e Send Law ilie: ) Heat Engine η W in H H L H L H, H H ) Ablute eerature H H L L Sale, L L W ) Fr a yle H H L L H 4) Fr an Ideal Ga Cyle H H L L L
δ reerible ree d
Claiu Inequality δ eerible Cyle fr a l l l l l l δ δ fr an Irreerible Cyle l l l l l l
Entry Definitin and Cange δ Claiu Inequality fr a yle ed f a reerible and an irreerible re δ δ S S irre DEFINE A POPEY, d irre irre irre d δ δ δ δ d irre d, re δ δ d S S, re ENOPY δ reerible irreerible
tal Entry Cange, S, fr an ilated yte Fr reerible yte, S Fr irreerile yte, S >
Liquid water enter an en feel water eater at.8 MPa and 5 C and tea enter at.8 MPa and 5 C. e leaing trea i aturated liquid at reure f.8 MPa. Deterine te rati ff te a flw rate f te water and tea. Deterine te rate at wi entry i rdued in te feed water eater.
@ tate int 7.87 6. 46.64 6. g S.896, S.94 Ma ( ) ( ) (.457 7.47).896(.457.55) S -.5.47 S.58 J/g K Balane Energy Balane PS5..94,.8 MPa 5 C.5 @ 5 C 46.64 J/g f f @ 5 C.55 J/g K.8 MPa, 5 C 6. 7.47.8 MPa 7.87 J/g f f @.8 MPa @.8 MPa.457 J/gK S.58 J/g K S, ( ).5.47
Cletely eerible Pre - Syte and urrunding returned t te riginal tate Internally eerible - Syte returned t te riginal tate. Externally eerible - Surrunding returned t te riginal tate.
eerature Entry Prerty Diagra d δ d nt W net in ut ( ) H L
eerature Entry Prerty Diagra Water
Entry Cange f an Ideal Ga d d d d d and d d Fr an idealga, d d d d - d d d d d d d d du d Subtituting int d d d du d d du d u fr definitin, d d d and d du Fr an idealga: d du d d du d SendLaw d δq Firt Law δw du δq
5) (7 V V @ V @ V (7-49) @ P @ P ntant,, Ientri re, r r r r
Oxygen at.8 ubi eter/g and 5 C i reed in a itn ylinder t. ubi eter/g and 87 C. Wat i te entry ange f te xygen? 87 C 5 C. /g.8 /g J.69 g K J.5 g K 7.5 K 87 7.5 K 5 C.59 C J g K. /g.8 /g 6-6
6- @ P Pa, C Cled, led tea radiatr @ 8 x S S f.8 g 7.566 J/g.9 g, f V S S fg C f x.8.9.47.9 fg.85 g ( ).85(.475 7.566) J.86 K.47 g.75.7 6.569 g 8 C.7 C Pa Vntant ntant
Stea at C and Pa ndene in a liter led radiatr wit bt te inlet and exit ale led t a teerature f 8 C.Deterine te entry ange f te tea. Cled, led tea radiatr C Pa Vnt @ P Pa, C.8 g 7.566 J/g @ 8 C f.9 g, g.47 g V V f.8.9 x.7 fg.47.9 x.75.7 6.569 f fg 8 C V..8 / g S S S S.85 J S S.86 K.85 ( ) (.475 7.566) g 6-
( ) ( ) ( ) ( ) i al ntant entry ntant adiabati re, ubtitute fr ntant n Ientri Adiabati Pre IdealGa Ientri, Adiabati ntant ntant integrating d _ d d d d d d d d d, ga an ideal fr d d δw du δ Adiabati re Law Firt δw du δ
U W Firt Law d du dw d ds dw dv ubitiuting, d du d u rerty definitin, i an exat differential d du d d ubitiuting, d d du d fr d d d Send Law Bundary Wr u rerty definitin d d d d d d w Exale: water ued fr ia t ia ( ) ( ia 5ia) 44f/i w 6.4lb/ft lbf 59 ft ft lbf w 69., (ft f fluid) lb 6.4 lb ft ft ft lbf BU w 69. 69.BU/lb lb 778 ft lb w.888 BU/lb Exale: water ued fr Pa t Pa w ( ) w.4 w.86 g ( ) Pa, f J/g
Exanin Pre η η η Atual Wr Ientri Wr w w a a
@Pa η W η ( W.9 g/e f tea exand in an 9 % effiient turbine fr 8 MPa, 5 C t Pa. Deterine te exit teerature and wer f te turbine. f 89..847 6. 67.9J/g W W x x ( 98. 67.9) W 98. 7.4 8.9 atural reereible i le tan aturatin fg ) g fg g 6.74.949 6.847 @ Pa (. bar) @ Pa (. bar).847 7.4J/g tw ae Pt 5 C 69. C Pwer W g/e 7.4J/g 5KW 8 MPa Pa Pa 98. 67.9 8.9 6.74 6.74 6-95
Wat i te wr dne by g/e f nitrgen exanded fr 9 Pa, 5 C t Pa at an 85% effiieny. 9 Pa 5 C W W atual atual ( 5 7)(.58) ientri i.857 i 9 i O i 7.4 K Watual η.85 W.85 g/e.9 99. J O ( K 7.4 K) i Pa
Crein Pre η η η Ientri Wr Atual Wr W W a a
. ubi eter/e f -4a i reed at 8% effiieny fr aturated ar at Pa t Ma. Wat i te diarge teerature and wr? @ Pa,.6.86J/g g g g.64 /g V./6.g/e.64 @MPa Pt 6 57.7 5 i 4.954J/g 9.6 88.9 8.9 77.84 68.68 K C.948.954.966 i a) b) i MPa Pa 77.84 by interlatin i η.8 (i ) /.8.86 (77.84.86)/.8 88.9J/g O 57.7 C by interlatin W ( ) W. g/e W.7J/e.7KW ( 88.9.86) 6-
( ) ( ) F 94 654..85 5 6.9 η 6.9.9 5 5 at 85% effiieny. t ia F 6 Air reed fr5 ia, O.857 O ia, 6 F ia 85% η
W Exanin Pre a a a a V V η V V fr V V H V H SteadyFlwEnergyEquatin
AI ABLE - able A-7, A-7E ( ) ( ) r r r r r r ) ( ) ( ) ( ) ( b) C F, able bae 4) (6 d d d u d eat eifi ariable a)
@ @ Air underge an adiabati, ientri exanin fr 9 Ka, K t Pa. @ r teerature ideal ga alue,.5,.4, able A 7 r r r r K,.4.6 ariable 4., @ ( ) K ntant alue, r ( ) 9 eifi 9 4.667 9 r.6.6 r.4.4.667, 5.8 575.5 eat 5.7 56 K K K able A -7.86 56. Pa Uing Ideal Ga Law r r r r.78 /g 56,.66 /g 9 Pa Pa.66 /g r 7. 647.9. 7. (.% differene).9 /g.86. 9Pa
6-4 Stea at 8 ia and 9 F enter an adiabati turbine and leae at 4 ia. Wat i te axiu aunt f wr tat te turbine an delier? 456, BU/lb O.64 BU/ lb @.64 and 4 ia f.64.94 x.97 fg.845 f x fg 6.4.97 9.69 4.7 BU/lb W 456, 4.7. ax 8 ia 9 F BU/lb 4 ia
658.8 BU/lb 7.69 7.69 7.69.9 x x.948 6.59 x f 4.54.948 4.7 495.6 Btu/lb @ 5 Pa, C 68.4 Btu/lb 7.6954 V V W V V W - 8 8 J/e 658.8 68.4 8 J/e S ( - ) W W η ientri ientri W W fg 4 ( 875.9.) 8. g 8.g ( 7.695-7.69) 5.765 J/ K 8. g 955 KW 8 8.8% 955 atual ientri 6-97 e wer utut f an adiabati turbine i 8 MW. Stea enter te turbine at 6 C, 6 MPa and 8 /e. Stea leae te turbine at 5 Pa, C and 4 /e. Deterine a) te turbine tea a flw rate, b) te ientri effiieny f te turbine. ) te entry ange in te exanin re ( 658.8 494.97.) 6 Ma 6 C 8 /e tea 5 Pa C 4 /e
6-7 Cnider te effet f arying te ientri effiieny f an adiabati nzzle fr 8% t % n te nzzle exit teerature and reure. Inlet nditin and te exit elity are eld ntant. Air enter te nzzle at 6 ia, F and a lw elity. Air leae te nzzle at wit a elity f 8 ft.e. Fr ηnzzle 9% O @ 48, r 5.4, 6.89 BU/lb V V V V 8 BU/lb 6.89 (778.)ft /e 5. BU/lb atual exit entaly O @ 5. BU/lb ablea 7E 4. η ( )/.9 6.89 ( 6.89 5. )/.9 49.68 BU/lb ablea 7E @ 49.68 BU/lb, Pr 46.4 r r r 46.4 6 ia 5. ia r 5.4 will ary wit effiieny. 6 ia F air 8 ft/e
arie wit effiieny η. 5. r 46.694 5.8.9 49.7 46.4 5..8 47.9 45.6 5.4 η
6-55 Stea enter a tw-tage adiabati turbine at a flw rate f 5 g/e, a reure f 7MPa and a teerature f 5 C. After te firt tage at a reure f MPa % f te tea i extrated t be ued in a eating re. Stea leae te end tage f te turbine at 5 Pa. Deterine te wer ut ut f te turbine fr an ientri exanin in bt tage and fr an ientri effiieny f 88% in bt tage. Pt 5 7MPa 4.4 6.8 MPa 6.8 5 Pa 6.8 MPa 5 Pa @MPa 5 94. 6.965 879.4 6.8 87.9 6.6957 6.8-6.6956 rati.45 6.965-6.6956 88. @ 5 Pa 6.8-.9 x.878 6.59 4.54.878 4.7 64.7 J/g a) b) tea ( ). ( ) Wientri.9 Wientri.9. 5 Wientri 5,54 KW Watual η.88 Wientri W.88 5,54 KW,47 KW atual 5 ( 4.4 64.7) ( 4.4 88. )
Kelin Plan Stateent f te Send Law SECOND LAW OF HEMODYNAMICS It i iible t ntrut an engine wi, erating in a yle,will rdue n ter effet tan te extratin f eat fr a ingle eat reerir and te erfrane f a equialent aunt f wr. Clauiu Stateent f te Send Law It i iible t ae a yte erating in a yle wi tranfer eat fr a ler t a tter bdy witut wr being dne n te yte by te urrunding. Fr a eerible Pre reerible re irreerib le re d d ENOPY ( S S) S reerible re d Fr an Irreerible re ( S S) Fr an ideal ga