Summary of heat engines so far
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1 ummary of ea engines so far - ermodynami sysem in a proess onneing sae o sae - In is proess, e sysem an do ork and emi/absorb ea - Wa proesses maximize ork done by e sysem? - We ave proven a reversible proesses (proesses a do no ange e oal enropy of e sysem and is environmen) maximize ork done by e sysem in e proess Reversible Hea oure Q RH Rev Work oure Proess of e sysem -dynami sysem Noes
2 Cyli Engine -o oninuously generae ork, a ea engine sould go roug a yli proess. - u an engine needs o ave a ea soure and a ea sink a differen emperaures. - e ne resul of ea yle is o exra ea from e ea soure and disribue i beeen e ea ransferred o e sink and useful ork. Hea soure Q Q Rev Work oure Hea sink Working body e. g. rubber band Noes
3 Carno yle s an example, e ill onsider a pariular yle onsising of o isoerms and o adiabas alled e Carno yle applied o a rubber band engine. s e ill see, Carno yle is reversible Hea soure Q Q Hea sink Here and are emperaure and enropy of e orking body Rev Work oure Working body e. g. rubber band D C Noes
4 . Carno Cyle: Isoermal Conraion () U () Q soure L L Hea soure Hea soure ForeΓ Q soure ( L L ) ( L L ) L L D C Noes
5 . Carno Cyle: diabai Conraion () (C) L Q L C Quasi-sai adiabai proess C U C U U C L ( ) D C Noes
6 3. Carno Cyle: Isoermal Expansion (C) U (D) L C Q sink Hea sink LD Hea sink C D Q sink ( L L ) ( L L ) C D L L D C Noes
7 4. Carno Cyle: diabai Expansion (D) () L Q L D U D U D U L ( ) D C Noes
8 oal ork done in one yle: Carno Cyle: ummary Qsoure + Qsink + L ere ( ) + L ( ) Qsoure + Qsink Q soure ( L L ) ( L L ) L L Q sink ( L L ) ( L L ) C D L L Carno engine is reversible beause ea of e four pars of e yle is reversible! Exerise: so a adiabai expansion of a rubber band ere all inernal energy goes ino ork is a reversible proess. Noe a sponaneous adiabai onraion (non-quasisai) ere inernal energy does no ange is irreversible! Noes
9 Hea Engine Effiieny Effiieny an be defined for a yli engine Effiieny of a yli engine is defined as e raio of e ne ork done in a yle o e ne amoun of ea exraed from e o body in one yle ε Q soure For Carno engine: Q soure Q Exerise: so a is is orre ( L L ) ( L L ) ( L L ) ( L L ) sink + Qsoure D C Noe a sine all reversible engines do e same ork (maximum), ey ave e same effiieny (e. g. same as Carno engine). Noes
10 Hea Engine Effiieny ere is a simpler ay o alulae Carno engine effiieny using e (,) plo of e Carno yle. Q soure + Q sink ine Q ( ) Q soure soure ( ) We obain ( ) ε Q D C ( ) soure Noes
11 Engine, refrigeraor, ea pump Hea engine an run in dire and reverse yles. If i runs in e reverse yle, ork is done o ransfer ea from e old o e o sysem (refrigeraor, ea pump). Hea soure Engine Hea sink Refrigeraor or ea pump Hea soure Hea sink δq δq δq δq δw δw Rev Work oure Rev Work oure Noes
12 Real versus Ideal Engines Compleely reversible engines are impossible o realize due o friion and oer loss meanisms. Even if su engines ere realizable, ey ould generae very lile poer sine ey ave o employ very slo quasi-sai proesses in order o be reversible. e reason y reversible engines are slo is beause ey employ ea ransfer beeen bodies of e same emperaure. ine ea flo is proporional o e gradien of emperaure (non-equilibrium ermodynamis resul), e flo of ea in e reversible engine as o be infiniely slo. Real engines are alays irreversible and us ave loer effiieny ompared o e reversible engines. Noes
13 Carno Cyle: Isoermal Conraion a very slo proess () () Q soure L L Hea soure Hea soure ForeΓ Q soure ( L L ) ( L L ) L L Noes
14 Endoreversible Engine o ransfer ea fas in real engines, e need o employ irreversible proesses. n example of su an engine is endoreversible engine. For endoreversible Carno engine, e isoermal proesses are done a a emperaures and a are iger an e emperaure of e ea sink bu loer an e emperaure of e ea soure. ine for bo isoermal proesses, e emperaure differene beeen e ea soure/sink and e orking body of e engine is non-zero, e isoermal ea ransfer proesses are no infiniely slo. Noes
15 Endoreversible Engine For endoreversible Carno engine, e isoermal proesses are done a a emperaures and a are iger an e emperaure of e ea sink bu loer an e emperaure of e ea soure. Rubber band is a ere > > > Rubber band is a ere D C and C D are irreversible no ile C and D are sill reversible Noes
16 Endoreversible Engine nalysis Non equilibrium ermodynamis resuls for ea flo rae: Q ( ) ere is ea onduiviy From is equaion e an alulae ime of e isoermal proesses of e endoreversible engine soure sink Qsoure ( ) Qsink ( ) yle soure + sink - ime of isoermal proess in ona i ea soure - ime of isoermal proess in ona i ea sink eause adiabai proesses an be very fas Noes
17 Endoreversible Engine nalysis W yle + ( ) ( ) sink soure yle Q Q + C D Q soure Q k sin ( ) W W Q soure W Q k sin Noes
18 + yle W P o find maximum poer delivered, e need o maximize P i respe o and P P + + ere Maximum Endoreversible Engine Poer Exerise: so is Noes
19 Maximum Endoreversible Engine Poer ubsiuing ino + yle W P e obain e maximum poer delivered by endoreversible engine max + yle W P Noes
20 Endoreversible Engine Effiieny Endoreversible engine effiieny a max poer: ε W Q soure ubsiuing D C + + We obain: ε No o is expression does no depend on e values of ermal onduiviies! Noes
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