The Second Law implies:

Transcription

1 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

2 δ reerible ree d

3 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

4 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

5 tal Entry Cange, S, fr an ilated yte Fr reerible yte, S Fr irreerile yte, S >

6 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.

7 @ tate int g S.896, S.94 Ma ( ) ( ) ( ).896( ) S S.58 J/g K Balane Energy Balane PS5..94,.8 MPa 5 5 C J/g f 5 C.55 J/g K.8 MPa, 5 C MPa 7.87 J/g f MPa.457 J/gK S.58 J/g K S, ( ).5.47

8 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.

9 eerature Entry Prerty Diagra d δ d nt W net in ut ( ) H L

10 eerature Entry Prerty Diagra Water

11 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

12 5) (7 V V P ntant,, Ientri re, r r r r

13 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 K 5 C.59 C J g K. /g.8 /g 6-6

14 P Pa, C Cled, led tea 8 x S S f.8 g J/g.9 g, f V S S fg C f x fg.85 g ( ).85( ) J.86 K.47 g g 8 C.7 C Pa Vntant ntant

15 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 P Pa, C.8 g C f.9 g, g.47 g V V f.8.9 x.7 fg.47.9 x f fg 8 C V..8 / g S S S S.85 J S S.86 K.85 ( ) ( ) g 6-

16 ( ) ( ) ( ) ( ) 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

17 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 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

18 Exanin Pre η η η Atual Wr Ientri Wr w w a a

19 @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 J/g W W x x ( ) W atural reereible i le tan aturatin fg ) g fg g Pa (. Pa (. bar) J/g tw ae Pt 5 C 69. C Pwer W g/e 7.4J/g 5KW 8 MPa Pa Pa

20 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 J O ( K 7.4 K) i Pa

21 Crein Pre η η η Ientri Wr Atual Wr W W a a

22 . ubi eter/e f -4a i reed at 8% effiieny fr aturated ar at Pa t Ma. Wat i te diarge teerature and Pa,.6.86J/g g g g.64 /g Pt i 4.954J/g K C i a) b) i MPa Pa by interlatin i η.8 (i ) /.8.86 ( )/ J/g O 57.7 C by interlatin W ( ) W. g/e W.7J/e.7KW ( ) 6-

23 ( ) ( ) F η at 85% effiieny. t ia F 6 Air reed fr5 ia, O.857 O ia, 6 F ia 85% η

24 W Exanin Pre a a a a V V η V V fr V V H V H SteadyFlwEnergyEquatin

25 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)

26 Air underge an adiabati, ientri exanin fr 9 Ka, K t r teerature ideal ga alue,.5,.4, able A 7 r r r r K,.4.6 ariable ( ) K ntant alue, r ( ) 9 eifi r.6.6 r , eat K K K able A Pa Uing Ideal Ga Law r r r r.78 /g 56,.66 /g 9 Pa Pa.66 /g r (.% differene).9 /g.86. 9Pa

27 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/ and 4 ia f x.97 fg.845 f x fg BU/lb W 456, 4.7. ax 8 ia 9 F BU/lb 4 ia

28 658.8 BU/lb x x x f Pa, C 68.4 Btu/lb V V W V V W J/e J/e S ( - ) W W η ientri ientri W W fg 4 ( ) 8. g 8.g ( ) 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 ( ) 6 Ma 6 C 8 /e tea 5 Pa C 4 /e

29 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% 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 5. BU/lb ablea 7E 4. η ( )/ ( )/ BU/lb ablea BU/lb, Pr 46.4 r r r ia 5. ia r 5.4 will ary wit effiieny. 6 ia F air 8 ft/e

30 arie wit effiieny η. 5. r η

31 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 MPa Pa 6.8 MPa rati Pa x 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 ( ) ( )

32 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