xx_ v_ volum(tam_iapw,pp_,xx ntropy(tam_iapw,pp_,xx_ u_ tnrgy(tam_iapw, vv_,pp ntropy(tam_iapw, vv_,pp_ mv*convrt(l,m^/v_ W_rv_m*(u_ - u_ -(_o7.5 *(_-_P_o*(v_-v_ "Entropy Balanc:" S_ - S_S_ DELAS_y DELAS_y m*(_ - _ S_ [kj/k] S_ [kj/k] W rv, [kj] "h xrgy dtruction or irrvribility i:" X_dtroyd (_o7.5*s_ W El [kj] W El [kj] W rv, [kj] X dtroyd [kj] X dtroyd [kj/k] W El [kj]

23 8-8-4 An ulatd cyldr i itially filld with aturatd R-4a vapor at a pcifid prur. h rfrigrant xpand a rvribl mannr until th prur drop to a pcifid valu. h chang th xrgy of th rfrigrant durg thi proc and th rvribl work ar to b dtrmd. Aumption h ktic and potntial nrgy chang ar ngligibl. h cyldr i wll-ulatd and thu hat tranfr i ngligibl. h thrmal nrgy tord th cyldr itlf i ngligibl. 4 h proc i tatd to b rvribl. Analyi hi i a rvribl adiabatic (i.., intropic proc, and thu. From th rfrigrant tabl (abl A- through A-, v v g P.8 MPa u u g at. MPa MPa.56 m kj/kg / kg.98 kj/kg K h ma of th rfrigrant i V.5 m m v.56 m / kg.95 kg R-4a.8 MPa Rvribl f x.975 fg.786 P. MPa v v f xv fg ( m /kg u u x u kj/kg f fg h rvribl work put, which rprnt th maximum work put W rv, can b dtrmd from th xrgy balanc by ttg th xrgy dtruction qual to zro, X X 44 Nt xrgy tranfr by hat,work,andma dtroyd Exrgy dtruction (rvribl X ΔXytm W W rv, rv, X X Φ Chang xrgy X X Φ hrfor, th chang xrgy and th rvribl work ar idntical thi ca. Ug th dfition of th clod ytm xrgy and ubtitutg, th rvribl work i dtrmd to b W rv, Φ Φ 8.5 kj m [( u u ( P (v v ] m[ ( u u P ( v v ] (.95 kg[( kj/kg ( kpa( m / kg[kj/kpa m ]

24 E Oxy ga i comprd from a pcifid itial tat to a fal pcifid tat. h rvribl work and th cra th xrgy of th oxy durg thi proc ar to b dtrmd. Aumption At pcifid condition, oxy can b tratd a an idal ga with contant pcific hat. Proprti h ga contant of oxy i R.66 Btu/lbm.R (abl A-E. h contant-volum pcific hat of oxy at th avrag tmpratur i avg v ( / (75 55 / F c, avg.64 Btu/lbm R Analyi h ntropy chang of oxy i v cv, avg ln R ln v 985 R.5 ft /lbm (.64 Btu/lbm R ln (.66 Btu/lbm R ln 55 R ft /lbm.894 Btu/lbm R O ft /lbm 75 F h rvribl work put, which rprnt th mimum work put W rv, thi ca can b dtrmd from th xrgy balanc by ttg th xrgy dtruction qual to zro, (rvribl X Xdtroyd ΔXytm Wrv, X X X 44 Nt xrgy tranfr by hat,work,andma Exrgy dtruction 44 Chang xrgy hrfor, th chang xrgy and th rvribl work ar idntical thi ca. Subtitutg th clod ytm xrgy rlation, th rvribl work put durg thi proc i dtrmd to b w rv, φ φ [( u {(.64 Btu/lbm R(55-985R (55 R(.894 Btu/lbm R (4.7 pia(.5ft 6.7 Btu/lbm u ( Alo, th cra th xrgy of oxy i φ φ w rv, 6.7 Btu/lbm P ( v v ] /lbm[btu/5.49 pia ft ]}

25 An ulatd tank conta CO ga at a pcifid prur and volum. A paddl-whl th tank tir th ga, and th prur and tmpratur of CO ri. h actual paddl-whl work and th mimum paddl-whl work by which thi proc can b accomplihd ar to b dtrmd. Aumption At pcifid condition, CO can b tratd a an idal ga with contant pcific hat at th avrag tmpratur. h urroundg tmpratur i 98 K. Analyi (a h itial and fal tmpratur of CO ar P V ( kpa(. m 98. K mr (. kg(.889 kpa m / kg K PV mr ( kpa(. m (. kg(.889 kpa m 57.9 K / kg K. m. kg CO kpa W pw avg v ( / ( / 8 K c, avg.684 kj/kg K h actual paddl-whl work don i dtrmd from th nrgy balanc on th CO ga th tank, W tak th contnt of th cyldr a th ytm. hi i a clod ytm c no ma ntr or lav. h nrgy balanc for thi tationary clod ytm can b xprd a E E 44 Nt nrgy tranfr by hat, work, and ma W pw, ΔEytm 44 Chang trnal, ktic, potntial, tc.nrgi ΔU mc ( v or, W pw, (. kg(.684 kj/kg K( K 87. kj (b h mimum paddl-whl work with which thi proc can b accomplihd i th rvribl work, which can b dtrmd from th xrgy balanc by ttg th xrgy dtruction qual to zro, (rvribl X Xdtroyd ΔXytm Wrv, X X X 44 Nt xrgy tranfr by hat,work,andma Exrgy dtruction 44 Chang xrgy Subtitutg th clod ytm xrgy rlation, th rvribl work put for thi proc i dtrmd to b c W rv, m m c [( u u ( P ( v v ] [ ( ( ] v,avg (. kg 7.74 kj [(.684 kj/kg K( K (98.(.5 kj/kg K ] v 57.9 K cv,avg ln R ln (.684 kj/kg K ln.5 kj/kg K v 98. K

26 An ulatd cyldr itially conta air at a pcifid tat. A ritanc hatr id th cyldr i turnd on, and air i hatd for 5 m at contant prur. h xrgy dtruction durg thi proc i to b dtrmd. Aumption Air i an idal ga with variabl pcific hat. Proprti h ga contant of air i R.87 kj/kg.k (abl A-. Analyi h ma of th air and th lctrical work don durg thi proc ar Alo, P V ( kpa(. m m.48 kg R (.87kPa m /kg K( K W W& Δt ( 5. kj / (5 6 5kJ K h 9. kj / kg and. 7 kj / kg K h nrgy balanc for thi tationary clod ytm can b xprd a E E ΔE 44 ytm 44 Nt nrgy tranfr by hat, work, and ma W, W W b,, Chang trnal, ktic, potntial, tc. nrgi ΔU m( h h c ΔU W b ΔH durg a contant prur quai-quilibrium proc. hu, Alo, h h W m, 5 kj kj/kg o.48 kg o AIR kpa P cont 65 K.4964 kj/kg K o o P o o R ln kj/kg K P h xrgy dtruction (or irrvribility aociatd with thi proc can b dtrmd from it dfition X dtroyd S whr th ntropy ration i dtrmd from an ntropy balanc on th cyldr, which i an ulatd clod ytm, S S 44 Nt ntropy tranfr by hat and ma S { Entropy ration S ΔSytm 44 Chang ntropy ΔS ytm m( W Subtitutg, X dtroyd S m ( ( K(.48 kg(.796 kj/kg K 9.9 kj

27 A fixd ma of hlium undrgo a proc from a pcifid tat to anothr pcifid tat. h cra th uful nrgy potntial of hlium i to b dtrmd. Aumption At pcifid condition, hlium can b tratd a an idal ga. Hlium ha contant pcific hat at room tmpratur. Proprti h ga contant of hlium i R.769 kj/kg.k (abl A-. h contant volum pcific hat of hlium i c v.56 kj/kg.k (abl A-. Analyi From th idal-ga ntropy chang rlation, c v,avg ln v R ln v H 8 kg 88 K 5 K.5 m /kg (.56 kj/kg K ln (.769 kj/kg K ln.87 kj/kg K 88 K m /kg h cra th uful potntial of hlium durg thi proc i imply th cra xrgy, [( u u ( P ( v ] Φ Φ m v (8 kg{(.56 kj/kg K(88 5 K (98 K(.87 kj/kg K ( kpa(.5m 698 kj / kg[kj/kpa m ]}

28 On id of a partitiond ulatd rigid tank conta argon ga at a pcifid tmpratur and prur whil th othr id i vacuatd. h partition i rmovd, and th ga fill th ntir tank. h xrgy dtroyd durg thi proc i to b dtrmd. Aumption Argon i an idal ga with contant pcific hat, and thu idal ga rlation apply. Proprti h ga contant of argon i R.8 kj/kg.k (abl A-. Analyi akg th ntir rigid tank a th ytm, th nrgy balanc can b xprd a E E ΔE Nt nrgy tranfr by hat, work, and ma c u u( for an idal ga. ytm Chang trnal, ktic, potntial, tc. nrgi ΔU m( u u u u h xrgy dtruction (or irrvribility aociatd with thi proc can b dtrmd from it dfition X dtroyd S whr th ntropy ration i dtrmd from an ntropy balanc on th ntir tank, which i an ulatd clod ytm, whr S S 44 Nt ntropy tranfr by hat and ma ΔS ytm S { Entropy ration S ΔSytm 44 Chang ntropy ΔS ytm m( ( V ln ln V m m c,avg ln v R mr V V ( kg(.8 kj/kg K ln(.4 kj/k Argon kpa 7 C Vacuum Subtitutg, X dtroyd S m ( (98 K(.4 kj/k 9 kj

29 E A hot coppr block i droppd to watr an ulatd tank. h fal quilibrium tmpratur of th tank and th work potntial watd durg thi proc ar to b dtrmd. Aumption Both th watr and th coppr block ar compribl ubtanc with contant pcific hat at room tmpratur. h ytm i tationary and thu th ktic and potntial nrgi ar ngligibl. h tank i wll-ulatd and thu thr i no hat tranfr. Proprti h dnity and pcific hat of watr at th anticipatd avrag tmpratur of 9 F ar ρ 6. lbm/ft and c p. Btu/lbm. F. h pcific hat of coppr at th anticipatd avrag tmpratur of F i c p.95 Btu/lbm. F (abl A-E. Analyi W tak th ntir contnt of th tank, watr coppr block, a th ytm, which i a clod ytm. h nrgy balanc for thi ytm can b xprd a or, E E 44 Nt nrgy tranfr by hat, work, and ma ΔU ΔEytm 44 Chang trnal, ktic, potntial, tc.nrgi ΔU Cu ΔU watr Watr 75 F Coppr 5 F whr [ mc ( ] Cu [ mc( ] watr m w ρv (6.lbm/ft (.5 ft 9.5 lbm Subtitutg, (7 lbm(.95 Btu/lbm F( 86.4 F R 5 F (9.5 lbm(. Btu/lbm F( 75 F h watd work potntial i quivalnt to th xrgy dtruction (or irrvribility, and it can b dtrmd from it dfition X dtroyd S whr th ntropy ration i dtrmd from an ntropy balanc on th ytm, which i an ulatd clod ytm, whr S S 44 Nt ntropy tranfr by hat and ma ΔS ΔS Subtitutg, coppr watr mc mc avg avg S { Entropy ration S ln ln ΔSytm 44 Chang ntropy ΔS ytm ΔS watr ΔS coppr R (7 lbm(.9 Btu/lbm R ln.696 Btu/R 7 R R (9.5 lbm(. Btu/lbm R ln.96 Btu/R 55 R X dtroyd (55 R( Btu/R 4.9 Btu

30 A hot iron block i droppd to watr an ulatd tank that i tirrd by a paddl-whl. h ma of th iron block and th xrgy dtroyd durg thi proc ar to b dtrmd. Aumption Both th watr and th iron block ar compribl ubtanc with contant pcific hat at room tmpratur. h ytm i tationary and thu th ktic and potntial nrgi ar ngligibl. h tank i wll-ulatd and thu thr i no hat tranfr. Proprti h dnity and pcific hat of watr at 5 C ar ρ 997 kg/m and c p 4.8 kj/kg. F. h pcific hat of iron at room tmpratur (th only valu availabl th tabl i c p.45 kj/kg. C (abl A-. Analyi W tak th ntir contnt of th tank, watr iron block, a th ytm, which i a clod ytm. h nrgy balanc for thi ytm can b xprd a whr E E 44 Nt nrgy tranfr by hat, work, and ma m W watr pw W W pw, ΔEytm 44 Chang trnal, ktic, potntial, tc.nrgi ΔU ΔU iron ΔU watr pw, [ mc( ] iron [ mc( ] watr ρv (997 kg/m (.m 99.7 kg W& Δt (. kj/( 6 4 kj pw, Subtitutg, 4 kj miron (.45 kj/kg C(4 85 C (99.7 kg(4.8 kj/kg C(4 C m 5. kg iron (b h xrgy dtruction (or irrvribility can b dtrmd from it dfition X dtroyd S whr th ntropy ration i dtrmd from an ntropy balanc on th ytm, which i an ulatd clod ytm, whr S S 44 Nt ntropy tranfr by hat and ma ΔS ΔS Subtitutg, iron watr mc avg mc avg S { Entropy ration S ln ln ΔS ytm 44 Chang ntropy ΔS ytm ΔS iron ΔS watr 97 K (5. kg(.45 kj/kg K ln 4.7 kj/k 58 K 97 K (99.7 kg(4.8 kj/kg K ln 5.65 kj/k 9 K X dtroyd S (9 K( kj/k 75. kj L C Iron 85 C Watr W pw

31 An iron block and a coppr block ar droppd to a larg lak whr thy cool to lak tmpratur. h amount of work that could hav bn producd i to b dtrmd. Aumption h iron and coppr block and watr ar compribl ubtanc with contant pcific hat at room tmpratur. Ktic and potntial nrgi ar ngligibl. Proprti h pcific hat of iron and coppr at room tmpratur ar c p, iron.45 kj/kg. C and c p,coppr.86 kj/kg. C (abl A-. Analyi h thrmal-nrgy capacity of th lak i vry larg, and thu th tmpratur of both th iron and th coppr block will drop to th lak tmpratur (5 C whn th thrmal quilibrium i tablihd. W tak both th iron and th coppr block a th ytm, which i a clod ytm. h nrgy balanc for thi ytm can b xprd a or, E E 44 Nt nrgy tranfr by hat, work, and ma ΔEytm 44 Chang trnal, ktic, potntial, tc.nrgi ΔU ΔU iron ΔU mc( ] [ mc( ] [ iron coppr coppr Iron 85 C Lak 5 C Coppr Iron Subtitutg, ( 5 kg(.45 kj/kg K( 5 88 K ( kg(.86 kj/kg K( kj K h work that could hav bn producd i qual to th watd work potntial. It i quivalnt to th xrgy dtruction (or irrvribility, and it can b dtrmd from it dfition X dtroyd S. h ntropy ration i dtrmd from an ntropy balanc on an xtndd ytm that clud th block and th watr thir immdiat urroundg o that th boundary tmpratur of th xtndd ytm i th tmpratur of th lak watr at all tim, whr S S 44 Nt ntropy tranfr by hat and ma b, S { Entropy ration S S ΔSytm 44 Chang ntropy ΔS ΔS ytm iron ΔS ΔS iron coppr ΔS lak coppr ΔS ΔS Subtitutg, iron coppr mc avg mc ln avg ln ( 5 kg(.45 kj/kg K 88 K ln kj/k 5 K 88 K 5 K ( kg(.86 kj/kg K ln.57 kj/k X dtroyd S 964 kj (9 K kj/k K kj

32 8-8-49E A rigid tank i itially filld with aturatd mixtur of R-4a. Hat i tranfrrd to th tank from a ourc until th prur id ri to a pcifid valu. h amount of hat tranfr to th tank from th ourc and th xrgy dtroyd ar to b dtrmd. Aumption h tank i tationary and thu th ktic and potntial nrgy chang ar zro. hr i no hat tranfr with th nvironmnt. Proprti From th rfrigrant tabl (abl A-E through A-E, P 4 pia x.55 u v v u f f f x u x x v fg fg fg Btu / lbm Btu / lbm R ft / lbm P ( v 6 pia v x u v v f v fg x Btu/lbm R u f f x u fg fg Btu/lbm Analyi (a h ma of th rfrigrant i V ft m v.654 ft / lbm 8.4 lbm W tak th tank a th ytm, which i a clod ytm. h nrgy balanc for thi tationary clod ytm can b xprd a Subtitutg, E E 44 Nt nrgy tranfr by hat, work, and ma m( u u ΔEytm 44 Chang trnal, ktic, potntial, tc.nrgi ΔU m( u u (8.4 lbm( Btu/lbm 446. Btu (b h xrgy dtruction (or irrvribility can b dtrmd from it dfition X dtroyd S. h ntropy ration i dtrmd from an ntropy balanc on an xtndd ytm that clud th tank and th rgion it immdiat urroundg o that th boundary tmpratur of th xtndd ytm whr hat tranfr occur i th ourc tmpratur, Subtitutg, S S 44 Nt ntropy tranfr by hat and ma b, S { Entropy ration S S ΔSytm 44 Chang ntropy ΔS m( ytm m(, ourc R-4a 4 pia Sourc C X dtroyd S 446. Btu (55 R (8.4 lbm(.9.46btu/lbm R R Btu

33 8-8-5 Chickn ar to b coold by chilld watr an immrion chillr that i alo gag hat from th urroundg. h rat of hat rmoval from th chickn and th rat of xrgy dtruction durg thi proc ar to b dtrmd. Aumption Stady opratg condition xit. hrmal proprti of chickn and watr ar contant. h tmpratur of th urroundg mdium i 5 C. Proprti h pcific hat of chickn i givn to b.54 kj/kg. C. h pcific hat of watr at room tmpratur i 4.8 kj/kg. C (abl A-. Analyi (a Chickn ar droppd to th chillr at a rat of 5 pr hour. hrfor, chickn can b conidrd to flow tadily through th chillr at a ma flow rat of &m chickn (5 chickn / h(. kg / chickn kg / h.56kg / akg th chickn flow tram th chillr a th ytm, th nrgy balanc for tadily flowg chickn can b xprd th rat form a (tady E E ΔEytm E& E& & 44 & & Rat of nt nrgy tranfr by hat, work, and ma mh & & Rat of chang trnal, ktic, potntial, tc.nrgi & & mh & chickn m& (c Δk Δp chickn hn th rat of hat rmoval from th chickn a thy ar coold from 5 C to ºC bcom & mc & Δ (.56 kg/(.54 kj/kg.º C(5 º C. kw c p ( chickn ( p chickn h chillr ga hat from th urroundg a a rat of kj/h.556 kj/. hn th total rat of hat ga by th watr i & & & watr chickn hat ga kw Notg that th tmpratur ri of watr i not to xcd ºC a it flow through th chillr, th ma flow rat of watr mut b at lat & watr.56 kw m& watr.56 kg/ ( c pδ watr (4.8 kj/kg.º C(º C (b h xrgy dtruction can b dtrmd from it dfition X dtroyd S. h rat of ntropy ration durg thi chillg proc i dtrmd by applyg th rat form of th ntropy balanc on an xtndd ytm that clud th chillr and th immdiat urroundg o that th boundary tmpratur i th urroundg tmpratur: (tady S S S& ΔS& & 44 & ytm { 4444 m& chickn m& m& m& watr m& Rat of nt ntropy tranfr by hat and ma chickn m& m& m& watr 4 4 urr urr Rat of ntropy ration S& S& Rat of chang of ntropy S& m& chickn ( m& watr ( 4 urr Notg that both tram ar compribl ubtanc, th rat of ntropy ration i dtrmd to b 4 & S& m& chicknc p ln m& watrc p ln urr kw (.56 kg/(.54 kj/kg.k ln (.56 kg/(4.8 kj/kg.k ln.8 kw/k K Fally, X & dtroyd S & (98 K(.8 kw/ K.8kW

34 Carbon tl ball ar to b annald at a rat of 5/h by hatg thm firt and thn allowg thm to cool lowly ambint air at a pcifid rat. h total rat of hat tranfr from th ball to th ambint air and th rat of xrgy dtruction du to thi hat tranfr ar to b dtrmd. Aumption h thrmal proprti of th ball ar contant. hr ar no chang ktic and potntial nrgi. h ball ar at a uniform tmpratur at th nd of th proc. Proprti h dnity and pcific hat of th ball ar givn to b ρ 78 kg/m and c p.465 kj/kg. C. Analyi (a W tak a gl ball a th ytm. h nrgy balanc for thi clod ytm can b xprd a E E 44 Nt nrgy tranfr by hat, work, and ma Chang trnal, ktic, potntial, tc. nrgi ΔU ball mc( ΔEytm 44 m( u u h amount of hat tranfr from a gl ball i πd π (.8 m m ρv ρ (78 kg/m. kg 6 6 mc ( (. kg(.465 kj/kg. C(9 C 78J p hn th total rat of hat tranfr from th ball to th ambint air bcom & n& ( ball/h (.78 kj/ball 96 kj/h 6 ball W.78kJ (pr ball (b h xrgy dtruction (or irrvribility can b dtrmd from it dfition X dtroyd S. h ntropy ratd durg thi proc can b dtrmd by applyg an ntropy balanc on an xtndd ytm that clud th ball and it immdiat urroundg o that th boundary tmpratur of th xtndd ytm i at 5 C at all tim: whr S S 44 Nt ntropy tranfr by hat and ma ΔS Subtitutg, ytm b m( S { Entropy ration S ΔSytm 44 Chang ntropy ΔS mc avg ytm ln S b ΔS ytm.78 kj S ΔSytm. kj/k.4 kj/k 8 K b hn th rat of ntropy ration bcom S & S n& ball 7 (. kg(.465 kj/kg.kln. kj/k 9 7 (pr ball (.4 kj/k ball( ball/h.74 kj/h.k.47 kw/k Fally, X & & (8 K(.47 kw/ K.46 kw 46 dtroyd S W

35 A tank contag hot watr i placd a largr tank. h amount of hat lot to th urroundg and th xrgy dtruction durg th proc ar to b dtrmd. Aumption Ktic and potntial nrgy chang ar ngligibl. Air i an idal ga with contant pcific hat. h largr tank i wll-ald. Proprti h proprti of air at room tmpratur ar R.87 kpa.m /kg.k, c p.5 kj/kg.k, c v.78 kj/kg.k (abl A-. h proprti of watr at room tmpratur ar ρ kg/m, c w 4.8 kj/kg.k. Analyi (a h fal volum of th air th tank i V a V a V w m h ma of th air th room i m a PV R a a ( kpa(.4 m.474 kg (.87 kpa m /kg K( 7 K h prur of air at th fal tat i Air, C Watr 85 C 5 L P ma Ra (.474 kg(.87 kpa m /kg K(44 7 K a V a.5 m h ma of watr i mw ρ wv w ( kg/m (.5 m 4.5 kg 7.9 kpa An nrgy balanc on th ytm conitg of watr and air i ud to dtrm hat lot to th urroundg [ m c m c ( ] (4.5 kg(4.8 kj/kg.k(44 85 (.474 kg(.78 kj/kg.k( kj w w ( w a v a (b An xrgy balanc writtn on th (ytm immdiat urroundg can b ud to dtrm xrgy dtruction. But w firt dtrm ntropy and trnal nrgy chang ΔS ΔS w a ΔU ΔU X m c m w a w c p ln w ln a (85 7 K (4.5 kg(4.8 kj/kg.kln 7.87 kj/k (44 7 K Pa R ln P ( 7 K kpa (.474 kg (.5 kj/kg.kln (.87 kj/kg.kln (44 7 K 7.9 kpa.9 kj/k w a dt m c m w a ΔX ΔU w ( c ( v w w w a ΔX 8.8 kj ΔS a w (4.5 kg(4.8 kj/kg.k(85-44k 49 kj (.474 kg(.78 kj/kg.k( - 44K.746 kj ΔU a ΔS a 49 kj (95 K(7.87 kj/k (-.746 kj (95 K(.9 kj/k

36 Hat i tranfrrd to a piton-cyldr dvic with a t of top. h work don, th hat tranfr, th xrgy dtroyd, and th cond-law fficincy ar to b dtrmd. Aumption h dvic i tationary and ktic and potntial nrgy chang ar zro. hr i no friction btwn th piton and th cyldr. Analyi (a h proprti of th rfrigrant at th itial and fal tat ar (abl A- through A- P kpa.6544 m /kg v C 48. kj/kg u.64 kj/kg.k P 8 kpa v C u.756 m /kg.96 kj/kg.8 kj/kg.k h boundary work i dtrmd to b R-4a.4 kg 4 kpa C W mp ( v (.4 kg(8 kpa( m /kg.57 kj b, v (b h hat tranfr can b dtrmd from an nrgy balanc on th ytm m u u W (.4 kg( kJ/kg.57 kj 9.8 kj ( b, (c h xrgy diffrnc btwn th lt and xit tat i ΔX m u [ u ( P ( v v ] (.4 kg 4.6 kj [( kJ/kg (98 K(.8.64kg.K ( kpa( m /kg] h uful work put for th proc i W u, Wb, mp ( v v.57 kj (.4 kg( kpa( m /kg.4 kj h xrgy dtroyd i th diffrnc btwn th xrgy diffrnc and th uful work put X ΔX kj dt W u, (d h cond-law fficincy for thi proc i Wu,.4 kj η II.78 ΔX 4.6 kj

37 8-7 Scond-Law Analyi of Control Volum 8-54 Stam i throttld from a pcifid tat to a pcifid prur. h watd work potntial durg thi throttlg proc i to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h tmpratur of th urroundg i givn to b 5 C. 4 Hat tranfr i ngligibl. Proprti h proprti of tam bfor and aftr th throttlg proc ar (abl A-4 through A-6 P 8 MPa h 45 C P h 6 MPa h 7. kj/kg kj/kg K kj/kg K Analyi h watd work potntial i quivalnt to th xrgy dtruction (or irrvribility. It can b dtrmd from an xrgy balanc or dirctly from it dfition X dtroyd S whr th ntropy ration i dtrmd from an ntropy balanc on th dvic, which i an adiabatic tady-flow ytm, S S & 44 & Rat of nt ntropy tranfr by hat and ma m & m & S& { Rat of ntropy ration S& ΔS& ytm 44 Rat of chang of ntropy S& m& ( or Stam Subtitutg, x dtroyd ( (98 K( kJ/kg K 6.6 kj/kg Dicuion Not that 6.6 kj/kg of work potntial i watd durg thi throttlg proc.

38 [Alo olvd by EES on nclod CD] Air i comprd tadily by an 8-kW compror from a pcifid tat to anothr pcifid tat. h cra th xrgy of air and th rat of xrgy dtruction ar to b dtrmd. Aumption Air i an idal ga with variabl pcific hat. Ktic and potntial nrgy chang ar ngligibl. Proprti h ga contant of air i R.87 kj/kg.k (abl A-. From th air tabl (abl A-7 9 K h 96. kj/kg o 44 K h kj/kg o. 668 kj / kg K. 887 kj / kg K Analyi h cra xrgy i th diffrnc btwn th xit and lt flow xrgi, whr Incra xrgy ψ ψ Subtitutg, ( o o [( h ( h h Δk h.956 kj/kg K P R ln P ( Δp ( ( kJ/kg K - (.87 kj/kg K ln Incra xrgy ψ ψ ] 6 kpa kpa [( kJ/kg - (9 K(.956 kj/kg K ] 78.6 kj/kg AIR kpa 7 C 6 kpa 67 C 8 kw hn th rvribl powr put bcom W & rv, m& ( ψ ψ (./ 6 kg/(78.6 kj/kg 6.5 kw (b h rat of xrgy dtruction (or irrvribility i dtrmd from it dfition, X & dtroyd W& W& kw rv, Dicuion Not that.75 kw of powr put i watd durg thi comprion proc.

39 EES Problm 8-55 i rconidrd. h problm i to b olvd and th actual hat tranfr, it dirction, th mimum powr put, and th compror cond-law fficincy ar to b dtrmd. Analyi h problm i olvd ug EES, and th olution i givn blow. Function Dirction$( If < thn Dirction$'' l Dirction$'' nd Function Violation$(ta If ta> thn Violation$'You hav violatd th nd Law!!!!!' l Violation$'' nd {"Input Data from th Diagram Wdow" _7 [C] P_ [kpa] W_dot_c 8 [kw] P_6 [kpa] S_dot dot_nt} {"Spcial ca" _67 [C] m_dot. [kg/m]} _o_ P_oP_ m_dot_m_dot*convrt(kg/m, kg/ "Stady-flow conrvation of ma" m_dot_ m_dot_ "Conrvation of nrgy for tady-flow i:" E_dot_ - E_dot_ DELAE_dot DELAE_dot E_dot dot_nt m_dot_*h_ W_dot_c "If _dot_nt <, hat i tranfrrd from th compror" E_dot_ m_dot_*h_ h_ nthalpy(air,_ h_ nthalpy(air, _ W_dot_nt-W_dot_c W_dot_rv-m_dot_*(h_ - h_ -(_7.5*(_-_ "Irrvribility, ntropy ratd, cond law fficincy, and xrgy dtroyd:" _ntropy(air, _,PP ntropy(air,_,pp ntropy(air,_,pp "hi yild th intropic _ for an intropic proc bwtn _, P_ and P_"I_dot(_o7.5*S_dot_"Irrvriblility for th Proc, KW" S_dot_(-_dot_nt/(_o7.5 m_dot_*(_-_ "Entropy ratd, kw" Eta_IIW_dot_rv/W_dot_nt"Dfition of compror cond law fficincy, Eq. 7_6" h_onthalpy(air,_o _ontropy(air,_o,pp_o Pi_h_-h_o-(_o7.5*(_-_o "availability function at tat " Pi_h_-h_o-(_o7.5*(_-_o "availability function at tat " X_dot_Pi_*m_dot_ X_dot_Pi_*m_dot_ DELAX_dotX_dot_-X_dot_ "Gnral Exrgy balanc for a tady-flow ytm, Eq. 7-47" (-(_o7.5/(_o7.5*_dot_nt-w_dot_ntm_dot_*pi_ - m_dot_*pi_ X_dot_dt "For th Diagram Wdow"

40 8-4 xt$dirction$(_dot_nt xt$violation$(eta_ii η II I [kw] X dt [kw] [C] [C] nt [kw] E- 5.47E How can ntropy dcra? [C] kpa actual idal kpa [kj/kg-k] X dt η II..5 nt. X dt η II

41 Air xpand an adiabatic turb from a pcifid tat to anothr pcifid tat. h actual and maximum work put ar to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. h dvic i adiabatic and thu hat tranfr i ngligibl. Air i an idal ga with contant pcific hat. 4 Potntial nrgy chang ar ngligibl. Proprti At th avrag tmpratur of (45 5/ 75 K, th contant prur pcific hat of air i c p. kj/kg.k (abl A-b. h ga contant of air i R.87 kj/kg.k (abl A-. Analyi hr i only on lt and on xit, and thu m & m& m&. W tak th turb a th ytm, which i a control volum c ma cro th boundary. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a Subtitutg, E & 44 & (tady E ΔEytm Rat of nt nrgy tranfr by hat, work, and ma w m& ( h c p V ( E& / W& w.kj/kg Rat of chang trnal, ktic, potntial, tc.nrgi E& W& c & ( m& ( h m& h h V p V V V V / V V (5 m/ (. kj/kg K(45 5K h ntropy chang of air i c p ln P R ln P (. kj/kg K ln.97 kj/kg K 5 K 45 K (5 m/ (.87 kj/kg K ln kpa 55 kpa 55 kpa 45 K 5 m/ kj/kg m / h maximum (rvribl work i th xrgy diffrnc btwn th lt and xit tat Air kpa 5 K 5 m/ w rv, c p w V V ( ( (. kj/kg (98 K(.97 kj/kg K 67.9 kj/kg Irrvribilit occurrg id th turb cau th actual work production to b l than th rvribl (maximum work. h diffrnc btwn th rvribl and actual work i th irrvribility.

42 E Air i comprd a compror from a pcifid tat to anothr pcifid tat. h mimum work put i to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. Air i an idal ga with contant pcific hat. 4 h lt tat of air i takn a th dad tat. Proprti h proprti of air at room tmpratur ar c p.4 Btu/lbm R and R.6855 Btu/lbm R (abl A-Ea. Analyi h ntropy chang of air i c p ln P R ln P (.4 Btu/lbm R ln.5 Btu/lbm R 66 R 57 R (.6855 Btu/lbm R ln h mimum (rvribl work i th xrgy diffrnc btwn th lt and xit tat w rv, c p ( ( 85.9 Btu/lbm 4 pia 4.7 pia (.4 Btu/lbm R( 77R (57 R(.5 Btu/lbm R hr i only on lt and on xit, and thu m & m& m&. W tak th compror a th ytm, which i a control volum c ma cro th boundary. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a E & 44 & (tady E ΔEytm Rat of nt nrgy tranfr by hat, work, and ma h w w E& h h Rat of chang trnal, ktic, potntial, tc.nrgi E& q h q & Inpction of thi rult rval that for th am lt and xit tat, any rjction of hat will cra th actual work that mut b upplid to th compror. h rvribl (or mimum powr put i dtrmd from th xrgy balanc applid on th compror, and ttg th xrgy dtruction trm qual to zro, X X & 44 & Ratof nt xrgy tranfr by hat,work,andma (rvribl (tady Xdtroyd ΔXytm & & Ratof xrgy dtruction X& m& ψ W& W& W& w rv, rv, rv, rv, X& m& ψ X& m& ( ψ ψ & m& c [( h h ( ] p Ratof chang of xrgy ( ( hat, & q Inpction of thi rult rval that for th am lt and xit tat, any rjction of hat will cra th rvribl (mimum work that mut b upplid to th compror. Air 4.7 pia 77 F 4 pia F

43 Rfrigrant-4a i comprd by an adiabatic compror from a pcifid tat to anothr pcifid tat. h mimum powr rquird i to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h dvic i adiabatic and thu hat tranfr i ngligibl. Proprti From th rfrigrant tabl (abl A- through A- 8 kpa 5 C P 6 kpa x P (at. vap. 8 kpa 5 C h mimum (rvribl powr i W & rv, m& h h h 4. kj/kg.949 kj/kg K kj/kg.98 kj/kg K [ h ( ] [( kJ/kg (98 K( kj/kg K] (. kg/.4 kw R-4a 6 kpa at. vapor. kg/

44 Stam i dclratd a diffur. h cond law fficincy of th diffur i to b dtrmd. Aumption h diffur oprat tadily. h chang potntial nrgi ar ngligibl. Proprti h proprti of tam at th lt and th xit of th diffur ar (abl A-4 through A-6 P 5 kpa h C P x kpa (at. vapor kj/kg 7.6 kj/kg K h 76. kj/kg 7.7 kj/kg K Analyi W tak th diffur to b th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a Subtitutg, E E & 44 & Rat of nt nrgy tranfr by hat, work, and ma m& ( h V V E& / V Rat of chang trnal, ktic, potntial, tc.nrgi E& m& ( h h (tady ΔEytm & h V / Δk actual Δk actual h h kj/kg An xrgy balanc on th diffur giv Subtitutg, X X & 44 & Ratof nt xrgy tranfr by hat,work,andma 69. kj/kg (rvribl (tady Xdtroyd ΔX ytm & & Ratof xrgy dtruction X& V V Δk rv X& Ratof chang of xrgy m&ψ m&ψ V h h ( h h V ( h h ( h h ( Δk rv h h ( ( kJ/kg (98 K( kj/kg K h cond law fficincy i thn Δk actual 49.5 kj/kg η II.884 Δk 69. kj/kg rv 5 kpa C m/ H O kpa at. vapor

45 Air i acclratd a nozzl whil log om hat to th urroundg. h xit tmpratur of air and th xrgy dtroyd durg th proc ar to b dtrmd. Aumption Air i an idal ga with variabl pcific hat. h nozzl oprat tadily. Proprti h ga contant of air i R.87 kj/kg.k (abl A-. h proprti of air at th nozzl lt ar (abl A-7 6 K h kj/kg o kj / kg K Analyi (a W tak th nozzl a th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a E E & 44 & Rat of nt nrgy tranfr by hat, work, and ma m& ( h V E& / Rat of chang trnal, ktic, potntial, tc.nrgi E& m& ( h (tady Eytm & Δ 4444 V / & 4 kj/kg 5 m/ AIR m/ or hrfor, h q h V h V V V h q At thi h valu w rad, from abl A-7, ( m/ (5 m/ kj/kg m /.8 kj/kg.5 K 9.5 C and.74 kj/kg K (b h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X dtroyd S whr th ntropy ration S i dtrmd from an ntropy balanc on an xtndd ytm that clud th dvic and it immdiat urroundg o that th boundary tmpratur of th xtndd ytm i urr at all tim. It giv whr S S & 44 & Rat of nt ntropy tranfr by hat and ma Δ air m m & o o & b,urr P R ln P S& { Rat of ntropy ration S& S& S& Δ ytm 44 Rat of chang of ntropy m& ( & urr ( kJ/kg K (.87 kj/kg K ln 95 kpa kpa.876 kj/kg K Subtitutg, th ntropy ration and xrgy dtruction pr unit ma of air ar dtrmd to b

46 8-46 x dtroyd urr q urr urr 4 kj/kg (9 K.876 kj/kg K 58.4 kj/kg 9 K Altrnativ olution h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc applid on th xtndd ytm that clud th dvic and it immdiat urroundg o that th boundary tmpratur of th xtndd ytm i nvironmnt tmpratur (or urr at all tim. Notg that xrgy tranfr with hat i zro whn th tmpratur at th pot of tranfr i th nvironmnt tmpratur, th xrgy balanc for thi tady-flow ytm can b xprd a X X & 44 & Ratof nt xrgy tranfr by hat,work,and ma Xdtroyd & 44 Ratof xrgy dtruction (tady Xytm X& & Δ 4444 Ratof chang of xrgy m& [( h h ( m& [ ( q m& ( & dtroyd Δk Δp ] m& [ ( ] c,fromnrgy balanc, q S& X& X& m& ψ m& ψ m& ( ψ ψ ( h hrfor, th two approach for th dtrmation of xrgy dtruction ar idntical. h Δk] h h Δk

47 EES Problm 8-6 i rconidrd. h ffct of varyg th nozzl xit vlocity on th xit tmpratur and xrgy dtroyd i to b vtigatd. Analyi h problm i olvd ug EES, and th olution i givn blow. "Known:" WorkFluid$ 'Air' P[] [kpa] [] 87 [C] P[] 95 [kpa] Vl[] 5 [m/] {Vl[] [m/]} _o 7 [C] _urr _o q_lo 4 [kj/kg] "Conrvation of Enrgy - SSSF nrgy balanc for nozzl -- nglctg th chang potntial nrgy:" h[]nthalpy(workfluid$,[] []ntropy(workfluid$,pp[],[] k[] Vl[]^/ k[]vl[]^/ h[]k[]*convrt(m^/^,kj/kg h[] k[]*convrt(m^/^,kj/kgq_lo []tmpratur(workfluid$,hh[] []ntropy(workfluid$,pp[],hh[] "h ntropy ratd i dtmd from th ntropy balanc:" [] - [] - q_lo/(_urr7 _ x_dtroyd (_o7*_ 8 [C] Vl [m/] x dtroyd [kj/kg] [] [C] Vl[] x dtroyd [kj/kg] Vl[]

48 Stam i dclratd a diffur. h ma flow rat of tam and th watd work potntial durg th proc ar to b dtrmd. Aumption h diffur oprat tadily. h chang potntial nrgi ar ngligibl. Proprti h proprti of tam at th lt and th xit of th diffur ar (abl A-4 through A-6 P kpa h 5 C h 5 C at.vapor v 59. kj/kg 8.74 kj/kg K 59. kj/kg kj/kg K.6 m /kg Analyi (a h ma flow rat of th tam i A.6 m / kg m& V v ( m (7 m/ 7.46 kg/ (b W tak th diffur to b th ytm, which i a control volum. Aumg th dirction of hat tranfr to b from th tm, th nrgy balanc for thi tady-flow ytm can b xprd th rat form a Subtitutg, E E & 44 & Rat of nt nrgy tranfr by hat, work, and ma & m& ( h V E& / & E& m& ( h m& h (tady ΔEytm & Rat of chang trnal, ktic, potntial, tc.nrgi V / & h V V (7 m/ (7.46 kg/ ( m/ kj/kg m / kj/ h watd work potntial i quivalnt to xrgy dtruction. h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X dtroyd S whr th ntropy ration S i dtrmd from an ntropy balanc on an xtndd ytm that clud th dvic and it immdiat urroundg o that th boundary tmpratur of th xtndd ytm i urr at all tim. It giv S S & 44 & Rat of nt ntropy tranfr by hat and ma m & m & & b,urr S& { Rat of ntropy ration S& S& Δ ytm 44 Rat of chang of ntropy S& Subtitutg, th xrgy dtruction i dtrmd to b X& dtroyd m& ( m/ & & S & m& ( kw (98 K (7.46 kg/( kj/kg K 8. kw 98 K urr H O 7 m/

49 E Air i comprd tadily by a compror from a pcifid tat to anothr pcifid tat. h mimum powr put rquird for th compror i to b dtrmd. Aumption Air i an idal ga with variabl pcific hat. Ktic and potntial nrgy chang ar ngligibl. Proprti h ga contant of air i R.6855 Btu/lbm.R (abl A-E. From th air tabl (abl A- 7E 5 R 94 R h 4.7 Btu/lbm o h o.597 Btu/lbm R 6. Btu/lbm.759 Btu/lbm R Analyi h rvribl (or mimum powr put i dtrmd from th rat form of th xrgy balanc applid on th compror and ttg th xrgy dtruction trm qual to zro, whr X X & 44 & Ratof nt xrgy tranfr by hat,work,and ma Δ Subtitutg, W & air rv, o o.9 Btu/lbm R (rvribl (tady Xdtroyd ΔXytm & & 4444 P R ln P Ratof xrgy dtruction X& m& ψ W& W& rv, rv, X& Ratof chang of xrgy m& ψ m& ( ψ ψ m& [( h ( Btu/lbm R (.6855 Btu/lbm R ln (/6 lbm/ 5. Btu/ 49.6 hp h ( pia 4.7 pia AIR 5 lbm/m 4.7 pia 6 F Δk [(6.4.7Btu/lbm (5 R(.9 Btu/lbm R ] Dicuion Not that thi i th mimum powr put ndd for thi compror. pia 48 F Δp ]

50 Stam xpand a turb from a pcifid tat to anothr pcifid tat. h actual powr put of th turb i givn. h rvribl powr put and th cond-law fficincy ar to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h tmpratur of th urroundg i givn to b 5 C. Proprti From th tam tabl (abl A-4 through A-6 P 6 MPa h 6 C P 5 kpa h C kj/kg 7.69 kj/kg K 68.4 kj/kg kj/kg K Analyi (b hr i only on lt and on xit, and thu m& m& m&. W tak th turb a th ytm, which i a control volum c ma cro th boundary. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a Subtitutg, E & 44 & (tady E ΔEytm Rat of nt nrgy tranfr by hat, work, and ma m& ( h V E& / W& Rat of chang trnal, ktic, potntial, tc.nrgi E& W& & m& ( h m& h h V V (8 m/ 5 kj/ m& m& 5.56 kg/ V / (4 m/ kj/kg m / m& ( ψ ψ m& [( h h ( 8 m/ 6 MPa 6 C SEAM 5 kpa C 4 m/ Δk Δp 5 MW h rvribl (or maximum powr put i dtrmd from th rat form of th xrgy balanc applid on th turb and ttg th xrgy dtruction trm qual to zro, (rvribl (tady X X Xdtroyd ΔXytm & 44 & & & 4444 Ratof nt xrgy tranfr by hat,work,and ma Ratof xrgy dtruction W& X& X& m& ψ W& rv, Ratof chang of xrgy rv, m& ψ Subtitutg, W & rv, m& [( h h ( ] (5.56 kg/ [ (98 K( kj/kg K] 584 kw (b h cond-law fficincy of a turb i th ratio of th actual work put to th rvribl work, W& 5 MW η II 85.6% W& 5.84 MW rv, Dicuion Not that 4.4% prcnt of th work potntial of th tam i watd a it flow through th turb durg thi proc. ]

51 Stam i throttld from a pcifid tat to a pcifid prur. h dcra th xrgy of th tam durg thi throttlg proc i to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h tmpratur of th urroundg i givn to b 5 C. 4 Hat tranfr i ngligibl. Proprti h proprti of tam bfor and aftr throttlg ar (abl A-4 through A-6 P 9 MPa h 5 C P 7 MPa h h 87.4 kj/kg 6.66 kj/kg K kj/kg K Analyi h dcra xrgy i of th tam i th diffrnc btwn th lt and xit flow xrgi, Dcra xrgy ψ ψ [ Δh Δk Δp ( ] ( (98 K( kJ/kg K. kj/kg Stam Dicuion Not that. kj/kg of work potntial i watd durg thi throttlg proc.

52 Combution ga xpand a turb from a pcifid tat to anothr pcifid tat. h xrgy of th ga at th lt and th rvribl work put of th turb ar to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Potntial nrgy chang ar ngligibl. h tmpratur of th urroundg i givn to b 5 C. 4 h combution ga ar idal ga with contant pcific hat. Proprti h contant prur pcific hat and th pcific hat ratio ar givn to b c p.5 kj/kg.k and k.. h ga contant R i dtrmd from R c c c c / k c ( / k (.5 kj/kg K(/..65 kj/kg K p v p p Analyi (a h xrgy of th ga at th turb lt i imply th flow xrgy, V ψ h h ( gz whr hu, p P c p ln R ln P 7 K (.5 kj/kg Kln (.65 kj/kg Kln 98 K.5 kj/kg K 8 kpa kpa ( m/ ψ (.5 kj/kg.k(9 5 C (98 K(.5 kj/kg K 8 kpa 9 C kj/kg m / GAS URBINE 4 kpa 65 C 75.8 kj/kg (b h rvribl (or maximum work put i dtrmd from an xrgy balanc applid on th turb and ttg th xrgy dtruction trm qual to zro, whr and X X & 44 & Ratof nt xrgy tranfr by hat,work,andma V Δk V (rvribl (tady Xdtroyd ΔXytm & & 4444 ( m/ Ratof xrgy dtruction W& X& X& m& ψ W& rv, ( m/ Ratof chang of xrgy rv, m& ( ψ ψ m& [( h h ( Δk Δp m& ψ kj/kg m / P c p ln R ln P 9 K 4 kpa (.5 kj/kg Kln (.65 kj/kg Kln 7 K 8 kpa.996 kj/kg K hn th rvribl work put on a unit ma bai bcom w rv, h h 9. kj/kg ( Δk c ( ( Δk p (.5 kj/kg K(9 65 C (98 K(.996 kj/kg K 9. kj/kg 4.9 kj/kg ]

53 E Rfrigrant-4a ntr an adiabatic compror with an intropic fficincy of.8 at a pcifid tat with a pcifid volum flow rat, and lav at a pcifid prur. h actual powr put and th cond-law fficincy to th compror ar to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h dvic i adiabatic and thu hat tranfr i ngligibl. Proprti From th rfrigrant tabl (abl A-E through A-E h pia 5. Btu / lbm P pia P 7 pia pia.8 Btu/lbm R h.8 Btu/lbm at.vapor v v.549 ft /lbm pia Analyi From th intropic fficincy rlation, 7 pia h h η c ha h ( h h / ηc ha h 5. (.8 5. / Btu/lbm R-4a hn, ft /m P 7 pia.74 Btu/lbm ha 4.67 pia V / 6 ft / Alo, &m &.5 lbm/ at. vapor v.549 ft / lbm hr i only on lt and on xit, and thu m& m& m&. W tak th actual compror a th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd a (tady E E Eytm & 44 & & Δ Rat of nt nrgy tranfr by hat, work, and ma Rat of chang trnal, ktic, potntial, tc.nrgi E& E& W& mh & mh & (c & Δk Δp a, W& m& ( h h a, Subtitutg, th actual powr put to th compror bcom hp W & a, (.5 lbm/( Btu/lbm.85 hp.768 Btu/ (b h rvribl (or mimum powr put i dtrmd from th xrgy balanc applid on th compror and ttg th xrgy dtruction trm qual to zro, (rvribl (tady X X Xdtroyd ΔXytm & 44 & & & 4444 Subtitutg, W & Ratof nt xrgy tranfr by hat,work,andma rv, (.5 lbm/ Ratof xrgy dtruction W& rv,.66 Btu/. 7 hp W& rv,.7 hp hu, η II 79.8% W&.85 hp act, rv, X& Ratof chang of xrgy m& ψ m& ψ W& X& m& ( ψ ψ m& [( h h ( Δk Δp [( Btu/lbm (55 R(.74.8Btu/lbm R] (c hp.768 Btu/ ]

54 Rfrigrant-4a i comprd by an adiabatic compror from a pcifid tat to anothr pcifid tat. h intropic fficincy and th cond-law fficincy of th compror ar to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h dvic i adiabatic and thu hat tranfr i ngligibl. Proprti From th rfrigrant tabl (abl A-E through A-E h 46.6 kj/kg P 4 kpa.976 kj/kg K C v.465 m /kg P 7 kpa h 6 C P 7 kpa h 98.4 kj/kg.56 kj/kg K 8.6 kj/kg Analyi (a h intropic fficincy i η c h h % h h a (b hr i only on lt and on xit, and thu m& m& m&. W tak th actual compror a th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd a E & 44 & (tady E ΔEytm Rat of nt nrgy tranfr by hat, work, and ma E& Rat of chang trnal, ktic, potntial, tc.nrgi E& & W& mh & mh & (c & Δk Δp a, W& m& ( h h a, hn th ma flow rat of th rfrigrant bcom W& a,.5 kj/ m&.96 kg/ ha h ( kJ/kg h rvribl (or mimum powr put i dtrmd from th xrgy balanc applid on th compror and ttg th xrgy dtruction trm qual to zro, (rvribl (tady X X Xdtroyd ΔXytm & 44 & & & 4444 Ratof nt xrgy tranfr by hat,work,andma Subtitutg, W & (.96 kg/ and Ratof xrgy dtruction W& rv, rv, X& Ratof chang of xrgy m& ψ m& ψ W& X& m& ( ψ ψ m& [( h h ( Δk Δp [( kj/kg ( K( kj/kg K ].47 kw rv, W& η II W& rv, a,.47 kw.5 kw 69.% R-4a 4 kpa - C 7 kpa 6 C.5 kw ]

55 Air i comprd tadily by a compror from a pcifid tat to anothr pcifid tat. h cra th xrgy of air and th rat of xrgy dtruction ar to b dtrmd. Aumption Air i an idal ga with variabl pcific hat. Ktic and potntial nrgy chang ar ngligibl. Proprti h ga contant of air i R.87 kj/kg.k (abl A-. From th air tabl (abl A-7 K 55 K h.9 kj/kg o h o.7 kj/kg K kj/kg.8 kj/kg K Analyi h rvribl (or mimum powr put i dtrmd from th rat form of th xrgy balanc applid on th compror and ttg th xrgy dtruction trm qual to zro, whr X X & 44 & Ratof nt xrgy tranfr by hat,work,andma o (rvribl (tady Xdtroyd ΔXytm & & 4444 o Ratof xrgy dtruction X& m& ψ W& W& rv, rv, X& Ratof chang of xrgy m& ψ m& ( ψ ψ m& [( h R P ln P (.8.7 kj / kg K (.87 kj / kg Kln.87 kj / kg K h ( 6 kpa 95 kpa AIR.6 kg/ 95 kpa 7 C Δk 6 kpa 77 C Δp ] Subtitutg, W & rv, [( kJ/kg - (98 K(.87 kj/kg ].7 kw (.6 kg/ K Dicuion Not that a mimum of.7 kw of powr put i ndd for thi comprion proc.

56 EES Problm 8-7 i rconidrd. h ffct of compror xit prur on rvribl powr i to b vtigatd. Analyi h problm i olvd ug EES, and th olution i givn blow. _7 [C] P_95 [kpa] m_dot.6 [kg/] {P_6 [kpa]} _77 [C] _o5 [C] P_o [kpa] m_dot_m_dot "Stady-flow conrvation of ma" m_dot_ m_dot_ h_ nthalpy(air,_ h_ nthalpy(air, _ W_dot_rvm_dot_*(h_ - h_ -(_7.5*(_- ntropy(air, _,PP ntropy(air,_,pp_ 4 P [kpa] W rv [kw] W rv [kw] P [kpa]

57 An xprion i to b drivd for th work potntial of th gl-pha contnt of a rigid adiabatic contar whn th itially mpty contar i filld through a gl opng from a ourc of workg fluid who proprti rma fixd. Analyi h conrvation of ma prcipl for thi ytm rduc to dm dt CV m& i whr th ubcript i tand for th lt tat. Whn th ntropy ration i t to zro (for calculatg work potntial and th combd firt and cond law i rducd to fit thi ytm, it bcom d U S W & ( rv ( h S i m & i dt Whn th ar combd, th rult i d U S dm W& ( CV rv ( h S i dt dt Rcognizg that thr i no itial ma th ytm, tgration of th abov quation produc Wrv ( h i m m ( h Wrv ( hi h ( i m whr th ubcript tand for th fal tat th contar.

58 A rigid tank itially conta aturatd liquid of rfrigrant-4a. R-4a i rlad from th vl until no liquid i lft th vl. h rvribl work aociatd with thi proc i to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc. It can b analyzd a a uniform-flow proc c th tat of fluid lavg th dvic rma contant. Ktic and potntial nrgi ar ngligibl. hr ar no work traction volvd. Proprti h proprti of R-4a ar (abl A- through A- v v f C u u f at. liquid C at. vapor v v u h u C C C C C.86m kj/kg.6 kj/kg K.5969 m 4. kj/kg C Analyi h volum of th contar i V m v.94 kj/kg K 6.59 kj/kg / kg / kg ( kg(.86m /kg.86 m h ma th contar at th fal tat i R-4a kg C at. liq. m m V.86 m v.5969 m /kg h amount of ma lavg th contar i m.69 kg m m kg h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S. h ntropy ration S thi ca i dtrmd from an ntropy dtroyd balanc on th ytm: Subtitutg, S S 44 Nt ntropy tranfr by hat and ma X dtroyd m S { Entropy ration S S ΔSytm 44 ΔS m Chang ntropy tank ( m m m m S ( m m m (9 K( kj tank

59 An adiabatic rigid tank that i itially vacuatd i filld by air from a upply l. h work potntial aociatd with thi proc i to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc. It can b analyzd a a uniform-flow proc c th tat of fluid ntrg th dvic rma contant. Ktic and potntial nrgi ar ngligibl. hr ar no work traction volvd. 4 Air i an idal ga with contant pcific hat. Proprti h proprti of air at room tmpratur ar c p.4 Btu/lbm R and R.6855 Btu/lbm R.74 kpa m /lbm R (abl A-Ea. Analyi W tak th tank a th ytm, which i a control volum c ma cro th boundary. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc for thi uniform-flow ytm can b xprd a Ma balanc: m m Δmytm mi m Air pia, F Enrgy balanc: E E 44 ΔEytm 44 Nt nrgy tranfr Chang trnal, ktic, by hat, work, and ma potntial, tc.nrgi mi hi mu Combg th two balanc: c p h i u c pi cv i ki c v Subtitutg, ki (.4(56 R 784 R h fal ma th tank i PV ( pia( ft m mi lbm R (.74 pia ft /lbm R(784 R h work potntial aociatd with thi proc i qual to th xrgy dtroyd durg th proc. h xrgy dtruction durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X dtroyd S. h ntropy ration S thi ca i dtrmd from an ntropy balanc on th ytm: S S S ΔS 44 ytm { 44 Subtitutg, Nt ntropy tranfr by hat and ma W rv Entropy ration mi i S S S Chang ntropy ΔS tank m m mi i m ( X dtyroyd m ( i m c p ln 784 R (6.887 lbm(54 R (.4 Btu/lbm Rln 56 R. Btu i ft

60 An rigid tank that i itially vacuatd i filld by air from a upply l. h work potntial aociatd with thi proc i to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc. It can b analyzd a a uniform-flow proc c th tat of fluid ntrg th dvic rma contant. Ktic and potntial nrgi ar ngligibl. hr ar no work traction volvd. 4 Air i an idal ga with contant pcific hat. Proprti h proprti of air at room tmpratur ar c p.4 Btu/lbm R and R.6855 Btu/lbm R.74 kpa m /lbm R (abl A-Ea. Analyi W tak th tank a th ytm, which i a control volum c ma cro th boundary. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc for thi uniform-flow ytm can b xprd a Ma balanc: m m Δmytm mi m Enrgy balanc: Air pia, F E E ΔE 44 ytm 44 Nt nrgy tranfr by hat, work, and ma Chang trnal, ktic, potntial, tc.nrgi mi hi mu mihi mu ft Combg th two balanc: m ( hi u h fal ma th tank i PV ( pia( ft m mi 9.64 lbm R (.74 pia ft /lbm R(56 R Subtitutg, m ( hi u m ( c pi cvi mi ( c p cv mi R (9.64 lbm(56 R(.6855 Btu/lbm R 7. Btu h work potntial aociatd with thi proc i qual to th xrgy dtroyd durg th proc. h xrgy dtruction durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X dtroyd S. h ntropy ration S thi ca i dtrmd from an ntropy balanc on th ytm: S S S ΔS 44 ytm { 44 Nt ntropy tranfr by hat and ma mi i Entropy ration S S m Chang ntropy ΔS tank m m i i S m ( i Notg that both th tmpratur and prur th tank i am a tho th upply l at th fal tat, ubtitutg giv, Wrv X dtroyd m ( i 7.Btu

61 Stam xpand a turb tadily at a pcifid rat from a pcifid tat to anothr pcifid tat. h powr potntial of th tam at th lt condition and th rvribl powr put ar to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h tmpratur of th urroundg i givn to b 5 C. Proprti From th tam tabl (abl A-4 through 6 P 8 MPa h 45 C 7. kj/kg kj/kg K 8 MPa 45 C P 5 kpa h at. vapor P kpa h 5 C 645. kj/kg 7.59 kj/kg K h 5 C 5 C 4.8 kj/kg.67 kj/kg K Analyi (a h powr potntial of th tam at th lt condition i quivalnt to it xrgy at th lt tat, SEAM 5, kg/h 5 kpa at. vapor Ψ & m & ψ m& h h (5, / 6 kg/ 555 kw V ( gz m& h ( h ( [(7. 4.8kJ/kg (98 K( kJ/kg K] (b h powr put of th turb if thr wr no irrvribiliti i th rvribl powr, i dtrmd from th rat form of th xrgy balanc applid on th turb and ttg th xrgy dtruction trm qual to zro, X X & 44 & Ratof nt xrgy tranfr by hat,work,and ma (rvribl (tady Xdtroyd ΔX ytm & & 4444 Ratof xrgy dtruction W& X& X& m& ψ W& rv, Ratof chang of xrgy rv, m& ( ψ ψ m& [( h h ( m& ψ Δk Δp ] Subtitutg, W & rv, m& [( h h ( ] (5,/6 kg/ 9 kw [( kj/kg (98 K( kj/kg K]

62 E Air i comprd tadily by a 4-hp compror from a pcifid tat to anothr pcifid tat whil bg coold by th ambint air. h ma flow rat of air and th part of put powr that i ud to jut ovrcom th irrvribiliti ar to b dtrmd. Aumption Air i an idal ga with variabl pcific hat. Potntial nrgy chang ar ngligibl. h tmpratur of th urroundg i givn to b 6 F. Proprti h ga contant of air i R.6855 Btu/lbm.R (abl A-E. From th air tabl (abl A-7E 5 R h o P 5 pia 8 R h P 5 pia 4.7 Btu/lbm.597 Btu/lbm R o 6.97 Btu/lbm Btu/lbm R Analyi (a hr i only on lt and on xit, and thu m& m& m&. W tak th actual compror a th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd a (tady E E Eytm & 44 & & Δ W& Rat of nt nrgy tranfr by hat, work, and ma a, m& ( h V E& / Rat of chang trnal, ktic, potntial, tc.nrgi E& m& ( h V / & W& Subtitutg, th ma flow rat of th rfrigrant bcom a, & m& h.768 Btu/ (5 ft/ ( 4 hp (5 / 6 Btu/ m& hp h V V 5,7 ft Btu/lbm It yild &m.85 lbm / (b h portion of th powr put that i ud jut to ovrcom th irrvribiliti i quivalnt to xrgy dtruction, which can b dtrmd from an xrgy balanc or dirctly from it dfition X S whr th ntropy ration S i dtrmd from an ntropy balanc on an dtroyd xtndd ytm that clud th dvic and it immdiat urroundg. It giv S S S& S& ytm & 44 & Δ { 44 Rat of nt ntropy tranfr by hat and ma m & m & & Rat of ntropy ration b,urr S& Rat of chang of ntropy S& m& ( & whr P 5 pia R ln ( Btu/lbm (.6855 Btu/lbm.R ln P 5 pia.7 Btu/lbm.R Subtitutg, th xrgy dtruction i dtrmd to b & X& ( dtroyd S& m& (5 R (.85 lbm/(.7 Btu/lbm R 5 Btu/m 5 R 5 / 6 Btu/ 5 pia 6 F hp.768 Btu/ 5 ft/ 5 pia 6 F AIR / 4 hp 6.7 hp

63 Hot combution ga ar acclratd an adiabatic nozzl. h xit vlocity and th dcra th xrgy of th ga ar to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Potntial nrgy chang ar ngligibl. h dvic i adiabatic and thu hat tranfr i ngligibl. 4 h combution ga ar idal ga with contant pcific hat. Proprti h contant prur pcific hat and th pcific hat ratio ar givn to b c p.5 kj/kg.k and k.. h ga contant R i dtrmd from R c c c c / k c ( / k (.5 kj/kg K(/..654 kj/kg K p v p p p Analyi (a hr i only on lt and on xit, and thu m& m& m&. W tak th nozzl a th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd a E & 44 & (tady E ΔEytm Rat of nt nrgy tranfr by hat, work, and ma m& ( h E& Rat of chang trnal, ktic, potntial, tc.nrgi E& & V / m& ( h V / (cw& & Δp h V h hn th xit vlocity bcom V 6 kpa 747 C 8 m/ Comb. ga 7 kpa 5 C V c ( V p m / (.5 kj/kg K(747 5K kj/kg 758 m/ (8 m/ (b h dcra xrgy of combution ga i imply th diffrnc btwn th itial and fal valu of flow xrgy, and i dtrmd to b ψ ψ w rv h h Δk Δp ( c p ( ( Δk whr and V Δk V (758 m/ (8 m/ kj/kg m / P c p ln R ln P 77 K (.5 kj/kg K ln (.654 kj/kg K ln K.98 kj/kg K 84. kj/kg 7 kpa 6 kpa Subtitutg, Dcra xrgy ψ ψ (.5 kj/kg K(747 5 C (9 K(.98 kj/kg K 84. kj/kg 8.56 kj/kg

64 Stam i acclratd an adiabatic nozzl. h xit vlocity of th tam, th intropic fficincy, and th xrgy dtroyd with th nozzl ar to b dtrmd. Aumption h nozzl oprat tadily. h chang potntial nrgi ar ngligibl. Proprti h proprti of tam at th lt and th xit of th nozzl ar (abl A-4 through A-6 P 7 MPa h 5 C P 5 MPa h 45 C P 5 MPa h 4.4 kj/kg 6.8 kj/kg K 7. kj/kg 6.8 kj/kg K. kj/kg Analyi (a W tak th nozzl to b th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a E & 44 & (tady E ΔEytm Rat of nt nrgy tranfr by hat, work, and ma m& ( h E& Rat of chang trnal, ktic, potntial, tc. nrgi E& h hn th xit vlocity bcom & V / m& ( h V / (cw& & Δp V h V V m / V ( h h ( kj/kg (7 m/ 49.6 m/ kj/kg (b h xit vlocity for th intropic ca i dtrmd from hu, m / V ( (4.4. kj/kg h h V (7 m/ kj/kg η N V V / / (49.6 m/ (47.9 m/ / / 86.4% 47.9 m/ (c h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X dtroyd S whr th ntropy ration S i dtrmd from an ntropy balanc on th actual nozzl. It giv S S & 44 & Rat of nt ntropy tranfr by hat and ma m & m & S& { Rat of ntropy ration S& ΔS& ytm 44 Rat of chang of ntropy S& m& ( or Subtitutg, th xrgy dtruction th nozzl on a unit ma bai i dtrmd to b x dtroyd ( (98 K( kJ/kg K 6.8 kj/kg 7 MPa 5 C 7 m/ SEAM 5 MPa 45 C

65 CO ga i comprd tadily by a compror from a pcifid tat to anothr pcifid tat. h powr put to th compror if th proc volvd no irrvribiliti i to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h dvic i adiabatic and thu hat tranfr i ngligibl. 4 CO i an idal ga with contant pcific hat. Proprti At th avrag tmpratur of ( 45/ 75 K, th contant prur pcific hat and th pcific hat ratio of CO ar k.6 and c p.97 kj/kg.k (abl A-. Analyi h rvribl (or mimum powr put i dtrmd from th xrgy balanc applid on th compror, and ttg th xrgy dtruction trm qual to zro, whr X X & 44 & Ratof nt xrgy tranfr by hat,work,and ma c (rvribl (tady Xdtroyd ΔXytm & & 4444 p ln Ratof xrgy dtruction X& m& ψ W& W& P R ln P.5 kj/kg K rv, rv, (.975 kj/kg K ln X& m& ψ m& ( ψ ψ m& [( h 45 K K Ratof chang of xrgy h ( Δk (.889 kj/kg K ln Δp 6 kpa kpa CO. kg/ kpa K ] 6 kpa 45 K Subtitutg, W & rv, [(.97 kj/kg K(45 K (98 K(.5 kj/kg ] 5.5 kw (. kg/ K Dicuion Not that a mimum of 5.5 kw of powr put i ndd for thi compror.

66 Liquid watr i hatd a chambr by mixg it with uprhatd tam. For a pcifid mixg tmpratur, th ma flow rat of th tam and th rat of xrgy dtruction ar to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. hr ar no work traction. Proprti Notg that < kpa. C, th cold watr and th xit mixtur tram xit a a comprd liquid, which can b approximatd a a aturatd liquid at th givn tmpratur. From abl A-4 through A-6, P 8.9 kj/kg kpa h h 6 kj/m o C C.9649 kj/kg K o C P kpa C P kpa h h 6 C h 7. kj/kg kj/kg K o C o C 5.8 kj/kg.8 kj/kg K Analyi (a W tak th mixg chambr a th ytm, which i a control volum. h ma and nrgy balanc for thi tady-flow ytm can b xprd th rat form a (tady Ma balanc: m & m& Δm& ytm m& m& m& Enrgy balanc: E & 44 & (tady E ΔEytm Rat of nt nrgy tranfr by hat, work, and ma E& mh & m& h Rat of chang trnal, ktic, potntial, tc.nrgi E& & & m& h Combg th two rlation giv & m& h m& h ( m& m& h m& ( h h m& ( h h Solvg for &m and ubtitutg, th ma flow rat of th uprhatd tam i dtrmd to b Alo, m& & m& h m & m& m&.5.48 ( h h (6/6 kj/ (.5 kg/( h ( kj/kg.648 kg/ kj/kg.48 kg/ (b h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S whr th ntropy ration S i dtrmd from an ntropy balanc on dtroyd an xtndd ytm that clud th mixg chambr and it immdiat urroundg. It giv S S S& S& ytm & 44 & Δ { 44 Rat of nt ntropy tranfr by hat and ma m& m& m& & Rat of ntropy ration b,urr S& Rat of chang of ntropy S& Subtitutg, th xrgy dtruction i dtrmd to b X& dtroyd m& C.5 kg/ C m& m& MIXING CHAMBER kpa & & S & m& m& m& b, urr (98 K( / 98kW/K 96.4 kw 6 C

67 A rigid tank itially conta aturatd R-4a vapor. h tank i connctd to a upply l, and R- 4a i allowd to ntr th tank. h ma of th R-4a that ntrd th tank and th xrgy dtroyd durg thi proc ar to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc, but it can b analyzd a a uniform-flow proc c th tat of fluid at th lt rma contant. Ktic and potntial nrgi ar ngligibl. hr ar no work traction volvd. 4 h dirction of hat tranfr i to th tank (will b vrifid. Proprti h proprti of rfrigrant ar (abl A- through A- v v g P. MPa u u g at. MPa MPa.67 m / kg 5.8 kj/kg.9 kj/kg K R-4a.6 MPa C v v f.4 MPa u u f at. liquid Pi.6 MPa hi i C MPa MPa 9.56 kj/kg.4554 kj/kg K.966 m 5.94 kj/kg / kg.455 kj/kg K Analyi W tak th tank a th ytm, which i a control volum. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc for thi uniform-flow ytm can b xprd a Ma balanc: m m Δm mi m m Enrgy balanc: E E 44 Nt nrgy tranfr by hat, work, and ma m h i i ytm ytm 44 Chang trnal, ktic, potntial, tc.nrgi m u ΔE m u (a h itial and th fal ma th tank ar m m V. m 5.98 kg v.67 m /kg V. m 9. kg v.966 m /kg hn from th ma balanc m i m m kg (c W k p h hat tranfr durg thi proc i dtrmd from th nrgy balanc to b m h m u m u (. kg (9.56 kj/kg (9.( 5.94 kj/kg ( 5.98 kg( 5.8 kj/kg 57 kj i i R-4a. m. MPa Sat. vapor

68 8-68 (b h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S. h ntropy ration S thi ca i dtrmd from an ntropy dtroyd balanc on an xtndd ytm that clud th tank and it immdiat urroundg o that th boundary tmpratur of th xtndd ytm i th urroundg tmpratur urr at all tim. It giv S S 44 Nt ntropy tranfr by hat and ma b, S { Entropy ration m S i i S ΔSytm 44 m Chang ntropy ΔS xrgy dtruction i dtrmd to b X dtroyd S m (8 K kj tank ( m m tank m mi i m m i i Subtitutg, th [ (57 kj/(8 K ]

69 A rigid tank itially conta aturatd liquid watr. A valv at th bottom of th tank i opnd, and half of ma liquid form i withdrawn from th tank. h tmpratur th tank i matad contant. h amount of hat tranfr, th rvribl work, and th xrgy dtruction durg thi proc ar to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc, but it can b analyzd a a uniform-flow proc c th tat of fluid lavg th dvic rma contant. Ktic and potntial nrgi ar ngligibl. hr ar no work traction volvd. 4 h dirction of hat tranfr i to th tank (will b vrifid. Proprti h proprti of watr ar (abl A-4 through A-6 v v f 7 C u u at. liquid 7 C h h at. liquid f C o C C.4 m /kg 78. kj/kg C.47 kj/kg K o 79.8 kj/kg C.47 kj/kg K o Analyi W tak th tank a th ytm, which i a control volum c ma cro th boundary. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc for thi uniform-flow ytm can b xprd a Ma balanc: m m Δm m m m ytm H O.6 m 7 C cont. m Enrgy balanc: E E 44 Nt nrgy tranfr by hat, work, and ma ΔE ytm 44 Chang trnal, ktic, potntial, tc.nrgi m h m u m u h itial and th fal ma th tank ar (c W k p m m V.6 m kg v.4 m /kg m ( kg 69.4 kg m Now w dtrm th fal trnal nrgy and ntropy, V v m x x v v f v.6 m.9 m 69.4 kg fg C u u f xu.464 f x fg fg /kg (.464( kj/kg (.464( kj/kg K h hat tranfr durg thi proc i dtrmd by ubtitutg th valu to th nrgy balanc quation,

70 8-7 mh mu 545 kj m u ( 69.4 kg( 79.8 kj/kg ( 69.4 kg( kj/kg ( kg( 78. kj/kg (b h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S. h ntropy ration S thi ca i dtrmd from an ntropy dtroyd balanc on an xtndd ytm that clud th tank and th rgion btwn th tank and th ourc o that th boundary tmpratur of th xtndd ytm at th location of hat tranfr i th ourc tmpratur ourc at all tim. It giv S S 44 Nt ntropy tranfr by hat and ma b, m S { Entropy ration S S ΔS ytm 44 m Chang ntropy ΔS tank ( m m m m Subtitutg, th xrgy dtruction i dtrmd to b X dtroyd S (98 K 4. kj m m m tank ourc ourc [ (545 kj/(5 K ] For proc that volv no actual work, th rvribl work put and xrgy dtruction ar idntical. hrfor, X Wrv, Wact, Wrv, dtroyd 4. kj dtroyd X

71 E An ulatd rigid tank quippd with an lctric hatr itially conta prurizd air. A valv i opnd, and air i allowd to cap at contant tmpratur until th prur id drop to pia. h amount of lctrical work don and th xrgy dtroy ar to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc, but it can b analyzd a a uniform-flow proc c th xit tmpratur (and nthalpy of air rma contant. Ktic and potntial nrgi ar ngligibl. h tank i ulatd and thu hat tranfr i ngligibl. 4 Air i an idal ga with variabl pcific hat. 5 h nvironmnt tmpratur i givn to b 7 F. Proprti h ga contant of air i R.74 pia.ft /lbm.r (abl A-E. h proprti of air ar (abl A-7E 6 R h 6 R u 6 R u 4.47 Btu/lbm.4 Btu/lbm.4 Btu/lbm Analyi W tak th tank a th ytm, which i a control volum. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc for thi uniform-flow ytm can b xprd a Ma balanc: m m Δm m m m ytm Enrgy balanc: E E 44 Nt nrgy tranfr by hat, work, and ma W, m h ytm 44 Chang trnal, ktic, potntial, tc.nrgi m u ΔE m u (c k p AIR 5 ft 75 pia 4 F W h itial and th fal ma of air th tank ar m m P V (75 pia(5 ft R (.74 pia ft /lbm R(6 R PV ( pia(5 ft R (.74 pia ft /lbm R(6 R hn from th ma and nrgy balanc, m m m lbm W m m m, h u u 5.6 lbm.5 lbm (.7 lbm(4.47 Btu/lbm (.5 lbm(.4 Btu/lbm (5.6 lbm(.4 Btu/lbm 49 Btu

72 8-7 (b h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S whr th ntropy ration S i dtrmd from an ntropy balanc on dtroyd th ulatd tank. It giv S S 44 Nt ntropy tranfr by hat and ma m S { Entropy ration S S ΔSytm 44 m m Chang ntropy ΔS tank m ( ( m m m m ( m m m ( tank m Aumg a contant avrag prur of (75 / 5.5 pia for th xit tram, th ntropy chang ar dtrmd to b c c p p ln ln P R ln P P R ln P (.6855 Btu/lbm R ln (.6855 Btu/lbm R ln Subtitutg, th xrgy dtruction i dtrmd to b X dtroyd S (5 R 68 Btu [ m ( m ( ] pia 5.5 pia 75 pia 5.5 pia.86 Btu/lbm R.445 Btu/lbm R [(.5 lbm(.86 Btu/lbm R (5.6 lbm(.445 Btu/lbm R ]

73 A cyldr itially conta hlium ga at a pcifid prur and tmpratur. A valv i opnd, and hlium i allowd to cap until it volum dcra by half. h work potntial of th hlium at th itial tat and th xrgy dtroyd durg th proc ar to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc, but it can b analyzd a a uniform-flow proc by ug contant avrag proprti for th hlium lavg th tank. Ktic and potntial nrgi ar ngligibl. hr ar no work traction volvd othr than boundary work. 4 h tank i ulatd and thu hat tranfr i ngligibl. 5 Hlium i an idal ga with contant pcific hat. Proprti h ga contant of hlium i R.769 kpa.m /kg.k.769 kj/kg.k. h pcific hat of hlium ar c p 5.96 kj/kg.k and c v.56 kj/kg.k (abl A-. Analyi (a From th idal ga rlation, th itial and th fal ma th cyldr ar dtrmd to b m P V ( kpa(. m R (.769 kpa m /kg K(9 K m m m /.49 /.47 kg.49 kg h work potntial of hlium at th itial tat i imply th itial xrgy of hlium, and i dtrmd from th clod-ytm xrgy rlation, whr Φ [ u u ( P ( v ] mφ m ( v and R v P R v P c (.769 kpa m /kg K(9 K.84 m kpa (.769 kpa m /kg K(9 K 6.45 m 95 kpa p ln P R ln P (5.96 kj/kg K ln.8 kj/kg K 9 K 9 K /kg /kg (.769 kj/kg K ln kpa kpa HELIUM kpa. m C hu, Φ (.49 kg{(.56 kj/kg K( C (9 K(.8 kj/kg K (95 kpa( m.44 kj /kg[kj/kpa m ]} (b W tak th cyldr a th ytm, which i a control volum. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc for thi uniform-flow ytm can b xprd a Ma balanc: m m Δm m m m Enrgy balanc: ytm

74 Nt nrgy tranfr by hat, work, and ma E m E h W b, Chang trnal, ktic, potntial, tc.nrgi m Combg th two rlation giv ( m m ( m m ( m m h h m u m u m h ΔEytm 44 m h m u m u m h W b, c th boundary work and ΔU comb to ΔH for contant prur xpanion and comprion proc. h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S whr th ntropy ration S can b dtrmd from an ntropy dtroyd balanc on th cyldr. Notg that th prur and tmpratur of hlium th cyldr ar matad contant durg thi proc and hat tranfr i zro, it giv S S 44 Nt ntropy tranfr by hat and ma m S { Entropy ration S S ΔSytm 44 ΔS cyldr ( m m m m m m m ( m m ( m m m m Chang ntropy cyldr c th itial, fal, and th xit tat ar idntical and thu. hrfor, thi dicharg proc i rvribl, and X dtroyd S

75 A rigid tank itially conta aturatd R-4a vapor at a pcifid prur. h tank i connctd to a upply l, and R-4a i allowd to ntr th tank. h amount of hat tranfr with th urroundg and th xrgy dtruction ar to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc, but it can b analyzd a a uniform-flow proc c th tat of fluid at th lt rma contant. Ktic and potntial nrgi ar ngligibl. hr ar no work traction volvd. 4 h dirction of hat tranfr i from th tank (will b vrifid. Proprti h proprti of rfrigrant ar (abl A- through A- u u g P MPa g at.vapor v v Pi.4 MPa hi i kj/kg 5.68 kj/kg.9558 kj/kg K. m.9889 kj/kg K Analyi (a W tak th tank a th ytm, which i a control volum c ma cro th boundary. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc for thi uniform-flow ytm can b xprd a Ma balanc: m m Δm mi m m Enrgy balanc: E E 44 Nt nrgy tranfr by hat, work, and ma m h i i ytm ytm 44 Chang trnal, ktic, potntial, tc.nrgi m u ΔE m u h itial and th fal ma th tank ar m V. m v. m / kg / kg (c W k p kg V f V g.m.m m m f m g kg v v.894 m / kg.675 m / kg U S mu m m f u m f f f f g mgu m hn from th ma and nrgy balanc, m i m m kg g g g ,58 kj kj/k h hat tranfr durg thi proc i dtrmd from th nrgy balanc to b m h m u m u , ,77 kj i i R-4a.4 MPa 6 C R-4a. m MPa Sat. vapor

76 8-76 (b h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S. h ntropy ration S thi ca i dtrmd from an ntropy dtroyd balanc on an xtndd ytm that clud th cyldr and it immdiat urroundg o that th boundary tmpratur of th xtndd ytm i th urroundg tmpratur urr at all tim. It giv S 44 Nt ntropy tranfr by hat and ma S b, S { Entropy ration m S i i S ΔS ytm 44 m Chang ntropy ΔS tank ( m m tank m mi i Subtitutg, th xrgy dtruction i dtrmd to b X dtroyd S m m mi i (98 K[ ,77 / 98] 599 kj

77 An ulatd cyldr itially conta aturatd liquid-vapor mixtur of watr. h cyldr i connctd to a upply l, and th tam i allowd to ntr th cyldr until all th liquid i vaporizd. h amount of tam that ntrd th cyldr and th xrgy dtroyd ar to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc, but it can b analyzd a a uniform-flow proc c th tat of fluid at th lt rma contant. h xpanion proc i quai-quilibrium. Ktic and potntial nrgi ar ngligibl. 4 h dvic i ulatd and thu hat tranfr i ngligibl. Proprti h proprti of tam ar (abl A-4 through A-6 P kpa h h x 9 /5.6 P kpa h at.vapor Pi MPa hi i 4 C i h f f x h x kpa kpa 64.5 kj/kg fg fg kj/kg K kj/kg kj/kg K 76. kj/kg 7.7 kj/kg K Analyi (a W tak th cyldr a th ytm, which i a control volum. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc for thi untady-flow ytm can b xprd a Ma balanc: m m Δmytm mi m m Enrgy balanc: E E 44 ΔEytm 44 Nt nrgy tranfr by hat, work, and ma m h W i i Chang trnal, ktic, potntial, tc.nrgi b, m u m u (c k p Combg th two rlation giv Wb, ( m m hi mu mu or, ( m m hi mh mh c th boundary work and ΔU comb to ΔH for contant prur xpanion and comprion proc. Solvg for m and ubtitutg, hi h ( kJ/kg m m (5 kg 8.66 kg hi h ( kJ/kg hu, m i m m kg (b h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X dtroyd S whr th ntropy ration S i dtrmd from an ntropy balanc on th ulatd cyldr, S S S ΔS 44 ytm { 44 Nt ntropy tranfr by hat and ma Entropy ration mi i S S Chang ntropy ΔS m ytm m m m m Subtitutg, th xrgy dtruction i dtrmd to b X dtroyd S [ m m m i i ] (98 K( kj i i H O kpa P cont. MPa 4 C

78 Each mmbr of a family of four tak a howr vry day. h amount of xrgy dtroyd by thi family pr yar i to b dtrmd. Aumption Stady opratg condition xit. h ktic and potntial nrgi ar ngligibl. Hat lo from th pip, mixg ction ar ngligibl and thu &. 4 Showr oprat at maximum flow condition durg th ntir howr. 5 Each mmbr of th houhold tak a howr vry day. 6 Watr i an compribl ubtanc with contant proprti at room tmpratur. 7 h fficincy of th lctric watr hatr i %. Proprti h dnity and pcific hat of watr ar at room tmpratur ar ρ kg/l kg/ and c 4.8 kj/kg. C (abl A-. Analyi h ma flow rat of watr at th howr had i m & ρv & ( kg/l( L/m kg/m h ma balanc for th mixg chambr can b xprd th rat form a (tady ytm m & m& Δm& & & & & & m m m m m whr th ubcript dnot th cold watr tram, th hot watr tram, and th mixtur. h rat of ntropy ration durg thi proc can b dtrmd by applyg th rat form of th ntropy balanc on a ytm that clud th lctric watr hatr and th mixg chambr (th - lbow. Notg that thr i no ntropy tranfr aociatd with work tranfr (lctricity and thr i no hat tranfr, th ntropy balanc for thi tady-flow ytm can b xprd a S S & 44 & Rat of nt ntropy tranfr by hat and ma m& m& m& S& { Rat of ntropy ration S& S& (tady S& Δ ytm 4444 m& Rat of chang of ntropy (c m& m& and work i ntropy fr Notg from ma balanc that m& m& m& and c hot watr ntr th ytm at th am tmpratur a th cold watr, th rat of ntropy ration i dtrmd to b S& m& ( m& m& m& ( m& c 4 7 ( kg/m(4.8 kj/kg.k ln.746 kj/m.k 5 7 p ln Notg that 4 popl tak a 6-m howr vry day, th amount of ntropy ratd pr yar i S S& Δt(No. of popl(no. of day ( (.746 kj/m.k(6 m/pron day(4 pron(65 day/yar,85 kj/k (pr yar h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X dtroyd dtroyd S (98 K(,85 kj/k 9,779, kj Dicuion h valu abov rprnt th xrgy dtroyd with th watr hatr and th -lbow th abnc of any hat lo. It do not clud th xrgy dtroyd a th howr watr at 4 C i dicardd or coold to th door tmpratur. Alo, an ntropy balanc on th mixg chambr alon (hot watr ntrg at 55 C tad of 5 C will xclud th xrgy dtroyd with th watr hatr.

79 Air i comprd a tady-flow dvic intropically. h work don, th xit xrgy of comprd air, and th xrgy of comprd air aftr it i coold to ambint tmpratur ar to b dtrmd. Aumption Air i an idal ga with contant pcific hat at room tmpratur. h proc i givn to b rvribl and adiabatic, and thu intropic. hrfor, intropic rlation of idal ga apply. h nvironmnt tmpratur and prur ar givn to b K and kpa. 4 h ktic and potntial nrgi ar ngligibl. Proprti h ga contant of air i R.87 kj/kg.k (abl A-. h contant prur pcific hat and pcific hat ratio of air at room tmpratur ar c p.5 kj/kg.k and k.4 (abl A-. Analyi (a From th contant pcific hat idal ga intropic rlation, ( k / k.4 /.4 P P kpa kpa ( K 579. K For a tady-flow intropic comprion proc, th work put i dtrmd from w comp, kr k ( ( k { / k P P } (.4(.87kJ/kg K( K.4/.4 {(/ } kj/kg AIR kpa K MPa (b h xrgy of air at th compror xit i imply th flow xrgy at th xit tat, ψ h c p h ( ( (.5 kj/kg.k( K 8.6 kj/kg V gz (c th procc - i intropic which i th am a th compror work put. hi i not urprig c th comprion proc i rvribl. (c h xrgy of comprd air at MPa aftr it i coold to K i aga th flow xrgy at that tat, ψ h h ( V gz c p ( ( ( (c K whr c p ln P R ln P P R ln P (.87 kj/kg Kln kpa kpa.66 kj/kg.k Subtitutg, ψ ( K (. 66 kj / kg.k 98 kj / kg Not that th xrgy of comprd air dcra from 8.6 to 98 a it i coold to ambint tmpratur.

80 Air i prhatd by hot xhaut ga a cro-flow hat xchangr. h rat of hat tranfr and th rat of xrgy dtruction th hat xchangr ar to b dtrmd. Aumption Stady opratg condition xit. h hat xchangr i wll-ulatd o that hat lo to th urroundg i ngligibl and thu hat tranfr from th hot fluid i qual to th hat tranfr to th cold fluid. Chang th ktic and potntial nrgi of fluid tram ar ngligibl. 4 Fluid proprti ar contant. Proprti h pcific hat of air and combution ga ar givn to b.5 and. kj/kg. C, rpctivly. h ga contant of air i R.87 kj/kg.k (abl A-. Analyi W tak th xhaut pip a th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a E E & 44 & Rat of nt nrgy tranfr by hat, work, and ma E& mh & & Rat of chang trnal, ktic, potntial, tc.nrgi E& & mc & (tady ΔEytm & p mh & ( (c Δk Δp hn th rat of hat tranfr from th xhaut ga bcom & mc & ( ] (. kg/(.kj/kg. C(8 C 95 C.85 kw [ p ga. h ma flow rat of air i PV (95 kpa(.8 m / m& &.94 kg/ R (.87 kpa.m /kg.k 9 K Notg that hat lo by xhaut ga i qual to th hat ga by th air, th air xit tmpratur bcom &.85 kw & [ mc & p ( ] C. C air mc & (.94 kg/(.5 kj/kg. C h rat of ntropy ration with th hat xchangr i dtrmd by applyg th rat form of th ntropy balanc on th ntir hat xchangr: (tady S S S& ΔS& & 44 & ytm { 4444 m& xhaut Rat of nt ntropy tranfr by hat and ma m& m& m& air m& m& xhaut m& m& air 4 4 p Rat of ntropy ration S& S& S& m& Rat of chang of ntropy (c xhaut ( m& Notg that both fluid tram ar liquid (compribl ubtanc, th rat of ntropy ration i S& m& xhaut c p ln m& air c p ln (. kg/(. kj/kg.kln (.94 kg/(.5 kj/kg.kln.45 kw/k h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X & dtroyd dtroyd S& (9 K(.45 kw/k. kw Air 95 kpa C.8 m / air ( 4 Exhaut ga. kg/, 95 C

81 Watr i hatd by hot oil a hat xchangr. h lt tmpratur of th oil and th rat of xrgy dtruction with th hat xchangr ar to b dtrmd. Aumption Stady opratg condition xit. h hat xchangr i wll-ulatd o that hat lo to th urroundg i ngligibl and thu hat tranfr from th hot fluid i qual to th hat tranfr to th cold fluid. Chang th ktic and potntial nrgi of fluid tram ar ngligibl. 4 Fluid proprti ar contant. Proprti h pcific hat of watr and oil ar givn to b 4.8 and. kj/kg. C, rpctivly. Analyi W tak th cold watr tub a th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a E E & 44 & Rat of nt nrgy tranfr by hat, work, and ma & E& mh & & Rat of chang trnal, ktic, potntial, tc.nrgi E& mh & mc & (tady ΔEytm & p (c Δk Δp ( hn th rat of hat tranfr to th cold watr thi hat xchangr bcom & mc & ( ] (4.5 kg/(4.8 kj/kg. C(7 C C kw [ p watr Notg that hat ga by th watr i qual to th hat lo by th oil, th lt tmpratur of th hot watr i dtrmd from & [ mc & p ( ] oil & mc & p 7 C 94.5 kw ( kg/(. kj/kg. 9. C C (b h rat of ntropy ration with th hat xchangr i dtrmd by applyg th rat form of th ntropy balanc on th ntir hat xchangr: m& watr S S & 44 & Rat of nt ntropy tranfr by hat and ma m& m& m& oil m& m& watr m& m& oil S& { Rat of ntropy ration 4 4 S& S& S& (tady ΔS& ytm 4444 m& Rat of chang of ntropy (c watr ( m& Notg that both fluid tram ar liquid (compribl ubtanc, th rat of ntropy ration i dtrmd to b S& 4 m& watrc p ln m& oilc p ln (4.5 kg/(4.8 kj/kg.k ln ( kg/(. kj/kg.k ln.76 kw/k h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X & dtroyd dtroyd S& (98 K(.76 kw/k 9 kw 7 C Watr C 4.5 kg/ oil ( 4 Oil 7 C kg/ ( tub pa

82 E Stam i condnd by coolg watr a condnr. h rat of hat tranfr and th rat of xrgy dtruction with th hat xchangr ar to b dtrmd. Aumption Stady opratg condition xit. h hat xchangr i wll-ulatd o that hat lo to th urroundg i ngligibl and thu hat tranfr from th hot fluid i qual to th hat tranfr to th cold fluid. Chang th ktic and potntial nrgi of fluid tram ar ngligibl. 4 Fluid proprti ar contant. 5 h tmpratur of th nvironmnt i 77 F. Proprti h pcific hat of watr i. Btu/lbm. F (abl A-E. h nthalpy and ntropy of vaporization of watr at F ar 5. Btu/lbm and fg.7686 Btu/lbm.R (abl A-4E. Analyi W tak th tub-id of th hat xchangr whr cold watr i flowg a th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a (tady E E ΔEytm & 44 & & Rat of nt nrgy tranfr Stam Rat of chang trnal, ktic, by hat, work, and ma potntial, tc.nrgi F E& E& 7 F & mh & mh & (c Δk Δp & mc & ( p hn th rat of hat tranfr to th cold watr thi hat xchangr bcom & [ mc & p ( ] watr (5. lbm/(. Btu/lbm. F(7 F 6 F 499 Btu/ Notg that hat ga by th watr i qual to th hat lo by th condng tam, th rat of condnation of th tam th hat xchangr i dtrmd from & 499 Btu/ & ( mh & fg tam m& tam.46 lbm/ h 5. Btu/lbm fg (b h rat of ntropy ration with th hat xchangr i dtrmd by applyg th rat form of th ntropy balanc on th ntir hat xchangr: (tady S S S& ΔS& & 44 & ytm { 4444 m& watr m& tam Rat of nt ntropy tranfr by hat and ma m& m& m& watr m& m& m& 4 tam Rat of ntropy ration 4 4 S& S& S& m& Rat of chang of ntropy (c watr ( m& Notg that watr i an compribl ubtanc and tam chang from aturatd vapor to aturatd liquid, th rat of ntropy ration i dtrmd to b S & m& watrc p ln m& tam ( f g m& watrc p ln m& tam fg 7 46 (5. lbm/(. Btu/lbm.Rln (.46 lbm/(.7686 Btu/lbm.R.6 Btu/.R 6 46 h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X & dtroyd dtroyd S& (57 R(.6 Btu/.R 4. Btu/ tam F ( 4 6 F Watr

83 Stam xpand a turb, which i not ulatd. h rvribl powr, th xrgy dtroyd, th cond-law fficincy, and th poibl cra th turb powr if th turb i wll ulatd ar to b dtrmd. Aumption Stady opratg condition xit. Potntial nrgy chang i ngligibl. Analyi (a h proprti of th tam at th lt and xit of th turb ar (abl A-4 through A-6 P MPa h 55 C P kpa h x kj/kg kj/kg.k 49. kj/kg kj/kg.k h nthalpy at th dad tat i 5 C h 4.8 kj/kg x h ma flow rat of tam may b dtrmd from an nrgy balanc on th turb (6 m/ m& 48.7 kj/kg kj/kg m / 5 kw 5 kw V m& h h rvribl powr may b dtrmd from W & rv m& h h ( V -V m& h V ( m/ m& 49. kj/kg m&.69 kg/ & (6 m/ (.69 ( (98( kW (b h xrgy dtroyd th turb i X & W& W& kW dt rv (c h cond-law fficincy i W& a 5 kw η II.74 W& 7 kw rv a (d h nrgy of th tam at th turb lt th givn dad tat i & m& ( h h (.69 kg/( kj/kg 995 kw W& a ( m/ kj/kg m / kj/kg m / h fraction of nrgy at th turb lt that i convrtd to powr i W& a 5 kw f.749 & 995 kw Aumg that th am fraction of hat lo from th turb could hav bn convrtd to work, th poibl cra th powr if th turb i to b wll-ulatd bcom W & f & (.749(5 kw 4. kw cra Stam MPa 55 C, 6 m/ urb kpa m/ x.95

84 Air i comprd a compror that i tntionally coold. h actual and rvribl powr put, th cond law fficincy, and th ma flow rat of coolg watr ar to b dtrmd. Aumption Stady opratg condition xit. Potntial nrgy chang i ngligibl. Air i an idal ga with contant pcific hat. Proprti h ga contant of air i R.87 kj/kg.k and th pcific hat of air at room i c p.5 kj/kg.k. th pcific hat of watr at room tmpratur i c w 4.8 kj/kg.k (abl A-, A-. Analyi (a h ma flow rat of air i ( kpa V & P m& ρ V& (4.5 m / 5.5 kg/ R (.87 kj/kg.k( 7 K h powr put for a rvribl-iothrmal proc i givn by W & rv P mr & ln P 9 kpa (5.5 kg/(.87 kj/kg.k( 7 Kln kw kpa Givn th iothrmal fficincy, th actual powr may b dtrmd from W& actual W& η rv kw.7 4 kw (b h givn iothrmal fficincy i actually th cond-law fficincy of th compror η II η.7 (c An nrgy balanc on th compror giv & V V m& C ( W& p actual, (8 m/ (5.5 kg/ (.5 kj/kg. C( 6 C 8 kw h ma flow rat of th coolg watr i & 8 kw m& w 8.5 kg/ c Δ (4.8 kj/kg. C( C w kj/kg m / 9 kpa 6 C 8 m/ Compror Air kpa C 4 kw

85 Watr i hatd a chambr by mixg it with aturatd tam. h tmpratur of th tam ntrg th chambr, th xrgy dtruction, and th cond-law fficincy ar to b dtrmd. Aumption Stady opratg condition xit. Ktic and potntial nrgy chang ar ngligibl. Hat lo from th chambr i ngligibl. Analyi (a h proprti of watr ar (abl A-4 through A-6 5 C h h 6.98 kj/kg x.447 kj/kg.k 45 C h kj/kg x.686 kj/kg.k An nrgy balanc on th chambr giv m & h m& h (4.6 kg/(6.98 kj/kg (. kg/ h m& h ( m& m& h (4.6. kg/(88.44 kj/kg h kj/kg h rmag proprti of th aturatd tam ar h kj/kg 4. C x 7.97 kj/kg.k (b h pcific xrgy of ach tram i ψ ψ h h ( ( kJ/kg (5 7 K( kJ/kg.K 68.8 kj/kg ψ h h ( ( kJ/kg (5 7 K( kJ/kg.K 6.8 kj/kg h xrgy dtruction i dtrmd from an xrgy balanc on th chambr to b X & dt m& ψ m& ψ ( m& m& ψ (. kg/(68.8 kj/kg (4.6. kg/(6.8 kj/kg 4.7 kw (c h cond-law fficincy for thi mixg proc may b dtrmd from ( m& m& ψ ηii m& ψ m& ψ Watr 5 C 4.6 kg/ Sat. vap.. kg/ (4.6. kg/(6.8 kj/kg.7 (. kg/(68.8 kj/kg Mixg chambr Mixtur 45 C

86 8-86 Rviw Problm 8-96 Rfrigrant-4a i xpandd adiabatically an xpanion valv. h work potntial of R-4a at th lt, th xrgy dtruction, and th cond-law fficincy ar to b dtrmd. Aumption Stady opratg condition xit. Ktic and potntial nrgy chang ar ngligibl. Analyi (a h proprti of th rfrigrant at th lt and xit of th valv and at dad tat ar (abl A- through A- P. MPa h 8. kj/kg 4 C.944 kj/kg.k P 8 kpa.47 kj/kg.k h h 8. kj/kg P kpa h 7.7 kj/kg C.98 kj/kg.k h pcific xrgy of th rfrigrant at th lt and xit of th valv ar ψ h h ( R-4a. MPa 4 C (8. 7.7kJ/kg - ( 7.5 K( kJ/kg.K 4.55 kj/kg 8 kpa ψ h h ( (8. 7.7kJ/kg ( 7.5 K( kj/kg.k. kj/kg (b h xrgy dtruction i dtrmd to b x dt ( ( 7.5 K( kJ/kg.K 8.4 kj/kg (c h cond-law fficincy for thi proc may b dtrmd from ψ η II ψ. kj/kg 4.55 kj/kg.794

87 Stam i acclratd an adiabatic nozzl. h xit vlocity, th rat of xrgy dtruction, and th cond-law fficincy ar to b dtrmd. Aumption Stady opratg condition xit. Potntial nrgy chang ar ngligibl. Analyi (a h proprti of th tam at th lt and xit of th turb and at th dad tat ar (abl A-4 through A-6 P.5 MPa h kj/kg C kj/kg.k P.6 kpa h 99.9 kj/kg 5 C kj/kg.k 8 C h kj/kg x.678 kj/kg.k Stam.5 MPa C h xit vlocity i dtrmd from an nrgy balanc on th nozzl.6 MPa 5 C V ( m/ kj/kg kj/kg m / V V h h V V 99.9 kj/kg 4. m/ kj/kg m / (b h rat of xrgy dtruction i th xrgy dcra of th tam th nozzl X & dt m& h h V V ( (4 m/ ( kJ/kg (.4 kg/ (9 K( kJ/kg.K 6.4kW (c h xrgy of th rfrigrant at th lt i X & V m& h h ( (.4 kg/ 44.7 kw kj/kg m / [( kj/kg (9 K( kJ/kg.K] h cond-law fficincy for thi dvic may b dfd a th xrgy put dividd by th xrgy put: X& X& dt 6.4 kw η II.94 X& X& 44.7 kw

88 R-4a i xpandd an adiabatic proc with an intropic fficincy of.85. h cond law fficincy i to b dtrmd. Aumption Ktic and potntial nrgy chang ar ngligibl. h dvic i adiabatic and thu hat tranfr i ngligibl. Analyi W tak th R-4a a th ytm. hi i a clod ytm c no ma ntr or lav. h nrgy balanc for thi tationary clod ytm can b xprd a E E 44 Nt nrgy tranfr by hat, work, and ma W ΔEytm 44 Chang trnal, ktic, potntial, tc.nrgi ΔU m( u u From th R-4a tabl (abl A- through A-, v.46 m /kg P 6 kpa u 8.9 kj/kg 8 C.9875 kj/kg K P kpa u h actual work put i.6 kj/kg wa, η w, η ( u u (.85(8.9.6kJ/kg 5.9 kj/kg h actual trnal nrgy at th nd of th xpanion proc i w, ( u u u u w, kj/kg a a Othr actual proprti at th fal tat ar (abl A- P u kpa v. kj/kg h uful work i dtrmd from w u.9 m /lbm.5 kj/kg K w w w P ( v v a, urr a, kj 5.9 kj/kg ( kpa(.9.46 m /kg kpa m.4 kj/kg h xrgy chang btwn itial and fal tat i φ φ u u 4.4 kj/kg P ( v v ( kj (8.9.kJ/kg ( kpa(.46.9 m /kg kpa m (98 K( kJ/kg K h cond law fficincy i thn w.4 kj/kg η u II.79 Δφ 4.4 kj/kg.6 MPa kpa

89 Stam i condnd a clod ytm at a contant prur from a aturatd vapor to a aturatd liquid by rjctg hat to a thrmal nrgy rrvoir. h cond law fficincy i to b dtrmd. Aumption Ktic and potntial nrgy chang ar ngligibl. Analyi W tak th tam a th ytm. hi i a clod ytm c no ma ntr or lav. h nrgy balanc for thi tationary clod ytm can b xprd a E 44 Nt nrgy tranfr by hat, work, and ma W E b, From th tam tabl (abl A-5, ΔEytm 44 Chang trnal, ktic, potntial, tc. nrgi ΔU m( u u Stam 4 kpa Sat. vapor q P 4 kpa Sat. vapor v v g u u g g.99 m /kg 476. kj/kg kj/kg K P 4 kpa Sat. liquid v v u u f f f.6 m 7.58 kj/kg h boundary work durg thi proc i /kg.6 kj/kg K 4 kpa kj P( v v (4 kpa(.99.6 m /kg kpa m w b, h hat tranfr i dtrmd from th nrgy balanc: q b 59.7 kj/kg w, ( u u 59.7 kj/kg ( kJ/kg 8.4 kj/kg h xrgy chang btwn itial and fal tat i φ φ u u P ( v v ( q kj ( kJ/kg ( kpa(.99.6 m /kg kpa m 98 K (98 K( kJ/kg K (8.4 kj/kg K 54. kj/kg h cond law fficincy i thn w b, 59.7 kj/kg η II.96 Δφ 54. kj/kg R

90 R-4a i vaporizd a clod ytm at a contant prur from a aturatd liquid to a aturatd vapor by tranfrrg hat from a rrvoir at two prur. h prur that i mor ffctiv from a cond-law pot of viw i to b dtrmd. Aumption Ktic and potntial nrgy chang ar ngligibl. Analyi W tak th R-4a a th ytm. hi i a clod ytm c no ma ntr or lav. h nrgy balanc for thi tationary clod ytm can b xprd a E 44 Nt nrgy tranfr by hat, work, and ma E W b, Chang trnal, ktic, potntial, tc. nrgi ΔU m( u W b, ΔEytm 44 ΔH m( h ΔU u h R-4a kpa at. liquid q At kpa: From th R-4a tabl (abl A-, u h kpa kpa kpa kj/kg 7.6 kj/kg kj/kg K kpa v kpa v g v f m /kg h boundary work durg thi proc i kj wb, P( v v Pv fg ( kpa(.98 m /kg 9.8 kj/kg kpa m h uful work i dtrmd from w u w, wurr P( v v P ( v v kj/kg b c P P kpa. h hat tranfr from th nrgy balanc i q h 7.6 kj/kg fg h xrgy chang btwn itial and fal tat i φ φ u u u fg P ( v v P v fg fg q ( q kj kj/kg ( kpa(.98 m /kg kpa m 98 K (7.6 kj/kg 7 K 5.8 kj/kg R R (98 K( kj/kg K h cond law fficincy i thn w kj/kg η u II Δφ 5.8 kj/kg

91 8-9 At kpa: u h v kpa kpa kpa kpa 86. kj/kg 6. kj/kg.786 kj/kg K v g v f m /kg w w P( v v Pv kj ( kpa(.994 m /kg kpa m b, fg u w b, w ( P P v urr fg P( v v P ( v v ( q h 6. kj/kg fg φ φ u η II u u fg P ( v v P v fg kpa(.994 m fg q ( q kj /kg kpa m kj 86. kj/kg ( kpa(.994 m /kg kpa m 98 K (6. kj/kg 7 K 8.9 kj/kg w u 9.9 kj/kg Δφ 8.9 kj/kg.59 h proc at kpa i mor ffctiv from a work production tandpot. R R 9.8 kj/kg 9.9 kj/kg (98 K(.786 kj/kg K

92 8-9 8-E Stam i xpandd a two-tag turb. Six prcnt of th lt tam i bld for fdwatr hatg. h intropic fficinci for th two tag of th turb ar givn. h cond-law fficincy of th turb i to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. h turb i wllulatd, and thr i no hat tranfr from th turb. Analyi hr i on lt and two xit. W tak th turb a th ytm, which i a control volum c ma cro th boundary. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a E & 44 & (tady E ΔEytm Rat of nt nrgy tranfr by hat, work, and ma E& w w m& h W& Rat of chang trnal, ktic, potntial, tc. nrgi E& m& ( h & h m& m& h m& h h.6h h W& m&.94h h.94( h h h h intropic and actual nthalpi at thr tat ar dtrmd ug tam tabl a follow: P 5 pia 6 F P pia h 98.6 Btu/lbm.559 Btu/lbm R.559 Btu/lbm R x h Btu/lbm h h η, h h η, ( h h 98.6 (.97( kJ/kg h h P h pia 57. Btu/lbm P 5 pia x.5646 kj/kg K Btu/lbm R x h Btu/lbm h h η, h h η,( h h 57. (.95( kj/kg h h h P 5 pia Btu/lbm x Btu/lbm R Subtitutg to th nrgy balanc pr unit ma flow at th lt of th turb, w obta w ( h h.94( h h ( ( Btu/lbm h rvribl work put pr unit ma flow at th turb lt i wrv h h (.94[ h h ( ] (57( ( (57( Btu/lbm h cond law fficincy i thn w. Btu/lbm η II.966 w. Btu/lbm rv 5 pia 6 F pia urb 5 pia 5 pia pia 5 pia [ ]

93 An lctrical radiator i placd a room and it i turnd on for a priod of tim. h tim priod for which th hatr wa on, th xrgy dtruction, and th cond-law fficincy ar to b dtrmd. Aumption Ktic and potntial nrgy chang ar ngligibl. Air i an idal ga with contant pcific hat. h room i wll-ald. 4 Standard atmophric prur of. kpa i aumd. Proprti h proprti of air at room tmpratur ar R.87 kpa.m /kg.k, c p.5 kj/kg.k, c v.78 kj/kg.k (abl A-. h proprti of oil ar givn to b ρ 95 kg/m, c oil. kj/kg.k. Analyi (a h ma of air and oil ar m a P V (. kpa(5 m 6.6 kg R (.87 kpa m /kg K( 7 K m oil ρ oilv oil (95 kg/m (. m 8.5 kg An nrgy balanc on th ytm can b ud to dtrm tim priod for which th hatr wa kpt on W& & Δt mc ( mc( (.8.5 kw Δt Δt 8 4 m (b h prur of th air at th fal tat i [ v ] a [ ] [(6.6 kg(.78 kj/kg. C( C] [(8.5 kg(. kj/kg. C(5 C] ( oil ma Ra (6.6 kg(.87 kpa m /kg K( 7 K P a 4.9 kpa V 5 m h amount of hat tranfr to th urroundg i & Δt (.5 kj/(8 7.5 kj h ntropy ration i th um of th ntropy chang of air, oil, and th urroundg ΔS ΔS ΔS a m c p ln P R ln P ( 7 K 4.9 kpa (6.6 kg (.5 kj/kg.kln (.87 kj/kg.kln ( 7 K. kpa.5548 kj/k (5 7 K mc ln (8.5 kg(. kj/kg.kln 8.89 kj/k ( 7 K oil 7.5 kj ( 7 K urr urr.5 kj/k S ΔSa ΔSoil ΔSurr kj/k h xrgy dtruction i dtrmd from X S ( 7 K(.65 kj/k 5 kj dt (c h cond-law fficincy may b dfd thi ca a th ratio of th xrgy rcovrd to th xrgy put. hat i, X a, m[ cv ( ] ΔS a (6.6 kg [(.78 kj/kg. C( - C] ( 7 K(.5548 kj/k 7.79 kj X oil, m[ C( ] ΔS a (8.5 kg [(. kj/kg. C(5 - C] ( 7 K(8.89 kj/k 6. kj X X rcovrd a, X oil, ( kj η II % X W& Δt (.8 kj/(8 upplid C Radiator Room

94 Hot xhaut ga lavg an trnal combution ng i to b ud to obta aturatd tam an adiabatic hat xchangr. h rat at which th tam i obtad, th rat of xrgy dtruction, and th cond-law fficincy ar to b dtrmd. Aumption Stady opratg condition xit. Ktic and potntial nrgy chang ar ngligibl. Air proprti ar ud for xhaut ga. 4 Prur drop th hat xchangr ar ngligibl. Proprti h ga contant of air i R.87 kjkg.k. h pcific hat of air at th avrag tmpratur of xhaut ga (65 K i c p.6 kj/kg.k (abl A-. Analyi (a W dnot th lt and xit tat of xhaut ga by ( and ( and that of th watr by ( and (4. h proprti of watr ar (abl A-4 C h 8.9 kj/kg x.9649 kj/kg.k 4 C h4 79. kj/kg x kj/kg.k An nrgy balanc on th hat xchangr giv m& ah m& wh m& ah m& wh4 m& c m& ( h h a p( w 4 (.8 kg/(.6 kj/kg C(4 5 C m& w( kJ/kg m&.57 kg/ (b h pcific xrgy chang of ach tram a it flow th hat xchangr i Δ a c p Δψ c Δ a ψ w p ln 9.6 kj/kg w (5 7 K (.8 kg/(.6 kj/kg.kln.86 kj/kg.k (4 7 K ( Δ a (.6 kj/kg. C(5-4 C ( 7 K(-.86 kj/kg.k h 4 h ( 4 ( kJ/kg ( 7 K( kJ/kg.K 9.9 kj/kg h xrgy dtruction i dtrmd from an xrgy balanc on th hat xchangr to b or X& X& dt dt m& Δψ m& a a 8.98 kw w Δψ w Exh. ga 4 C 5 kpa Sat. vap. C Hat Exchangr 5 C Watr C (.8 kg/(-9.6 kj/kg (.57 kg/(9.9 kj/kg 8.98 kw (c h cond-law fficincy for a hat xchangr may b dfd a th xrgy cra of th cold fluid dividd by th xrgy dcra of th hot fluid. hat i, m& wδψ w ηii m& Δψ a a (.57 kg/(9.9 kj/kg.64 (.8 kg/(-9.6 kj/kg

95 h nr and r urfac of a wdow gla ar matad at pcifid tmpratur. h amount of hat lo and th amount of xrgy dtruction 5 h ar to b dtrmd Aumption Stady opratg condition xit c th urfac tmpratur of th gla rma contant at th pcifid valu. Analyi W tak th gla to b th ytm, which i a clod ytm. h amount of hat lo i dtrmd from & Δt (4.4 kj/(5 6 79, kj Gla Undr tady condition, th rat form of th ntropy balanc for th gla implifi to S S & 44 & Rat of nt ntropy tranfr by hat and ma & b, & b, 44 W 44 W S& 8 K 76 K S& { Rat of ntropy ration S&,gla,wall ΔS& ytm 44 Rat of chang of ntropy S&,gla.94 W/K C C hn th amount of ntropy ration ovr a priod of 5 h bcom S, gla S&,glaΔt (. 94 W/ K( J/K h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, dtroyd X dtroyd S (78 K(7.98 kj/k 97 kj Dicuion h total ntropy ratd durg thi proc can b dtrmd by applyg th ntropy balanc on an xtndd ytm that clud th gla and it immdiat urroundg on both id o that th boundary tmpratur of th xtndd ytm i th room tmpratur on on id and th nvironmnt tmpratur on th othr id at all tim. Ug thi valu of ntropy ration will giv th total xrgy dtroyd durg th proc, cludg th tmpratur gradint zon on both id of th wdow.

96 Hat i tranfrrd tadily to boilg watr th pan through it bottom. h nr and r urfac tmpratur of th bottom of th pan ar givn. h rat of xrgy dtruction with th bottom plat i to b dtrmd. Aumption Stady opratg condition xit c th urfac tmpratur of th pan rma contant at th pcifid valu. Analyi W tak th bottom of th pan to b th ytm, which i a clod ytm. Undr tady condition, th rat form of th ntropy balanc for thi ytm can b xprd a S S & 44 & Rat of nt ntropy tranfr by hat and ma & b, & b, 8 W 8 W S& 78 K 77 K S& S& { Rat of ntropy ration S&,ytm,ytm,ytm ΔS& ytm 44 Rat of chang of ntropy.56 W/K h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, dtroyd 8 W 4 C 5 C X & dtroyd S& (98 K(.56 W/K.67 W 8-6 A lvation, ba ara, and th dpth of a cratr lak ar givn. h maximum amount of lctricity that can b ratd by a hydrolctric powr plant i to b dtrmd. Aumption h vaporation of watr from th lak i ngligibl. Analyi h xrgy or work potntial of th watr i th potntial nrgy it po rlativ to th ground lvl, Exrgy PE mgh hrfor, Exrgy PE dpe gzdm gz( ρadz ρag.5( kg/m z z ((5 m (4 m 9.55 zdz ρag( z 4 kwh ( z 4 m / h 6 (9.8m/ kj/kg m / m 4 m z dz

97 E h nd -law fficincy of a rfrigrator and th rfrigration rat ar givn. h powr put to th rfrigrator i to b dtrmd. Analyi From th dfition of th cond law fficincy, th COP of th rfrigrator i dtrmd to b COP R,rv η II H / L COPR COP R,rv hu th powr put i W& & L COP R 55 / 495 COP R Btu/m η COP II R,rv hp 4.4 Btu/m hp 75 F R 5 F η II.45 Btu/m 8-8 Writg nrgy and ntropy balanc, a rlation for th rvribl work i to b obtad for a clod ytm that xchang hat with urroundg at th amount of a wll a a hat rrvoir at tmpratur R th amount R. Aumption Ktic and potntial chang ar ngligibl. Analyi W tak th dirction of hat tranfr to b to th ytm (hat put and th dirction of work tranfr to b from th ytm (work put. h rult obtad i till ral c quantiti wit oppoit dirction can b handld th am way by ug ngativ ign. h nrgy and ntropy balanc for thi tationary clod ytm can b xprd a Enrgy balanc: E E ΔEytm R W U U W U U R ( Entropy balanc: S R ( S S ΔSytm S ( S S Solvg for from ( and ubtitutg ( yild R W ( U U ( S S R S R h uful work rlation for a clod ytm i obtad from W u W W urr ( U U ( S S R S P ( V V R hn th rvribl work rlation i obtad by ubtitutg S, Sytm R Sourc R W ( U U ( S S P ( V V R R rv A poitiv rult for W rv dicat work put, and a ngativ rult work put. Alo, th R i a poitiv quantity for hat tranfr to th ytm, and a ngativ quantity for hat tranfr from th ytm.

98 Writg nrgy and ntropy balanc, a rlation for th rvribl work i to b obtad for a tady-flow ytm that xchang hat with urroundg at at a rat of & a wll a a hat rrvoir at tmpratur R th amount & R. Analyi W tak th dirction of hat tranfr to b to th ytm (hat put and th dirction of work tranfr to b from th ytm (work put. h rult obtad i till ral c quantiti wit oppoit dirction can b handld th am way by ug ngativ ign. h nrgy and ntropy balanc for thi tationary clod ytm can b xprd a Enrgy balanc: E & & & & & E ΔEytm E E V Vi & & R W& m& ( h gz m& i ( hi gzi or Entropy balanc: Vi V m& i hi gzi m& ( h gz & W & ( & R ( S& S& S& S& ΔS& S& ytm S& Sytm & S& R m& m& ii ( R Solvg for & from ( and ubtitutg ( yild V i V W& i i gzi i m h gz S R m& ( h & ( & & R hn th rvribl work rlation i obtad by ubtitutg S, W& rv V i V i i i i R m& ( h gz m& ( h gz & R A poitiv rult for W rv dicat work put, and a ngativ rult work put. Alo, th R i a poitiv quantity for hat tranfr to th ytm, and a ngativ quantity for hat tranfr from th ytm.

99 Writg nrgy and ntropy balanc, a rlation for th rvribl work i to b obtad for a uniform-flow ytm that xchang hat with urroundg at th amount of a wll a a hat rrvoir at tmpratur R th amount R. Aumption Ktic and potntial chang ar ngligibl. Analyi W tak th dirction of hat tranfr to b to th ytm (hat put and th dirction of work tranfr to b from th ytm (work put. h rult obtad i till ral c quantiti wit oppoit dirction can b handld th am way by ug ngativ ign. h nrgy and ntropy balanc for thi tationary clod ytm can b xprd a Enrgy balanc: ytm E E E Δ cv i i i i R U U gz V h m gz V h m W ( ( ( or, R cv i i i i U U gz V h m gz V h m W ( ( ( ( Entropy balanc: ytm S S S S Δ ( m m S S S R R i i cv ( Solvg for from ( and ubtitutg ( yild [ ] R R cv i i i i i S S S U U gz V h m gz V h m W ( ( ( ( h uful work rlation for a clod ytm i obtad from [ ] ( ( ( ( ( urr V V P S S S U U gz V h m gz V h m W W W R R cv i i i i i u hn th rvribl work rlation i obtad by ubtitutg S, [ ] R R cv i i i i i P S S U U gz V h m gz V h m W rv ( ( ( ( ( V V A poitiv rult for W rv dicat work put, and a ngativ rult work put. Alo, th R i a poitiv quantity for hat tranfr to th ytm, and a ngativ quantity for hat tranfr from th ytm. Sytm m Sourc R

100 8-8- An lctric ritanc hatr i immrd watr. h tim it will tak for th lctric hatr to rai th watr tmpratur to a pcifid tmpratur, th mimum work put, and th xrgy dtroyd durg thi proc ar to b dtrmd. Aumption Watr i an compribl ubtanc with contant pcific hat. h nrgy tord th contar itlf and th hatr i ngligibl. Hat lo from th contar i ngligibl. 4 h nvironmnt tmpratur i givn to b C. Proprti h pcific hat of watr at room tmpratur i c 4.8 kj/kg C (abl A-. Analyi akg th watr th contar a th ytm, which i a clod ytm, th nrgy balanc can b xprd a Subtitutg, E E 44 Nt nrgy tranfr by hat, work, and ma W W&,, Chang trnal, ktic, potntial, tc.nrgi ( ΔU Δt mc( ΔEytm 44 watr watr (8 J/Δt (4 kg(48 J/kg C(8 - C Solvg for Δt giv Δt, m.484 h Aga w tak th watr th tank to b th ytm. Notg that no hat or ma cro th boundari of thi ytm and th nrgy and ntropy contnt of th hatr ar ngligibl, th ntropy balanc for it can b xprd a S S 44 Nt ntropy tranfr by hat and ma S { Entropy ration S ΔS ΔSytm 44 Chang ntropy watr hrfor, th ntropy ratd durg thi proc i S ΔS watr mc ln 4 kg 4.84 kj/kg K 5 K 9 K ( ( ln.8 kj/k h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X dtroyd dtroyd S (9 K(.8 kj/k 96 kj h actual work put for thi proc i W W& Δt (.8 kj/(,55,4 kj act, act, hn th rvribl (or mimum rquird work put bcom W rv, W X, kj act, dtroyd Watr 4 kg Hatr

101 8-8- A hot watr pip at a pcifid tmpratur i log hat to th urroundg air at a pcifid rat. h rat at which th work potntial i watd durg thi proc i to b dtrmd. Aumption Stady opratg condition xit. Analyi W tak th air th vicity of th pip (xcludg th pip a our ytm, which i a clod ytm.. h ytm xtnd from th r urfac of th pip to a ditanc at which th tmpratur drop to th urroundg tmpratur. In tady opration, th rat form of th ntropy balanc for thi ytm can b xprd a S S & 44 & Rat of nt ntropy tranfr by hat and ma & & S& b, b, 75 W 75 W S& 5 K 78 K S& { Rat of ntropy ration,ytm,ytm ΔS& ytm 44 Rat of chang of ntropy S&,ytm.898 W/K h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X & dtroyd dtroyd S& (78 K(.898 W/K 5 W L m D 5 cm 8 C Air, 5 C

102 8-8- Air xpand an adiabatic turb from a pcifid tat to anothr pcifid tat. h cond-law fficincy i to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. h dvic i adiabatic and thu hat tranfr i ngligibl. Air i an idal ga with contant pcific hat. 4 Ktic and potntial nrgy chang ar ngligibl. Proprti At th avrag tmpratur of (45 5/ 75 K, th contant prur pcific hat of air i c p. kj/kg.k (abl A-b. h ga contant of air i R.87 kj/kg.k (abl A-. Analyi hr i only on lt and on xit, and thu m & m& m&. W tak th turb a th ytm, which i a control volum c ma cro th boundary. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a E & 44 & (tady E ΔEytm Rat of nt nrgy tranfr by hat, work, and ma E& w mh & W& Rat of chang trnal, ktic, potntial, tc.nrgi E& W& m& ( h c p & ( mh & h 55 kpa 45 K Air Subtitutg, w p c ( (. kj/kg K(45 5K. kj/kg kpa 5 K h ntropy chang of air i P c p ln R ln P (. kj/kg K ln.97 kj/kg K 5 K 45 K (.87 kj/kg K ln kpa 55 kpa h maximum (rvribl work i th xrgy diffrnc btwn th lt and xit tat wrv, c p ( ( w (. kj/kg (98 K(.97 kj/kg K 57.9 kj/kg h cond law fficincy i thn w. kj/kg η II.64 w 57.9 kj/kg rv,

103 8-8-4 Stam i acclratd a nozzl. h actual and maximum lt vlociti ar to b dtrmd. Aumption h nozzl oprat tadily. h chang potntial nrgi ar ngligibl. Proprti h proprti of tam at th lt and th xit of th nozzl ar (abl A-4 through A-6 P 5 kpa h C P x kpa (at. vapor kj/kg 7.6 kj/kg K h 76. kj/kg 7.7 kj/kg K Analyi W tak th nozzl to b th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a Subtitutg, E E & 44 & Rat of nt nrgy tranfr by hat, work, and ma m& ( h V V E& / V Rat of chang trnal, ktic, potntial, tc.nrgi E& m& ( h h (tady ΔEytm & h V / Δk actual Δk actual h h kj/kg h actual vlocity at th xit i thn 5 kpa C m/ H O kpa at. vapor V V V Δk V actual Δk actual ( m/ m / (49.5 kj/kg kj/kg m/ h maximum ktic nrgy chang i dtrmd from Δk max h h ( (98( kj/kg h maximum vlocity at th xit i thn V,max V Δk max V,max V Δk 58.5 m/ max ( m/ m / (69. kj/kg kj/kg

104 A throttl valv i placd th tam l upplyg th turb lt ordr to control an intropic tam turb. h cond-law fficincy of thi ytm whn th valv i partially opn to whn it i fully opn i to b compard. Aumption hi i a tady-flow proc c thr i no chang with tim. h turb i wllulatd, and thr i no hat tranfr from th turb. Analyi Valv i fully opn: h proprti of tam at variou tat ar P P 6 MPa h h 894. kj/kg 7 C kj/kg K P 7 kpa x h kj/kg h cond law fficincy of th ntir ytm i thn w h h h h η II. w h h ( h h rv c for thi ytm. Valv i partly opn: 7 kpa p 6 MPa MPa P h MPa h 894. kj/kg kj/kg K (from EES P 7 kpa h 76.8 kj/kg (from EES w η II w rv h h h h ( (98(

105 wo rigid tank that conta watr at diffrnt tat ar connctd by a valv. h valv i opnd and tam flow from tank A to tank B until th prur tank A drop to a pcifid valu. ank B lo hat to th urroundg. h fal tmpratur ach tank and th work potntial watd durg thi proc ar to b dtrmd. Aumption ank A i ulatd and thu hat tranfr i ngligibl. h watr that rma tank A undrgo a rvribl adiabatic proc. h thrmal nrgy tord th tank thmlv i ngligibl. 4 h ytm i tationary and thu ktic and potntial nrgy chang ar ngligibl. 5 hr ar no work traction. Analyi (a h tam tank A undrgo a rvribl, adiabatic proc, and thu. From th tam tabl (abl A-4 through A-6, ank A : v, P 4 kpa u, x.8 P kpa x, A (.8( (.8( kj/kg (.8( kj/kg ( at. mixtur v, A v f x, Av fg.7 (.7895( u u x u 56. (.7895( 98. kj/kg 5.9 ankb : v, P kpa u, 5 C A A, A, A, A B B, B v u f f f x v at@kpa, A f x u x fg fg, A.989 m /kg 7.4 kj/kg kj/kg K f fg fg C h itial and th fal ma tank A ar and m m, A, A V A v, A V A v, A m.48 kg.479m /kg fg. m.54 kg.75 m /kg hu, kg of ma flow to tank B. hn, m, B m, B... kg h fal pcific volum of tam tank B i dtrmd from V B mv B kg.989 m /kg v, B.5 m m m. m, B ( ( ( /kg, B.75 m K.4785 m kj/kg W tak th ntir contnt of both tank a th ytm, which i a clod ytm. h nrgy balanc for thi tationary clod ytm can b xprd a E E ΔE 44 ytm 44 Nt nrgy tranfr by hat, work, and ma Chang trnal, ktic, potntial, tc.nrgi ΔU ( ΔU A ( ΔU ( mu mu A ( mu mu B B A V. m tam P 4 kpa x.8 (c W KE PE /kg B /kg 9 kj m kg tam 5 C P kpa

106 8-6 Subtitutg, 9 hu, v u, B, B { } {(.48( 5.9 (.54( 6. } (. u ( ( m /kg 45.9 kj/kg, B u, B 45.9 kj/kg, B. C kj/kg K (b h total ntropy ration durg thi proc i dtrmd by applyg th ntropy balanc on an xtndd ytm that clud both tank and thir immdiat urroundg o that th boundary tmpratur of th xtndd ytm i th tmpratur of th urroundg at all tim. It giv S S 44 Nt ntropy tranfr by hat and ma b,urr S { Entropy ration S ΔSytm 44 Chang ntropy ΔS A ΔS B Rarrangg and ubtitutg, th total ntropy ratd durg thi proc i dtrmd to b S ΔS A ΔS B, B ( m m ( m m {(.48( (.54( } {(.( ( ( 7.7 }.4 kj/k b,urr A B b,urr 9 kj 7 K h work potntial watd i quivalnt to th xrgy dtroyd durg a proc, which can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X dtroyd dtroyd S (7 K(.4 kj/k 7 kj

107 E A cyldr itially filld with hlium ga at a pcifid tat i comprd polytropically to a pcifid tmpratur and prur. h actual work conumd and th mimum uful work put ndd ar to b dtrmd. Aumption Hlium i an idal ga with contant pcific hat. h cyldr i tationary and thu th ktic and potntial nrgy chang ar ngligibl. h thrmal nrgy tord th cyldr itlf i ngligibl. 4 h comprion or xpanion proc i quai-quilibrium. 5 h nvironmnt tmpratur i 7 F. Proprti h ga contant of hlium i R.685 pia.ft /lbm.r.496 Btu/lbm.R (abl A-E. h pcific hat of hlium ar c v.75 and c v.5 Btu/lbm.R (abl A-E. Analyi (a Hlium at pcifid condition can b tratd a an idal ga. h ma of hlium i P V m R (5 pia(5 ft.64 lbm (.685 pia ft /lbm R(5 R h xponnt n and th boundary work for thi polytropic proc ar dtrmd to b P V PV P V n P n V V P P P (76 R(5 pia V (5 ft 7.68 ft P (5 R(7 pia V V n n n.59 hn th boundary work for thi polytropic proc can b dtrmd from Alo, W b, ( PV P V mr PdV n n (.64 lbm(.496 Btu/lbm R( R 55.9 Btu HELIUM 5 ft PV n cont hu, W W urr, u, P ( V V (4.7 pia(7.68 5ft W b, W urr, Btu Btu 5.49 pia ft 9.9 Btu (b W tak th hlium th cyldr a th ytm, which i a clod ytm. akg th dirction of hat tranfr to b from th cyldr, th nrgy balanc for thi tationary clod ytm can b xprd a Subtitutg, E 44 Nt nrgy tranfr by hat, work, and ma E W b, Chang trnal, ktic, potntial, tc.nrgi ΔU m( u m( u W b, ΔEytm 44 u mc ( u W v b, (.64 lbm(.75 Btu/lbm R( 76 5 R. Btu 55.9 Btu

108 8-8 h total ntropy ration durg thi proc i dtrmd by applyg th ntropy balanc on an xtndd ytm that clud th cyldr and it immdiat urroundg o that th boundary tmpratur of th xtndd ytm i th tmpratur of th urroundg at all tim. It giv S S 44 Nt ntropy tranfr by hat and ma b,urr S { Entropy ration S ΔSytm 44 Chang ntropy ΔS whr th ntropy chang of hlium i ΔS y ΔS hlium m c p,avg y ln P R ln P 76 R 7 pia (.64 lbm (.5 Btu/lbm Rln (.496 Btu/lbm Rln 5 R 5 pia. 59 Btu/ R Rarrangg and ubtitutg, th total ntropy ratd durg thi proc i dtrmd to b S. Btu (.59 Btu/R 45 Btu/R 5 R ΔS hlium. h work potntial watd i quivalnt to th xrgy dtroyd durg a proc, which can b dtrmd from an xrgy balanc or dirctly from it dfition X S, dtroyd X dtroyd S (5 R(.45 Btu/R.77 Btu h mimum work with which thi proc could b accomplihd i th rvribl work put, W rv,. which can b dtrmd dirctly from W rv, W X Btu act, dtroyd Dicuion h rvribl work put, which rprnt th mimum work put W rv, thi ca can b dtrmd from th xrgy balanc by ttg th xrgy dtruction trm qual to zro, (rvribl X X Xdtroyd ΔXytm Wrv, X X Nt xrgy tranfr Exrgy Chang by hat,work,andma dtruction xrgy Subtitutg th clod ytm xrgy rlation, th rvribl work put durg thi proc i dtrmd to b W rv ( U U (.64 lbm(.75 Btu/lbm R( 7 F (5 R(-.59 Btu/R (4.7 pia(7.68 5ft 4.4 Btu ( S S P ( V V [Btu/5.49 pia ft ]

109 Stam xpand a two-tag adiabatic turb from a pcifid tat to pcifid prur. Som tam i xtractd at th nd of th firt tag. h watd powr potntial i to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h turb i adiabatic and thu hat tranfr i ngligibl. 4 h nvironmnt tmpratur i givn to b 5 C. Analyi h watd powr potntial i quivalnt to th rat of xrgy dtruction durg a proc, which can b dtrmd from an xrgy balanc or dirctly from it dfition X S. 9 MPa 5 C.4 MPa SEAM 5 kg/ % I dtroyd h total rat of ntropy ration durg thi proc i dtrmd by takg th ntir turb, which i a control volum, a th ytm and applyg th ntropy balanc. Notg that thi i a tady-flow proc and thr i no hat tranfr, S S S& ΔS& ytm & 44 & { 44 Rat of nt ntropy tranfr by hat and ma m& m& m&.m& m&.9m& Rat of ntropy ration S& S& Rat of chang of ntropy S& and X S m&.9. ] dtroyd [ From th tam tabl (abl A-4 through 6 P 9 MPa h 87.4 kj / kg 5 C 6.66 kj / kg K and, η P.4 MPa h h h 88.4 kj / kg h h h P.4 MPa h 94. kj/kg P 5 kpa x h m& [.9 h η ( h h ( kj/kg h f kj / kg K fg x f. ] 9% h kj/kg fg SEAM.5 kg/ 5 kpa II and η h h h h η ( h h h h P 5 kpa x h 44. kj/kg ( kj/kg h f h f h fg x Subtitutg, th watd work potntial i dtrmd to b X & dtroyd kj/kg K fg S& (98 K(5 kg/( kj/kg 54 kw

110 8-8-9 Stam xpand a two-tag adiabatic turb from a pcifid tat to anothr pcifid tat. Stam i rhatd btwn th tag. For a givn powr put, th rvribl powr put and th rat of xrgy dtruction ar to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h turb i adiabatic and thu hat tranfr i ngligibl. 4 h nvironmnt tmpratur i givn to b 5 C. Proprti From th tam tabl (abl A- 4 through 6 P 8 MPa h 5 C P MPa h 5 C P MPa h 5 C P4 kpa h x kj / kg kj / kg K kj / kg kj / kg K 468. kj / kg 7.47 kj / kg K h f f x h 4 x 4 fg fg kj/kg kj/kg K Analyi W tak th ntir turb, xcludg th rhat ction, a th ytm, which i a control volum. h nrgy balanc for thi tady-flow ytm can b xprd th rat form a E & 44 & (tady E ΔEytm Rat of nt nrgy tranfr by hat, work, and ma E& mh & mh & W& Rat of chang trnal, ktic, potntial, tc.nrgi E& mh & & mh & 4 W& m& [( h h ( h h4 ] Subtitutg, th ma flow rat of th tam i dtrmd from th tady-flow nrgy quation applid to th actual proc, W& 5 kj/ m& 4.5 kg/ h h h h ( kJ/kg 4 MPa 5 C 8 MPa 5 C Stag I Stag II h rvribl (or maximum powr put i dtrmd from th rat form of th xrgy balanc applid on th turb and ttg th xrgy dtruction trm qual to zro, Hat MPa 5 C kpa x 97% 5 MW

111 8- X X & 44 & Ratof nt xrgy tranfr by hat,work,andma hn th rvribl powr bcom W & rv, m& h (rvribl (tady Xdtroyd ΔXytm & & 4444 Ratof xrgy dtruction rv, m& ( ψ ψ m& ( ψ ψ m& [( h h ( m& [( h Ratof chang of xrgy X& X& m& ψ m& ψ m& ψ m& ψ W& W& h ( [ h h h ( ] 5457 kw rv, (4.5 kg/[( kJ/kg (98 K( kJ/kg K] hn th rat of xrgy dtruction i dtrmd from it dfition, X & W& W& kw dtroyd rv, 4 Δk 4 Δk 4 Δp Δp ] ]

112 8-8- On ton of liquid watr at 8 C i brought to a room. h fal quilibrium tmpratur th room and th ntropy ratd ar to b dtrmd. Aumption h room i wll ulatd and wll ald. h thrmal proprti of watr and air ar contant at room tmpratur. h ytm i tationary and thu th ktic and potntial nrgy chang ar zro. 4 hr ar no work traction volvd. Proprti h ga contant of air i R.87 kpa.m /kg.k (abl A-. h contant volum pcific hat of watr at room tmpratur i c v.78 kj/kg C (abl A-. h pcific hat of watr at room tmpratur i c 4.8 kj/kg C (abl A-. Analyi h volum and th ma of th air th room ar V 4x5x6 m³ m P V ( kpa( m air R (.87 kpa m /kg K(95 K akg th contnt of th room, cludg th watr, a our ytm, th nrgy balanc can b writtn a E E ΔE 44 ytm 44 Nt nrgy tranfr by hat, work, and ma Chang trnal, ktic, potntial, tc.nrgi ΔU ( ΔU watr ( ΔU air or [ ( ] [ mc ( ] mc v watr air o 4.74 kg o o f f Subtitutg, ( kg( 4.8 kj/kg C( 8 C ( 4.74 kg(.78 kj/kg C( C It giv th fal quilibrium tmpratur th room to b f 78.6 C (b W aga tak th room and th watr it a th ytm, which i a clod ytm. Conidrg that th ytm i wll-ulatd and no ma i ntrg and lavg, th ntropy balanc for thi ytm can b xprd a whr S S 44 Nt ntropy tranfr by hat and ma ΔS ΔS air watr mc v mc ln S { Entropy ration ΔS ytm 44 Chang ntropy S ΔS ΔS ln air V mr ln V watr ( 4.74 kg(.78 kj/kg 5.6 K ( kg( 4.8 kj/kg K ln 6.6 kj/ K 5 K 5.6 K K ln 7.87 kj/ K 95 K Subtitutg, th ntropy ration i dtrmd to b S kj/k h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X dtroyd dtroyd S (8 K(.5kJ/K 47 kj (c h work potntial (th maximum amount of work that can b producd durg a proc i imply th rvribl work put. Notg that th actual work for thi proc i zro, it bcom X W W W 47 kj dtroyd rv, act, rv, X dtroyd 4 m 5 m 6 m Watr 8 C ROOM C kpa o Hat

113 8-8- An ulatd cyldr i dividd to two part. On id of th cyldr conta N ga and th othr id conta H ga at diffrnt tat. h fal quilibrium tmpratur th cyldr and th watd work potntial ar to b dtrmd for th ca of piton bg fixd and movg frly. Aumption Both N and H ar idal ga with contant pcific hat. h nrgy tord th contar itlf i ngligibl. h cyldr i wll-ulatd and thu hat tranfr i ngligibl. Proprti h ga contant and th contant volum pcific hat ar R.968 kpa.m /kg.k i c v.74 kj/kg C for N, and R.769 kpa.m /kg.k i c v.56 kj/kg C for H (abl A- and A- Analyi h ma of ach ga th cyldr i m m N H P V R P V R N H ( 5 kpa( m (.968 kpa m /kg K( 5 K ( 5 kpa( m (.769 kpa m /kg K( 98 K 4.77 kg.88 kg akg th ntir contnt of th cyldr a our ytm, th t law rlation can b writtn a Subtitutg, E E 44 Nt nrgy tranfr by hat, work, and ma Chang trnal, ktic, potntial, tc.nrgi ΔU [ mc v ΔEytm 44 ( ΔU ( ΔU ( N ] N H [ mc v ( ] o o o o ( 4.77 kg(.74 kj/kg C( 8 C (.88 kg(.56 kj/kg C( 5 C f f It giv f 57. C whr f i th fal quilibrium tmpratur th cyldr. h anwr would b th am if th piton wr not fr to mov c it would ffct only prur, and not th pcific hat. (b W tak th ntir cyldr a our ytm, which i a clod ytm. Notg that th cyldr i wllulatd and thu thr i no hat tranfr, th ntropy balanc for thi clod ytm can b xprd a S S 44 Nt ntropy tranfr by hat and ma S { Entropy ration ΔS ytm 44 Chang ntropy S ΔS ΔS But firt w dtrm th fal prur th cyldr: hn, N P total N N V total N total N R u H m M N N m M H H (.7 kmol( 8.4 kpa m /kmol K(. K m H 4.77 kg.88 kg.7 kmol 8 kg/kmol 4 kg/kmol N m 5 kpa 8 C 5.6 kpa H m 5 kpa 5 C

114 8-4 ΔS ΔS S N H m c p ln P R ln P N. K 5.6 kpa 5 kpa ( 4.77 kg (.9 kj/kg K ln (.968 kj/kg K ln.6 kj/k m c ln P R ln P 5 K. K (.88 kg ( 5.96 kj/kg K ln (.769 kj/kg K ΔS N p ΔS H H 98 K kj/ K 5.6 kpa ln.95 kj/k 5 kpa h watd work potntial i quivalnt to th xrgy dtroyd durg a proc, and it can b dtrmd from an xrgy balanc or dirctly from it dfition X dtroyd S, X dtroyd S (98 K(.4 kj/k. kj If th piton wr not fr to mov, w would till hav. K but th volum of ach ga would rma contant thi ca: ΔS ΔS S N H mc mc ΔS N v v ln ln ΔS V R ln V V R ln V H N H ( 4.77 kg(.74 kj/kg K kj/k (.88 kg(.56 kj/kg K. K ln.7 kj/k 5 K. K ln.58 kj/k 98 K and X dtroyd S (98 K(.kJ/K 6.6 kj

115 An ulatd cyldr i dividd to two part. On id of th cyldr conta N ga and th othr id conta H ga at diffrnt tat. h fal quilibrium tmpratur th cyldr and th watd work potntial ar to b dtrmd for th ca of piton bg fixd and movg frly. Aumption Both N and H ar idal ga with contant pcific hat. h nrgy tord th contar itlf, xcpt th piton, i ngligibl. h cyldr i wll-ulatd and thu hat tranfr i ngligibl. 4 Initially, th piton i at th avrag tmpratur of th two ga. Proprti h ga contant and th contant volum pcific hat ar R.968 kpa.m /kg.k i c v.74 kj/kg C for N, and R.769 kpa.m /kg.k i c v.56 kj/kg C for H (abl A- and A-. h pcific hat of coppr piton i c.86 kj/kg C (abl A-. Analyi h ma of ach ga th cyldr i m m N H P V R P V R N H ( 5 kpa( m (.968 kpa m /kg K( 5 K ( 5 kpa( m (.769 kpa m /kg K( 5 K 4.77 kg.88 kg akg th ntir contnt of th cyldr a our ytm, th t law rlation can b writtn a whr E 44 Nt nrgy tranfr by hat, work, and ma ΔU [ mc E v ( ΔU ( ΔU ( ΔU ( N ] Chang trnal, ktic, potntial, tc.nrgi N ΔEytm 44 H [ mc v (, Cu (8 5 / 5.5 C Subtitutg, o 4.77 kg.74 kj/kg C 8 It giv Cu ] H [ mc( ] o o o ( ( ( f C (.88 kg(.56 kj/kg C( f 5 C o o ( kj/kg C( 5.5 C f 56. C whr f i th fal quilibrium tmpratur th cyldr. h anwr would b th am if th piton wr not fr to mov c it would ffct only prur, and not th pcific hat. (b W tak th ntir cyldr a our ytm, which i a clod ytm. Notg that th cyldr i wllulatd and thu thr i no hat tranfr, th ntropy balanc for thi clod ytm can b xprd a S S 44 Nt ntropy tranfr by hat and ma S { Entropy ration ΔS ytm 44 Chang ntropy S ΔS ΔS ΔS But firt w dtrm th fal prur th cyldr: N H piton Cu N m 5 kpa 8 C f H m 5 kpa 5 C Coppr

116 8-6 N P total N N N total Ru V total N H m M N m M H (.7 kmol( 8.4 kpa m /kmol K( 9 K m 4.77 kg.88 kg.7 kmol 8 kg/kmol 4 kg/kmol 58.8 kpa hn, ΔS ΔS ΔS N H piton S m c p ln P R ln P P m c p ln R ln P mc ln piton ΔS ΔS ΔS 9 K ( 4.77 kg (.9 kj/kg K ln (.968 kj/kg K 5 K 9 K (.88 kg ( 5.96 kj/kg K ln (.769 kj/kg K N H 5 K ( 5 kg(.86 kj/kg K piton N H 58.8 kpa ln.86 kj/k 5 kpa 9 K ln. kj/k 5.5 K kpa ln.74 kj/k 5 kpa kj/k h watd work potntial i quivalnt to th xrgy dtroyd durg a proc, and it can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X dtroyd dtroyd S (98 K(. kj/k 9.8 kj If th piton wr not fr to mov, w would till hav. K but th volum of ach ga would rma contant thi ca: ΔS ΔS S N H mc v mc ΔS v N ln ln ΔS V R ln V V R ln V H ΔS piton N ( 4.77 kg(.74 kj/kg K 9 K ln.5 kj/k 5 K 9 K (.88 kg(.56 kj/kg K ln.49 kj/k 5 K H kj/k and X dtroyd S (98 K(. kj/k 6. kj

117 8-7 8-E Argon ntr an adiabatic turb at a pcifid tat with a pcifid ma flow rat, and lav at a pcifid prur. h intropic fficincy of turb i to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. h dvic i adiabatic and thu hat tranfr i ngligibl. 4 Argon i an idal ga with contant pcific hat. Proprti h pcific hat ratio of argon i k.667. h contant prur pcific hat of argon i c p.5 Btu/lbm.R (abl A-E. Analyi hr i only on lt and on xit, and thu m& m& m&. W tak th intropic turb a th ytm, which i a control volum c ma cro th boundary. h nrgy balanc for thi tadyflow ytm can b xprd th rat form a & & (tady E E ΔEytm Rat of nt nrgy tranfr Rat of chang trnal, ktic, by hat, work, and ma potntial, tc.nrgi E& mh & W&, E& W& m& ( h &, mh & h (c & Δk Δp Ar η 7 kw From th intropic rlation, ( k / k.667 /.667 P P pia (96 R pia hn th powr put of th intropic turb bcom 97.5 R hp W &, mc & p 4.4 Btu/m ( (4 lbm/m(.5 Btu/lbm R( R. hp hn th intropic fficincy of th turb i dtrmd from W& a, 95 hp η % W&. hp, (b Ug th tady-flow nrgy balanc rlation W& mc & ( a, p abov, th actual turb xit tmpratur i dtrmd to b W& a, 95 hp 4.4 Btu/m F 56. R (4 lbm/m(.5 Btu/lbm R hp mc & p h ntropy ration durg thi proc can b dtrmd from an ntropy balanc on th turb, whr S S & 44 & Rat of nt ntropy tranfr by hat and ma m & m & S& { Rat of ntropy ration S& S& ΔS& ytm 44 Rat of chang of ntropy m& (

118 8-8 c p ln P R ln P (.5 Btu/lbm R ln.86 Btu/lbm.R 56. R 96 R (.497 Btu/lbm R ln pia pia h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X & dtroyd dtroyd S& m & ( (4 lbm/m(57 R(.86 Btu/lbm R 4. hp hn th rvribl powr and cond-law fficincy bcom W& W& X& hp rv, a, dtroyd hp 4.4 Btu/m and W& η II W& rv 95 hp 9. hp 86.9%

119 h fdwatr of a tam powr plant i prhatd ug tam xtractd from th turb. h ratio of th ma flow rat of th xtractd tam and th fdwatr ar to b dtrmd. Aumption hi i a tady-flow proc c thr i no chang with tim. Ktic and potntial nrgy chang ar ngligibl. Hat lo from th dvic to th urroundg i ngligibl and thu hat tranfr from th hot fluid i qual to th hat tranfr to th cold fluid. Proprti h proprti of tam and fdwatr ar (abl A-4 through A-6 P MPa h 88.kJ/kg C kj/kg K h h f P MPa f at. MPa 76.5 kj/kg.8 kj/kg K C P 9.4 kj/kg.5 MPa h h o C 5 C.78 kj/kg K o C 4 P.5 MPa kj/kg 4 h h o C C 7 C 4.47 kj/kg K 4 o C Analyi (a W tak th hat xchangr a th ytm, which i a control volum. h ma and nrgy balanc for thi tadyflow ytm can b xprd th rat form a follow: at. liquid Ma balanc (for ach fluid tram: (tady m& m& Δm& ytm m& m& m& m& m& and m& m& 4 & Enrgy balanc (for th hat xchangr: (tady E E ΔEytm E& E& & 44 & & 4444 Rat of nt nrgy tranfr by hat, work, and ma m& h m& h m& h m& h Rat of chang trnal, ktic, potntial, tc.nrgi m& h 4 4 h m& fw h4 Combg th two, ( ( (c & W& Δk Δp h m fw Dividg by &m fw and ubtitutg, m& h h4 ( kj/kg.47 m& fw h h ( kj/kg (b h ntropy ration durg thi proc pr unit ma of fdwatr can b dtrmd from an ntropy balanc on th fdwatr hatr xprd th rat form a S S S& ΔS& ytm & 44 & { 44 Rat of nt ntropy tranfr by hat and ma Rat of ntropy ration Rat of chang of ntropy m& m& m& m& 44 S& m& ( m& fw ( 4 S& S& m& ( ( 4 (.47( ( kj/k kg fw m& fw m& fw Notg that thi proc volv no actual work, th rvribl work and xrgy dtruction bcom quivalnt c X dtroyd Wrv, Wact, Wrv, X dtroyd. h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X dtroyd S (98 K(. kj/ K kgfw 6.5 kj/kgfdwatr Stam from turb MPa C dtroyd Fdwatr.5 MPa 5 C

120 8-8-5 EES Problm 8-4 i rconidrd. h ffct of th tat of th tam at th lt of th fdwatr hatr on th ratio of ma flow rat and th rvribl powr i to b vtigatd. Analyi Ug EES, th problm i olvd a follow: "Input Data" "Stam (lt ttam data:" Fluid$'Stam_IAPWS' _t[] [C] {P_t[] [kpa]} P_t[] P_t[] x_t[] "aturatd liquid, quality %" _t[]tmpratur(tam, PP_t[], xx_t[] "Fdwatr (lt fwfdwatr data:" _fw[]5 [C] P_fw[]5 [kpa] P_fw[]P_fw[] "aum no prur drop for th fdwatr" _fw[]_t[]- "Surroundg:" _o 5 [C] P_o [kpa] "Aumd valu for th urrroundg prur" "Conrvation of ma:" "hr i on ntranc, on xit for both th tam and fdwatr." "Stam: m_dot_t[] m_dot_t[]" "Fdwatr: m_dot_fw[] m_dot_fw[]" "Lt m_ratio m_dot_t/m_dot_fw" "Conrvation of Enrgy:" "W writ th conrvation of nrgy for tady-flow control volum havg two ntranc and two xit with th abov aumption. Sc nithr of th flow rat i know or can b found, writ th conrvation of nrgy pr unit ma of th fdwatr." E_ - E_ DELAE_cv DELAE_cv "Stady-flow rquirmnt" E_ m_ratio*h_t[] h_fw[] h_t[]nthalpy(fluid$, _t[], PP_t[] h_fw[]nthalpy(fluid$,_fw[], PP_fw[] E_ m_ratio*h_t[] h_fw[] h_fw[]nthalpy(fluid$, _fw[], PP_fw[] h_t[]nthalpy(fluid$, xx_t[], PP_t[] "h rvribl work i givn by Eq. 7-47, whr th hat tranfr i zro (th fdwatr hatr i adiabatic and th Exrgy dtroyd i t qual to zro" W_rv m_ratio*(pi_t[]-pi_t[] (Pi_fw[]-Pi_fw[] Pi_t[]h_t[]-h_t_o -(_o 7*(_t[]-_t_o _t[]ntropy(fluid$,_t[], PP_t[] h_t_onthalpy(fluid$, _o, PP_o _t_ontropy(fluid$, _o, PP_o Pi_t[]h_t[]-h_t_o -(_o 7*(_t[]-_t_o _t[]ntropy(fluid$,xx_t[], PP_t[] Pi_fw[]h_fw[]-h_fw_o -(_o 7*(_fw[]-_fw_o h_fw_onthalpy(fluid$, _o, PP_o _fw[]ntropy(fluid$,_fw[], PP_fw[] _fw_ontropy(fluid$, _o, PP_o

121 8- Pi_fw[]h_fw[]-h_fw_o -(_o 7*(_fw[]-_fw_o _fw[]ntropy(fluid$,_fw[], PP_fw[] m ratio [kg/kg] W rv [kj/kg] P t, [kpa] m ratio [kg t/kg,fw] P t[] [kpa] 7 6 W rv [kj/kg fw] P t[] [kpa]

122 8-8-6 A -ton ( kg of watr i to b coold a tank by pourg ic to it. h fal quilibrium tmpratur th tank and th xrgy dtruction ar to b dtrmd. Aumption hrmal proprti of th ic and watr ar contant. Hat tranfr to th watr tank i ngligibl. hr i no tirrg by hand or a mchanical dvic (it will add nrgy. Proprti h pcific hat of watr at room tmpratur i c 4.8 kj/kg C, and th pcific hat of ic at ab C i c. kj/kg C (abl A-. h mltg tmpratur and th hat of fuion of ic at atm ar C and.7 kj/kg.. Analyi (a W tak th ic and th watr a th ytm, and dirgard any hat tranfr btwn th ytm and th urroundg. hn th nrgy balanc for thi proc can b writtn a E E 44 Nt nrgy tranfr by hat, work, and ma o Chang trnal, ktic, potntial, tc.nrgi ΔU ΔU ΔEytm 44 ic ΔU watr o if [ mc( C olid mh mc( C liquid ] ic [ mc( ] watr Subtitutg, It giv o o o o ( 8 kg{(. kj / kg C[ (-5] C.7 kj / kg (4.8 kj / kg C( C}.4 C ( kg( 4.8 kj / kg C( C which i th fal quilibrium tmpratur th tank. (b W tak th ic and th watr a our ytm, which i a clod ytm.conidrg that th tank i wll-ulatd and thu thr i no hat tranfr, th ntropy balanc for thi clod ytm can b xprd a whr hn, S S 44 Nt ntropy tranfr by hat and ma ΔS watr ΔS ic S { Entropy ration S mc ln ΔSytm 44 Chang ntropy ΔS ic Δ S watr ( ΔS ΔS ΔS olid ln mc watr mltg 5.78 kj/k mltg ( kg( 4.8 kj/kg olid liquid mh ig mltg ic 7 K ( 8 kg (. kj/kg K ln ( 4.8 kj/kg 68 K S ΔS watr ΔSic o K ln mc ln 7 K o.7 kj/kg 85.4 K 9.59 kj/k 9 K liquid 6.9 kj/k ic 85.4 K K ln 7 K h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X dtroyd dtroyd S (9 K(6.9 kj/k 85 kj WAER ton ic -5 C 8 kg

123 8-8-7 An vacuatd bottl i urroundd by atmophric air. A valv i opnd, and air i allowd to fill th bottl. h amount of hat tranfr through th wall of th bottl whn thrmal and mchanical quilibrium i tablihd and th amount of xrgy dtroyd ar to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc, but it can b analyzd a a uniform-flow proc c th tat of fluid at th lt rma contant. Air i an idal ga. Ktic and potntial nrgi ar ngligibl. 4 hr ar no work traction volvd. 5 h dirction of hat tranfr i to th air th bottl (will b vrifid. Proprti h ga contant of air i.87 kpa.m /kg.k (abl A-. Analyi W tak th bottl a th ytm, which i a control volum c ma cro th boundary. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc can b xprd a Ma balanc: m Δm m m (c m m Enrgy balanc: E m ytm i itial E 44 Nt nrgy tranfr by hat, work, and ma m h Combg th two balanc: whr m P V m R i i i ( u 9 K h i Chang trnal, ktic, potntial, tc.nrgi m u ΔEytm 44 (c W E ( kpa(. m (.87 kpa m /kg K( 9 K abl A-7 hi u E 9.6 kj/kg 6.9 kj/kg itial.44 kg k p Subtitutg, (.44 kg( kj/kg -. kj. kj Not that th ngativ ign for hat tranfr dicat that th aumd dirction i wrong. hrfor, w rvrd th dirction. h ntropy ratd durg thi proc i dtrmd by applyg th ntropy balanc on an xtndd ytm that clud th bottl and it immdiat urroundg o that th boundary tmpratur of th xtndd ytm i th tmpratur of th urroundg at all tim. h ntropy balanc for it can b xprd a S S 44 Nt ntropy tranfr by hat and ma S { Entropy ration Chang ntropy i i S ΔS tank m m b, m ΔSytm 44 hrfor, th total ntropy ratd durg thi proc i. kj S mi i m m ( i.45 kj/k b, b, urr 9 K h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X dtroyd dtroyd S (9 K(.45 kj/k. kj m L Evacuatd kpa 7 C

124 A hat ng oprat btwn two tank filld with air at diffrnt tmpratur. h maximum work that can b producd and th fal tmpratur of th tank ar to b dtrmd. Aumption Air i an idal ga with contant pcific hat at room tmpratur. Proprti h ga contant of air i.87 kpa.m /kg.k (abl A-. h contant volum pcific hat of air at room tmpratur i c v.78 kj/kg.k (abl A-. Analyi For maximum powr production, th ntropy ration mut b zro. W tak th two tank (th hat ourc and hat k and th hat ng a th ytm. Notg that th ytm volv no hat and ma tranfr and that th ntropy chang for cyclic dvic i zro, th ntropy balanc can b xprd a S S 44 Nt ntropy tranfr by hat and ma S S ΔS ytm 44 Entropy ration ΔS Chang ntropy ΔS tank,ourc tank,ourc ΔS ΔS tank,k tank,k ΔS hat ng AIR kg 9 K H mc v ln V mr ln V ourc mc v ln V mr ln V k HE W ln A B A B whr A and B ar th itial tmpratur of th ourc and th k, rpctivly, and i th common fal tmpratur. hrfor, th fal tmpratur of th tank for maximum powr production i AIR kg K L A (9 K( K 59.6 K B h nrgy balanc E E ΔE ytm for th ourc and k can b xprd a follow: Sourc: ourc, ΔU mc ( ourc, mc ( v A v A ourc, mc ( ( kg(.78 kj/kg K(9 59.6K 89 kj v A Sk: k, mcv ( B ( kg(.78 kj/kg K(59.6 K 47 kj hn th work producd thi ca bcom W max, H L ourc, k, kj hrfor, a maximum of 46 kj of work can b producd durg thi proc.

125 A hat ng oprat btwn two contant-prur cyldr filld with air at diffrnt tmpratur. h maximum work that can b producd and th fal tmpratur of th cyldr ar to b dtrmd. Aumption Air i an idal ga with contant pcific hat at room tmpratur. Proprti h ga contant of air i.87 kpa.m /kg.k (abl A-. h contant prur pcific hat of air at room tmpratur i c p.5 kj/kg.k (abl A-. Analyi For maximum powr production, th ntropy ration mut b zro. W tak th two cyldr (th hat ourc and hat k and th hat ng a th ytm. Notg that th ytm volv no hat and ma tranfr and that th ntropy chang for cyclic dvic i zro, th ntropy balanc can b xprd a S S 44 Nt ntropy tranfr by hat and ma S S ΔSytm 44 Entropy ration ΔS Chang ntropy ΔS cyldr,ourc cyldr,ourc ΔS ΔS cyldr,k cyldr,k ΔS hat ng AIR kg 9 K H mc p ln P mr ln P ourc mc p ln P mr ln P k HE W ln A B A B whr A and B ar th itial tmpratur of th ourc and th k, rpctivly, and i th common fal tmpratur. hrfor, th fal tmpratur of th tank for maximum powr production i AIR kg K L (9 K( K 59.6 K A B h nrgy balanc E E ΔE ytm for th ourc and k can b xprd a follow: Sourc: ourc, W b, ΔU ourc, ΔH mc p ( A ourc, mc ( ( kg(.5 kj/kg K(9 59.6K,469 kj p A Sk: k, W b, ΔU k, ΔH mc p ( A k, mc p ( B ( kg(.5 kj/kg K(59.6 K 66 kj hn th work producd bcom W max,, H L ourc, k, kj hrfor, a maximum of 4847 kj of work can b producd durg thi proc

126 A hat ng oprat btwn a nitro tank and an argon cyldr at diffrnt tmpratur. h maximum work that can b producd and th fal tmpratur ar to b dtrmd. Aumption Nitro and argon ar idal ga with contant pcific hat at room tmpratur. Proprti h contant volum pcific hat of nitro at room tmpratur i c v.74 kj/kg.k. h contant prur pcific hat of argon at room tmpratur i c p.5 kj/kg.k (abl A-. Analyi For maximum powr production, th ntropy ration mut b zro. W tak th tank, th cyldr (th hat ourc and th hat k and th hat ng a th ytm. Notg that th ytm volv no hat and ma tranfr and that th ntropy chang for cyclic dvic i zro, th ntropy balanc can b xprd a S S 44 Nt ntropy tranfr by hat and ma S S ΔSytm 44 Entropy ration Chang ntropy ΔS tank,ourc ΔS cyldr,k ΔS hat ng N kg K ( ΔS ourc ( ΔS k H V ln ln P mc ln ln v mr mc p mr HE V ourc P k Subtitutg, L ( kg(.74 kj / kg K ln ( kg(.5 kj / kg K ln K K Ar Solvg for yild kg K 7.8 K whr i th common fal tmpratur of th tank for maximum powr production. h nrgy balanc E E ΔE for th ourc and k can b xprd a follow: ytm W Sourc: ourc, ΔU mcv ( ourc, mcv ( A A ourc, mc ( ( kg(.74 kj/kg K( 7.8K 985 kj v A Sk: k, W b, ΔU k, ΔH mc p ( A k, mcv ( A hn th work producd bcom W max, ( kg(.5 kj/kg K(7.8 K 47 kj kj H L ourc, k, hrfor, a maximum of 79 kj of work can b producd durg thi proc

127 A rigid tank contag nitro i conidrd. Hat i now tranfrrd to th nitro from a rrvoir and nitro i allowd to cap until th ma of nitro bcom on-half of it itial ma. h chang th nitro' work potntial i to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc. Ktic and potntial nrgi ar ngligibl. hr ar no work traction volvd. 4 Nitro i an idal ga with contant pcific hat. Proprti h proprti of nitro at room tmpratur ar c p.9 kj/kg K, c v.74 kj/kg K, and R.968 kj/kg K (abl A-a. Analyi h itial and fal ma th tank ar m PV ( kpa(. m (.968 kpa m /kg K(9 K R m.5 kg m m h fal tmpratur th tank i.575 kg PV ( kpa(. m m R (.575 kg(.968 kpa m /kg K.5 kg 586 K Nitro L kpa C m W tak th tank a th ytm, which i a control volum c ma cro th boundary. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc for thi uniform-flow ytm can b xprd a Ma balanc: Enrgy balanc: m m Δmytm m m E E 44 Nt nrgy tranfr by hat, work, and ma mh Chang trnal, ktic, potntial, tc.nrgi mu m h ΔEytm 44 mu m u m u Ug th avrag of th itial and fal tmpratur for th xitg nitro,.5(.5(( K thi nrgy balanc quation bcom mh mu mu mc p mcv mcv (.575(.9(49.5 (.575(.74(586 (.5(.74(9 6.6 kj h work potntial aociatd with thi proc i qual to th xrgy dtroyd durg th proc. h xrgy dtruction durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X dtroyd S. h ntropy ration S thi ca i dtrmd from an ntropy balanc on th ytm:

128 8-8 S S 44 Nt ntropy tranfr by hat and ma R m S { Entropy ration S S ΔSytm 44 ΔS m Chang ntropy tank m m m m Notg that prur ar am, rarrangg and ubtitutg giv hn, S W rv m m c p m ln (.575(.9 ln(586 (.5(.9 ln(9 (.575(.9 ln( kj/k m m c p R ln m c p ln X S (9 K(.66kJ/K 78. kj dtroyd R R Altrnativ Mor Accurat Solution hi problm may alo b olvd by conidrg th variation of ga tmpratur at th lt of th tank. h ma and nrgy balanc ar dm m& dt d mu & ( h dt dm dt cvd( m c p dt dm dt Combg th xprion and rplacg th lat trm giv & c v d( m c p PV dm dt Rm dt Intgratg thi ovr th tim rquird to rla on-half th ma produc c p PV m cv ( m m ln R m h rducd combd firt and cond law bcom W& rv & d( U dt S dm ( h dt R whn th ma balanc i ubtitutd and th ntropy ration i t to zro (for maximum work production. Expandg th ytm tim drivativ giv

129 8-9 W& rv & R & R & R d( mu m dm ( h dt dt d( mu d dm dm m ( h dt dt dt dt d( mu h dt dm dt m dh dt Subtitutg & from th firt law, d mu dm d mu dm W& ( ( rv h h m dt dt R dt dt d( mu dm dh h m R dt dt dt d( m dm d cv c p mc p R dt dt dt At any tim, PV mr which furthr rduc thi rult to W& rv R c p PV dm mr dt c p m d dt R dp P dt Whn thi tgratd ovr th tim to complt th proc, th rult i W rv R 69.4 kj c p PV m ln R m 9 (.9(( dh dt c p PV R (.9((. ln (

130 8-8- A rigid tank contag nitro i conidrd. Nitro i allowd to cap until th ma of nitro bcom on-half of it itial ma. h chang th nitro' work potntial i to b dtrmd. Aumption hi i an untady proc c th condition with th dvic ar changg durg th proc. Ktic and potntial nrgi ar ngligibl. hr ar no work traction volvd. 4 Nitro i an idal ga with contant pcific hat. Proprti h proprti of nitro at room tmpratur ar c p.9 kj/kg K, c v.74 kj/kg K, k.4, and R.968 kj/kg K (abl A-a. Analyi h itial and fal ma th tank ar m PV ( kpa(. m (.968 kpa m /kg K(9 K R m.5 kg m m.575 kg.5 kg W tak th tank a th ytm, which i a control volum c ma cro th boundary. Notg that th microcopic nrgi of flowg and nonflowg fluid ar rprntd by nthalpy h and trnal nrgy u, rpctivly, th ma and nrgy balanc for thi uniform-flow ytm can b xprd a Ma balanc: Enrgy balanc: m m Δmytm m m E E 44 Nt nrgy tranfr by hat, work, and ma m h Chang trnal, ktic, potntial, tc.nrgi m u ΔEytm 44 m u Ug th avrag of th itial and fal tmpratur for th xitg nitro, thi nrgy balanc quation bcom m h m c m u v v (.575(.9(.5(9 (.575(.74 Solvg for th fal tmpratur, w gt 4. K h fal prur th tank i p m c m u m c m R (.575 kg(.968 kpa m /kg K(4. K P V. m h avrag tmpratur and prur for th xitg nitro i.5(.5( K P.5(.5( kpa (.5(.74(9 8.8 kpa Nitro L kpa C h work potntial aociatd with thi proc i qual to th xrgy dtroyd durg th proc. h xrgy dtruction durg a proc can b dtrmd from an xrgy balanc or dirctly from it m

131 8- dfition X S. h ntropy ration S thi ca i dtrmd from an ntropy dtroyd balanc on th ytm: S S 44 Nt ntropy tranfr by hat and ma m S { Entropy ration S S Rarrangg and ubtitutg giv ΔSytm 44 ΔS m Chang ntropy tank m m m m hn, S W rv m m m m ( c ln R ln P m ( c ln R ln P m ( c p [ (.968 ln(8.8 ] (.5[.9 ln(9 (.968 ln( ] [ (.968 ln(69.4 ] ( ln(4. ( ln( kj/k p p ln X S (9 K(.75 kj/k. kj dtroyd R ln P h ntropy ration cannot b ngativ for a thrmodynamically poibl proc. hi rult i probably du to ug avrag tmpratur and prur valu for th xitg ga and ug contant pcific hat for nitro. hi nitivity occur bcau th ntropy ration i vry mall thi proc. Altrnativ Mor Accurat Solution hi problm may alo b olvd by conidrg th variation of ga tmpratur and prur at th lt of th tank. h ma balanc thi ca i & m dm dt which whn combd with th rducd firt law giv d( mu dm h dt dt Ug th pcific hat and th idal ga quation of tat rduc thi to V dp dm cv c p R dt dt which upon rarrangmnt and an additional u of idal ga quation of tat bcom dp c p dm P dt c m dt Whn thi i tgratd, th rult i P v k.4 m P m h fal tmpratur i thn 78.9 kpa

132 8- PV (78.9 kpa(. m m R (.575 kg(.968 kpa m /kg K h proc i thn on of m k. K m k cont P or cont h rducd combd firt and cond law bcom d U S dm W & ( rv ( h dt dt whn th ma balanc i ubtitutd and th ntropy ration i t to zro (for maximum work production. Rplacg th nthalpy trm with th firt law rult and canclg th common du/dt trm rduc thi to d m dm W& ( rv dt dt Expandg th firt drivativ and canclg th common trm furthr rduc thi to d W& rv m dt k k Lttg a P / m and / b m, th prur and tmpratur of th nitro th ytm ar rlatd to th ma by k P am and bm accordg to th firt law. hn, k k k dp akm dm and d b( k m dm h ntropy chang rlation thn bcom d dp dm d c p R [( k c p Rk] P m Now, multiplyg th combd firt and cond law by dt and tgratg th rult giv W rv md md[ ( k c p Rk] [( k c Rk] ( m m p (9.5 kj [(.4 (.9 (.968(.4] dm ( Onc aga th ntropy ration i ngativ, which cannot b th ca for a thrmodynamically poibl proc. hi i probably du to ug contant pcific hat for nitro. hi nitivity occur bcau th ntropy ration i vry mall thi proc.

133 8-8- A ytm conitg of a compror, a torag tank, and a turb a hown th figur i conidrd. h chang th xrgy of th air th tank and th work rquird to compr th air a th tank wa bg filld ar to b dtrmd. Aumption Chang th ktic and potntial nrgi ar ngligibl. 4 Air i an idal ga with contant pcific hat. Proprti h proprti of air at room tmpratur ar R.87 kpa m /kg K, c p.5 kj/kg K, c v.78 kj/kg K, k.4 (abl A-a. Analyi h itial ma of air th tank i 5 ( 6 PitialV kpa(5 m mitial.5946 R (.87 kpa m /kg K(9 K itial and th fal ma th tank i 5 ( 6 PfalV 6 kpa(5 m mfal.568 R (.87 kpa m /kg K(9 K fal Sc th compror oprat a an intropic dvic, P P ( k / k h conrvation of ma applid to th tank giv dm m & dt whil th firt law giv d mu dm & ( h dt dt Employg th idal ga quation of tat and ug contant pcific hat, xpand thi rult to c dp dp & V V v c p R dt R dt Ug th tmpratur rlation acro th compror and multiplyg by dt put thi rult th form dt & ( k / k V v c R P dp c p P V dp R Whn thi tgratd, it yild (i and f tand for itial and fal tat Vc v R ( P 5 (5 (.78.4 (.5(5 (6.87 ( f k c pv Pf P i Pf k R Pi 8 kj ( k / k P i 5 kg kg /.4 h ngativ rult how that hat i tranfrrd from th tank. Applyg th firt law to th tank and compror giv

134 8-4 ( & W & dt d( mu h dm which tgrat to W ( m f u f i i m u h ( m f m i Upon rarrangmnt, W ( c p c v ( m 8 kj f m i (.5.78(9[( ] h ngativ ign how that work i don on th compror. Whn th combd firt and cond law i rducd to fit th compror and tank ytm and th ma balanc corporatd, th rult i W& rv & d( U dt S dm ( h dt R which whn tgratd ovr th proc bcom W rv mi i i f f f R [(.78.59] [(.78.59] ( (.87 ln [( u h ( ] m [( u h ( ] kj hi i th xrgy chang of th air tord th tank. 6

135 h air tord th tank of th ytm hown th figur i rlad through th intropic turb. h work producd and th chang th xrgy of th air th tank ar to b dtrmd. Aumption Chang th ktic and potntial nrgi ar ngligibl. 4 Air i an idal ga with contant pcific hat. Proprti h proprti of air at room tmpratur ar R.87 kpa m /kg K, c p.5 kj/kg K, c v.78 kj/kg K, k.4 (abl A-a. Analyi h itial ma of air th tank i 5 ( 6 PitialV 6 kpa(5 m mitial.568 R (.87 kpa m /kg K(9 K itial and th fal ma th tank i 5 ( 6 PfalV kpa(5 m mfal.5946 R (.87 kpa m /kg K(9 K fal h conrvation of ma i dm m & dt whil th firt law giv d mu dm & ( h dt dt Employg th idal ga quation of tat and ug contant pcific hat, xpand thi rult to c dp & V v V c p R dt R cv c p dp V R dt dp V dt dp dt Whn thi i tgratd ovr th proc, th rult i (i and f tand for itial and fal tat V ( P f P 5 ( 6.5 i Applyg th firt law to th tank and compror giv & W& dt d( mu hdm ( which tgrat to 5 8 kj kg kg

136 8-6 kj (.5(9(.568 (.5(9 (.568 (.78(9 ( ( ( ( ( ( f i p p i v f f i i i f f f i i i f f f i i i f f m m c m c c m m m h m u u m W m m h m u u m W m m h m u u m W hi i th work put from th turb. Whn th combd firt and cond law i rducd to fit th turb and tank ytm and th ma balanc corporatd, th rult i ( ( ( ( ( ( ( ( rv i f v p R v p R R R P P dt dm c c dt d m dt dm c c dt dm h dt u d m dt dm u dt dm h dt S U d W V & & & & & whr th lat tp u ntropy chang quation. Whn thi i tgratd ovr th proc it bcom kj rv ( (9(.5946 ( ( ( ( i f i f v p R P P m m c c W V hi i th xrgy chang of th air th torag tank.

137 A hat ng oprat btwn a tank and a cyldr filld with air at diffrnt tmpratur. h maximum work that can b producd and th fal tmpratur ar to b dtrmd. Aumption Air i an idal ga with contant pcific hat at room tmpratur. Proprti h pcific hat of air ar c v.78 kj/kg.k and c p.5 kj/kg.k (abl A-. Analyi For maximum powr production, th ntropy ration mut b zro. W tak th tank, th cyldr (th hat ourc and th hat k and th hat ng a th ytm. Notg that th ytm volv no hat and ma tranfr and that th ntropy chang for cyclic dvic i zro, th ntropy balanc can b xprd a S S 44 Nt ntropy tranfr by hat and ma S S ΔSytm 44 Entropy ration Chang ntropy ΔS ( ΔS tank,ourc ourc ΔS ( ΔS k cyldr,k ΔS hat ng Air kg 8 K H mc ln v V mr ln V ourc mc p ln P mr ln P k HE W ln A c c p v ln B A B k k /( k ( whr A and B ar th itial tmpratur of th ourc and th k, rpctivly, and i th common fal tmpratur. hrfor, th fal tmpratur of th tank for maximum powr production i (.4 (8 K( K K Sourc: ΔU mc 4 ourc, v A B ( A ourc, mc ( A v Air kg 9 K L ourc, mc ( ( kg(.78 kj/kg K(8 44.6K 5 kj v A Sk: k, W b, ΔU k, ΔH mc p ( A k, mcv ( A hn th work producd bcom W max, ( kg(.5 kj/kg K(44.6 9K 68 kj kj H L ourc, k, hrfor, a maximum of 64 kj of work can b producd durg thi proc.

138 Ug an compribl ubtanc a an xampl, it i to b dmontratd if clod ytm and flow xrgi can b ngativ. Analyi h availability of a clod ytm cannot b ngativ. Howvr, th flow availability can b ngativ at low prur. A clod ytm ha zro availability at dad tat, and poitiv availability at any othr tat c w can alway produc work whn thr i a prur or tmpratur diffrntial. o that th flow availability can b ngativ, conidr an compribl ubtanc. h flow availability can b writtn a ψ h h ( ( u u v( P P ( ξ v( PP h clod ytm availability ξ i alway poitiv or zro, and th flow availability can b ngativ whn P << P. 8-7 A rlation for th cond-law fficincy of a hat ng opratg btwn a hat ourc and a hat k at pcifid tmpratur i to b obtad. Analyi h cond-law fficincy i dfd a th ratio of th availability rcovrd to availability upplid durg a proc. h work W producd i th availability rcovrd. h dcra th availability of th hat upplid H i th availability upplid or vtd. hrfor, W η II H ( H W H L Not that th firt trm th dnomator i th availability of hat upplid to th hat ng whra th cond trm i th availability of th hat rjctd by th hat ng. h diffrnc btwn th two i th availability conumd durg th proc. Sourc H HE L Sk H L W

139 E Larg bra plat ar hatd an ovn at a rat of /m. h rat of hat tranfr to th plat th ovn and th rat of xrgy dtruction aociatd with thi hat tranfr proc ar to b dtrmd. Aumption h thrmal proprti of th plat ar contant. h chang ktic and potntial nrgi ar ngligibl. h nvironmnt tmpratur i 75 F. Proprti h dnity and pcific hat of th bra ar givn to b ρ 5.5 lbm/ft and c p.9 Btu/lbm. F. Analyi W tak th plat to b th ytm. h nrgy balanc for thi clod ytm can b xprd a E E 44 Nt nrgy tranfr by hat, work, and ma Chang trnal, ktic, potntial, tc.nrgi ΔU ΔEytm 44 plat m( u u mc( h ma of ach plat and th amount of hat tranfr to ach plat i m ρv ρla (5.5 lbm/ft [(. / ft( ft( ft] lbm mc( ( lbm/plat(.9 Btu/lbm. F( 75 F 7,9 Btu/plat hn th total rat of hat tranfr to th plat bcom & total n& ( plat/m (7,9 Btu/plat 5,79, Btu/m 89,65 Btu/ plat, pr plat W aga tak a gl plat a th ytm. h ntropy ratd durg thi proc can b dtrmd by applyg an ntropy balanc on an xtndd ytm that clud th plat and it immdiat urroundg o that th boundary tmpratur of th xtndd ytm i at F at all tim: whr S S 44 Nt ntropy tranfr by hat and ma b S { Entropy ration S ΔSytm 44 Chang ntropy ΔS ytm S b ΔS ( 46 R ΔSytm m( mcavg ln ( lbm(.9 Btu/lbm.R ln 9.46 Btu/R (75 46 R Subtitutg, ytm 7,9 Btu S ΔSytm 9.46 Btu/R 9.7 Btu/R 46 R b hn th rat of ntropy ration bcom S & S n& ball (pr plat (9.7 Btu/R plat( plat/m 78 Btu/m.R 46.5 Btu/.R h xrgy dtroyd durg a proc can b dtrmd from an xrgy balanc or dirctly from it dfition X S, X & dtroyd S& dtroyd (55 R(46.5 Btu/.R 4,797 Btu/