Chapter 11: Thermodynamics

Transcription

1 Captr 11: Trmodynamis Answrs and Solutions 1. Pitur t Problm: Tis is a follow-up qustion to Guidd Exampl Jogging along t ba on day, you do J of work and dras your trmal nrgy by J. You ar doing work on t nvironmnt, so W is positiv, but at is laving your body, maning Q is ngativ. Stratgy: T signs of W and Q av bn dtrmind abov, and t ang in trmal nrgy is givn in t qustion statmnt. Us t first law of trmodynamis to find t magnitud of t at mittd wil running. Solution: Calulat Q: Δ E = Q W Q =Δ E+ W = + ( J) ( J) = = = J 70 kj 88 kal Insigt: Noti t importan of using t orrt signs for Q, W, and Δ E. Wn t propr signs ar usd, t first law is simply a way of kping trak of all t nrgy xangs tat our in a systm. 2. Pitur t Problm: A swimmr dos work and givs off at during a workout. Stratgy: Baus t swimmr is doing work on t nvironmnt, W is positiv, but at is laving r body, maning Q is ngativ. Us t first law of trmodynamis to find t ang in trmal nrgy. Solution: 1. Find t ang in trmal nrgy: 2. T work don is positiv: Δ E = Q W = = 5 W = J J J J 5. T at mittd is ngativ: Q = J Insigt: T loss of trmal nrgy Δ E amounts to 600 kj or 14 kal, t sam as 14 nutritional aloris. T swimmr as burnd off t about numbr of aloris in a andy bar!. Pitur t Problm: Trmodynami systms ang tir intrnal nrgy wn at flows and wn work is don. Stratgy: Us t first law of trmodynamis to find t ang in intrnal nrgy for a systm. Solution: 1. (a) Calulat Δ E : Δ E a a = Q W = 50 J 50 J = 0 J 2. (b) Calulat E : B. () Calulat E : Δ E Q W ( ) Δ b = = 50 J 50 J = 0 J Δ E Q W ( ) Δ = = 50 J 50 J = 100 J Insigt: In part () 50 J of at nrgy flows out of t systm, and t systm dos work on t xtrnal world, rmoving an additional 50 J of nrgy from t systm. T nt fft is 100 J of nrgy is rmovd from t systm. 4. Pitur t Problm: Tis is a follow-up qustion to Guidd Exampl A at ngin prforms 1250 J of work and givs off 5250 J of at to t old rsrvoir. Stratgy: Find t amount of nrgy drawn from t ot rsrvoir by using t quation W = Q Q. Tn apply t dfinition of ffiiny of an ngin, = W Q. Solution: 1. Rarrang t quation for nrgy onsrvation and solv for Q : 2. Calulat t ffiiny: W = Q Q Q = W + Q = 1250 J J = 6500 J W 1250 J = = = = 19.2% Q 6500 J Insigt: Noti tat wn t ffiiny of a at ngin is lss tan on-alf (50%), as in tis as, t amount of at givn off as wast to t old rsrvoir (5250 J) is mor tan t amount of at onvrtd to work (1250 J). Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr. 11 1

2 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 5. Pitur t Problm: A at ngin dos work as it xtrats at from t ot rsrvoir and xausts at to t old rsrvoir. Stratgy: Us t nrgy onsrvation quation to alulat Q and tn t ffiiny quation to alulat t ffiiny: Solution: 1. Solv t nrgy onsrvation quation for : W = Q Q Q Q = W + Q 2. Insrt t xprssion from W W 40 J = = = = stp 1 into t ffiiny quation: Q W + Q 40 J J 0.28 Insigt: Baus t work W is always lss tan W + Q t ffiiny must always b lss tan Pitur t Problm: A at ngin dos work as it xtrats at from t ot rsrvoir and rjts at to t old rsrvoir. Stratgy: Us t nrgy onsrvation quation to alulat W and tn t ffiiny quation to alulat t ffiiny. Solution: 1. (a) Calulat work from t nrgy onsrvation quation: W = Q Q = 690 J 40 J = 260 J 2. (b) Calulat from t ffiiny quation: W 260 J = = = Q 690 J 0.8 Insigt: Drasing Q wil kping Q onstant will always inras t work don and inras t ffiiny. 7. T first law of trmodynamis traks t trmal nrgy addd to, or rmovd from, a systm. It says tat any ang in t trmal nrgy of a systm is ausd by t at addd to t systm minus t work don by t systm. 8. T nrgy of a at ngin dos not ang as it gos troug on yl. T nrgy tat ntrs t ngin (Q ) is qual to t nrgy tat lavs it (W + Q ). 9. Only in as B as t ffiiny of t at ngin inrasd. T ffiiny of a at ngin is t fration of t at supplid to t ngin tat is onvrtd to work. In as B mor work is produd for t sam at supplid, inrasing t ffiiny. In as A t sam amount of work is produd for a largr amount of nrgy supplid, wi mans tat t ffiiny as atually drasd. 10. Wn an objt slids aross a floor and oms to rst, its kinti nrgy as bn onvrtd to trmal nrgy by mans of t for of frition btwn t objt and t floor. In tis as manial nrgy is not onsrvd, but t total nrgy (inluding trmal nrgy) is onsrvd. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr. 11 2

3 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 11. Pitur t Problm: T work and at flow amounts ar givn for four systms. Stratgy: Us t first law of trmodynamis to rlat t trmal nrgy ang to t work and at flow amounts. Solution: 1. Calulat t trmal nrgy Δ EA = QA WA = J = 10 J ang for a of t four systms: Δ EB = QB WB = ( 20) ( 10 ) J = 10 J Δ EC = QC WC = ( 50) 0 J = 80 J Δ E = Q W = J = 10 J D D D ( ) ( ) 2. By omparing t angs in trmal nrgy w arriv at t ranking C < B < A = D. Insigt: Systm C uss 0 J of nrgy to do work on its nvironmnt, and tn donats an additional 50 J of at flow to t surroundings, for a total of 80 J tat is subtratd from its trmal nrgy. 12. Pitur t Problm: T nrgis drawn from t ot and old rsrvoirs of four diffrnt at ngins ar givn. Stratgy: Us t prinipl of nrgy onsrvation for at ngins to dtrmin t amount of work don by a at ngin. Tn divid t work don by t nrgy Q drawn from t ot rsrvoir to find t ffiiny of a at ngin. Finally, ompar t ffiinis and rank tm. Solution: 1. Calulat t work don by WA = Q,A Q,A = J = 20 J a of t four at ngins: WB = Q,B Q,B = J = 20 J WC = Q,C Q,C = J = 40 J W = Q Q = J = 20 J D,D,D 2. Calulat t ffiiny of a at ngin: W 20 J W 20 J A B A = = = B = = = Q, A 40 J Q, B 140 J W 40 J W 20 J C D C = = = D = = = Q,C 80 J Q, D 240 J. By omparing t ffiinis w arriv at t ranking D < B < A = C. Insigt: Bot ngins A and C onvrt alf of tir ful nrgy Q into manial work W. 1. Pitur t Problm: A systm s trmal nrgy drass wil it prforms work. Stratgy: T work don by a systm rprsnts nrgy tat is laving t systm. If w ombin tis fat wit t dras in t systm s trmal nrgy, w an onlud tat at must flow out of t systm baus t dras in trmal nrgy is largr in magnitud tan t work tat is prformd. Us t first law of trmodynamis to find t amount of at tat is transfrrd. Solution: Calulat Q: E Q W Q E W ( ) ( ) Δ = = Δ + = 20 J + 10 J = 10 J Insigt: T ngativ sign mans tat trmal nrgy flowd out of t systm in t form of at. 14. Pitur t Problm: A systm s trmal nrgy drass wil it prforms work. Stratgy: T work don by a systm rprsnts nrgy tat is laving t systm. If w ombin tis fat wit t dras in t systm s trmal nrgy, w an onlud tat at must flow into t systm baus t dras in trmal nrgy is smallr in magnitud tan t work tat is prformd. Us t first law of trmodynamis to find t amount of at tat is transfrrd. Solution: Calulat Q: E Q W Q E W ( ) ( ) Δ = = Δ + = 40 J J = 60 J Insigt: Only 60 J of at flowd into t systm wil 100 J flowd out as t gas did work to xpand against its surroundings. T rmaining 40 J ad to b witdrawn from t trmal nrgy of t gas. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr. 11

4 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 15. Pitur t Problm: A ors dos work and givs off at wil it pulls a sld. Stratgy: T at and work ar givn in t problm. Baus t ors is doing work on t nvironmnt, W is positiv, but at is laving its body, maning Q is ngativ. Us t first law of trmodynamis to find t ang in trmal nrgy. Solution: 1. Find t ang in trmal nrgy: 2. T work don is positiv:. T at mittd is ngativ: Δ E = Q W = = 5 W = J 5 Q = J J J J Insigt: T loss of trmal nrgy amounts to 1.08 MJ or 258 kal, t sam as 258 nutritional aloris. T ors nds to at at last tat mu nutrition to ompnsat for its xrtion. 16. Pitur t Problm: A at ngin dos work as it xtrats at from t ot rsrvoir and rjts at to t old rsrvoir. Stratgy: Us t nrgy onsrvation quation to alulat W and tn t ffiiny quation to alulat t ffiiny J Solution: 1. (a) Calulat work from t nrgy onsrvation quation: 2. (b) Calulat from t ffiiny quation: W = Q Q = 1220 J 680 J = 540 J W 540 J = = = 0.44 Q 1220 J 680 J Insigt: Tis ngin onvrts 44% of its ful nrgy Q into manial work wil xausting 56%. 17. Pitur t Problm: An idal gas xpands at onstant prssur. Stratgy: Solv t quation for work don during a onstant prssur pross to find t gas prssur. Solution: 1. Solv t onstant-prssur work quation for t prssur: ( f i) 2. Substitut t numrial valus: PV W V = W P = V V f i 9 J P = = 60 Pa 2. m 0.74 m Insigt: T prssur is proportional to t amount of work don. For xampl, omprssing a gas at tn tims t prssur (or 600 Pa) btwn t sam two volums rquirs tn tims t work (or 90 J). 18. Pitur t Problm: An idal gas xpands at onstant prssur. Stratgy: Solv t quation for work don during a onstant prssur pross to find t volum ang. Solution: 1. Solv t onstant-prssur W PΔ V = W Δ V = work quation for t volum ang: P 6,000 J 2. Substitut t numrial valus: Δ V = = 0.1 m Pa Insigt: T volum ang would av bn ngativ if work ad instad bn don on t gas to omprss it. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr. 11 4

5 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 19. Pitur t Problm: Tis is a follow-up qustion to Guidd Exampl A gas xpands from an initial volum of 0.40 m to a final volum of 0.62 m as t prssur inrass linarly from 110 kpa to 260 kpa. Stratgy: T work don by tis gas is qual to t sadd ara in t skt. W an alulat tis ara as t sum of t ara of a rtangl and t ara of a triangl, as indiatd in t skt. In partiular, t rtangl as t igt P i = 110 kpa and t widt Δ V = ( Vf Vi). Similarly, t triangl as t igt (P f P i ) and t bas Δ V = ( Vf Vi). Solution: 1. Calulat t ara of t rtangular portion of t sadd ara: 2. Nxt, alulat t ara of t triangular portion of t sadd ara. Rall tat t ara of a triangl is on-alf t bas tims t igt: ( ) A = P V V A rtangl i f i rtangl ( Pa)( m ) = = 24.2 kj ( )( ) A = V V P P A 1 triangl 2 f i f i triangl ( m )( Pa) 1 = 2 = 16.5 kj. Add t aras to find t work don by t gas: W = Artangl + Atriangl 4 = kj = 40.7 kj = J Insigt: T work is sligtly igr tan tat in Guidd Exampl 11.5 baus t final prssur is igr, making t triangular portion of t sadd ara sligtly largr Pitur t Problm: T PV plots at rigt sow tr diffrnt multi-stp prosss, labld A, B, and C. Stratgy: T work don by a gas is qual to t ara undr t PV plot as long as t gas is xpanding (t volum inrass). In a of t dpitd prosss t gas xpands, so t work is positiv in a as. Find t ara undr a plot to dtrmin t ranking of t work don. Solution: 1. Find W A : WA = P1Δ V1 + P2Δ V2 + PΔV = kpa 1 m + 0 = 4 kj ( )( ) 2. (b) Find W B : W ( )( ) ( )( 1 B P1 V1 P2 V2 P V 2 ). () Find W C : WC = P1Δ V1 + P2Δ V2 + PΔ V = 0 + ( 1 kpa)( m ) + 0 = kj = Δ + Δ + Δ = 1 kpa 1 m + 1+ kpa 2 m + 0 = 5 kj 4. (d) By omparing t valus of t work don in a pross w arriv at t ranking C < A < B. Insigt: Evn if pross B ad bgun at 0 kpa of prssur and inrasd linarly to t point (5 m, kpa) to form a 1 kpa m = 4.5 kj and t ranking would rmain t sam. triangl sap, t work don would b 2 ( )( ) 21. Pitur t Problm: Tis is a follow-up qustion to Guidd Exampl A systm undrgos an adiabati pross in wi its trmal nrgy drass by 470 J. Stratgy: W know tat t trmal nrgy drass by 470 J and tat no trmal nrgy is xangd (Q = 0) in an adiabati pross. Tus, w an find W by substituting Δ E and Q into t first law of trmodynamis, Δ E = Q W. Solution: Solv t first law of trmodynamis for W: Δ E = Q W ( ) W = Q Δ E = J = 470 J Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr. 11 5

6 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr Insigt: T positiv rsult indiats work don by t systm on its surroundings. Baus no nrgy an ntr or lav t systm in t form of at, all t work don by t systm oms at t xpns of its trmal nrgy. As a rsult, t intrnal nrgy, and trfor t tmpratur, of t systm drass. Tis is adiabati ooling. 22. Pitur t Problm: A gas xpands adiabatially and dos work on its surroundings. Stratgy: W know tat t trmal nrgy drass in ordr to do work on its surroundings, and tat no trmal nrgy is xangd (Q = 0) baus it is an adiabati pross. Tus, w an find Δ E by substituting W and Q into t first law of trmodynamis, Δ E = Q W. Solution: Calulat Δ E by E Q W ( ) substituting t numrial valus: Δ = = J = 520 J Insigt: Baus no nrgy an ntr or lav t systm in t form of at, all t work don by t systm oms at t xpns of its trmal nrgy. As a rsult, t intrnal nrgy, and trfor t tmpratur, of t systm drass. Tis is adiabati ooling. 2. (a) Fals. A tru statmnt would b T work don in a onstant-volum pross is zro, but t trmal nrgy ould ang if tr was a at flow. (b) Fals. A tru statmnt would b T work don in a onstant-prssur pross is PΔ V. () Tru. (d) Tru. () Tru. 24. Ys. Hat an flow into t systm if at t sam tim t systm xpands, as in an isotrmal xpansion of a gas. In tis as t at flow into t systm is baland by t work don to xpand against its surroundings, t trmal nrgy dos not ang, and t tmpratur rmains onstant. 25. In an adiabati pross tr is no at xangd wit t surroundings. Baus of tis, t ang in trmal nrgy is qual and opposit to t work in an adiabati pross. Any work don on t systm (ngativ W) rsults in an inras of t trmal nrgy (positiv Δ E ). 26. In an adiabati pross tr is no at xangd wit t surroundings. Baus of tis, t ang in trmal nrgy is qual and opposit to t work in an adiabati pross. Any work don by t systm (positiv 50 J) oms at t xpns of trmal nrgy. W onlud tat t ang in trmal nrgy of tis gas is 50 J. 27. Pitur t Problm: A gas dos work on its surroundings as it xpands at onstant tmpratur. Stratgy: W know tat for an idal gas t trmal nrgy rmains onstant during an isotrmal pross. As a rsult, any work don by t gas on its surroundings must b ompnsatd by a at flow into t gas. St Δ E = 0 and solv t first law of trmodynamis, Δ E = Q W for t amount of at Q. Solution: Calulat Q by substituting t numrial valus: Δ E = Q W = 0 Q = W = 10 J Insigt: A positiv Q implis an nrgy flow into t systm, wras a positiv W implis an nrgy flow out of t systm. During an isotrmal pross ts two ar qual and tr is no ang to t trmal nrgy of t systm. 28. Pitur t Problm: A known amount of at flows into a gas wos volum rmains onstant. Stratgy: W know tat for a onstant volum pross t work must b zro. Solution: T work W = 0 for a onstant volum pross. Insigt: T positiv at Q implis tat 25 J of nrgy flow into t systm, and baus t systm an do no work at onstant volum, t trmal nrgy E must also inras by 25 J. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr. 11 6

7 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 29. Pitur t Problm: An idal gas xpands at onstant prssur. Stratgy: Solv t quation for work don during a onstant prssur pross to find t initial volum V. Solution: 1. Solv t onstant-prssur W PV work quation for t volum: ( f Vi) = W= P( 2 V V) = PV V= P 110 J 2. Substitut t numrial valus: V = = m = m Pa Insigt: Baus tr ar 1000 litrs in a ubi mtr, tis volum ang is t sam as 1.2 L. 0. Pitur t Problm: An idal gas is omprssd at onstant prssur to on-alf of its initial volum. Stratgy: Baus tis is a onstant prssur pross, solv t quation for work don during a onstant prssur pross for t initial volum. Baus t work is don on t gas, W is ngativ. Solution: 1. Writ t work quation in trms of initial and final volums: 2. Substitut t numri valus: 1 1 2W PVf Vi = W= P 2Vi Vi = 2 PVi Vi = P ( ) ( ) 2( 790 J) Vi = = 0.01 m Pa Insigt: If t initial volum wr largr tan 0.01 m, mor work would b ndd to omprss t gas to alf its volum at t sam prssur. For instan, it would rquir 1200 J to omprss a gas wit an initial volum of m to m at a onstant prssur of 120 kpa. 1. Pitur t Problm: Tis is a follow-up qustion for Guidd Exampl T ntropy of a unk of i inrass as it mlts at 0 C. Stratgy: T ntropy ang is t at dividd by t absolut tmpratur, and t at rquird to mlt t i is t mass of t i multiplid by t latnt at of fusion. Solv tis xprssion for t mass of t i. T Klvin tmpratur tat orrsponds to 0 C is 27 K. Solution: 1. Solv t ntropy quation for t mass of t i: 2. Substitut t numrial valus: Q mlf TΔS Δ S = = m = T T L ( 27 K)( 275 J/K) m = = J/kg f kg Insigt: T avrag i ub as a mass of 25 grams, so t amount of i is quivalnt to about 9 i ubs. 2. Pitur t Problm: Hat is addd to a blok of i at 0 C, inrasing its ntropy. Stratgy: T amount of at absorbd by t i is ml, f and t ntropy ang is Δ S = Q T. Combin ts xprssions to dtrmin t amount of i tat mlts, givn tat T = 0 C = 27 K and L f = J/kg. Q TΔS ( 27 K)( 98 J/K) Solution: St Q = mlf = TΔ S and solv for m: m = = = = kg L L J/kg f f Insigt: A littl mor tan on-alf of t 0.14-kg blok of i as mltd. Mlting t ntir blok of i would rsult in an inras in ntropy of 172 J/K.. T sond law of trmodynamis stats tat wn objts of diffrnt tmpraturs ar brougt into ontat, t flow of trmal nrgy is always from t igr-tmpratur objt to t lowr-tmpratur objt. 4. Carnot s torm tat t maximum ffiiny of a at ngin is max = 1 T T implis tat a 100% ffiint at ngin is impossibl. In ordr to aiv 100% ffiiny t old rsrvoir must b at absolut zro T = 0, and t tird law of trmodynamis says tat su a rsrvoir dos not xist in our univrs. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr. 11 7

8 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 5. Frzing liquid watr to form i rsults in a dras in t ntropy of t watr baus t frozn stat is a lss disordrd stat tan t liquid stat. Howvr, in ordr to frz, t watr must b in ontat wit a systm tat is oldr tan 0 C, and wn at flows from t warm watr to t old systm, t ntropy of t univrs inrass. 6. Entropy masurs t amount of disordr in a systm. Trfor, if t ntropy of a systm inrass, its disordr inrass and so dos its randomnss. 7. Entropy masurs t amount of disordr in a systm. Trfor, in a as you an did wi systm as mor ntropy by onsidring t amount of disordr in a systm: (a) poppd poporn; (b) an omlt; () a pil of briks; (d) t as aftr t papr as bn burnd. 8. Pitur t Problm: T rsrvoir tmpraturs of four diffrnt at ngins ar givn. Stratgy: Us Carnot s torm for at ngins to dtrmin t maximum ffiiny of a at ngin. Tn ompar t ffiinis and rank tm. Solution: 1. Calulat t maximum ffiiny of a at ngin: max, A max, C 2. By omparing t ffiinis w arriv at t ranking B < D < C < A. T, A 200 K T, B 420 K = 1 = 1 = 0.50 max, B = 1 = 1 = T, A 400 K T, B 440 K T,C 600 K T, D 1020 K = 1 = 1 = 0.25 max, D = 1 = 1 = 0.18 T 800 K T 1240 K,C Insigt: T maximum ffiiny is strongly dpndnt upon t tmpratur of t old rsrvoir. For instan, ngin D as t largst tmpratur diffrn (220 K) btwn its rsrvoirs, but it as t lowst maximum ffiiny baus its old rsrvoir as su a ig tmpratur. Likwis, ngin A as a igr maximum ffiiny vn toug it as t sam 200 K tmpratur diffrn as ngin C, but its 200 K old rsrvoir is mu oldr tan t 600 K rsrvoir for ngin C., D 9. Pitur t Problm: T rsrvoir tmpraturs of a at ngin ar givn. Stratgy: Us Carnot s torm for at ngins to dtrmin t maximum ffiiny of t at ngin. T 260 K Solution: Calulat t max = 1 = 1 = 0.21 maximum ffiiny: T 0 K Insigt: Most at ngins oprat wit t nvironmnt as t old rsrvoir, and Eart s nvironmnt is around 00 K. Tis old rsrvoir of 260 K = 1 C = 8.6 F ould b a old wintr s day at ig latituds. 40. Pitur t Problm: T maximum ffiiny and t tmpratur of t ot rsrvoir for a at ngin ar known. Stratgy: Solv Carnot s torm for at ngins for t tmpratur of t old rsrvoir. Solution: Solv Carnot s torm for T : T T ( ) ( )( ) = 1 = 410 K = 12 K max Insigt: Wn t ot tmpratur rsrvoir is fixd, a igr maximum ffiiny orrsponds to a lowr tmpratur for t old rsrvoir. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr. 11 8

9 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 41. Pitur t Problm: A at ngin dos work as it xtrats at from t ot rsrvoir and rjts at to t old rsrvoir. Stratgy: Us t nrgy onsrvation quation to alulat Q and tn t ffiiny quation to alulat t ffiiny. Q 40 J Solution: 1. (a) Calulat Q from t nrgy onsrvation quation: 2. (b) Calulat from t ffiiny quation: Q = W + Q = 40 J J = 1210 J W 40 J = = = 0.28 Q 1210 J 870 J Insigt: Tis ngin onvrts 28% of its ful nrgy Q into manial work wil xausting 72%. 42. Pitur t Problm: An idal at ngin oprats btwn t tmpraturs of 240 K and 90 K. Stratgy: Us t givn tmpraturs to find t ffiiny of t at ngin. Tn us t ffiiny quation to find t at input Q and t onsrvation of nrgy quation to find t at rjtd Q. Solution: 1. (a) Find t ffiiny: 2. Us t ffiiny quation to alulat Q : max T 240 K = = = T 90 K W 1200 J Q = = = 120 J =.1 kj (b) Solv t nrgy onsrvation quation for Q : Q = Q W =.1 kj 1.2 kj = 1.9 kj 1200 J Insigt: T rsrvoir tmpraturs fix t ffiiny at 8.5%. Trfor, t work W tat t ngin produs is dirtly proportional to t amount of ful Q supplid to t ngin. 4. Pitur t Problm: Hat is rmovd from watr at its frzing point, onvrting t watr to i. Stratgy: T amount of at absorbd by t i is ml, f and t ntropy ang is Δ S = Q T. Combin ts xprssions to dtrmin t ang in ntropy, givn tat T = 0 C = 27 K and L f = J/kg. Not tat t at flows out of t i, so tat Q is ngativ in tis situation. Solution: Calulat t ntropy ang: S Q T ml T (.1 kg)( J/kg) f Δ = = = = 27 K Insigt: As at is takn from t watr, t ntropy of t watr drass. Howvr, t ntropy of t univrs inrass baus t at is flowing from a warm rgion (t i watr) to a old rgion..8 kj K 44. In t quation for t first law of trmodynamis, Q rprsnts an nrgy input and W rprsnts an nrgy output of a systm. Trfor, t two av opposit signs wn aounting for t ang in trmal nrgy of t systm. 45. If t trmal nrgy of a systm rmains onstant, any nrgy flow into t systm must b matd by an nrgy flow out of t systm. W onlud tat t systm dos 100 J of work if it rivs 100 J of at. 46. Effiiny is t ratio of work don to t nrgy input from t ot rsrvoir. Engin 2 dos mor work for t sam nrgy input, so w onlud tat t ffiiny of ngin 1 is lss tan t ffiiny of ngin 2. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr. 11 9

10 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 47. Effiiny is t ratio of work don to t nrgy input from t ot rsrvoir. Engin 1 onvrts 20% of its input nrgy into work, but ngin 2 onvrts 10% of its input nrgy into work. W onlud tat t ffiiny of ngin 1 is gratr tan t ffiiny of ngin Pitur t Problm: A runnr dos work and givs off at during a workout. Stratgy: T at and work ar givn in t problm. Baus t runnr is doing work on t nvironmnt, W is positiv, but at is laving r body, maning Q is ngativ. Us t first law of trmodynamis to find t ang in trmal nrgy. Solution: 1. Find t ang in trmal nrgy: 2. T work don is positiv: J J J Δ E = Q W = = 5 W = J 5. T at mittd is ngativ: Q =. 10 J Insigt: T loss of trmal nrgy amounts to 1.15 MJ or 275 kal, t sam as 275 nutritional aloris. Tis is about on-tnt of t nrgy tat a 160-lb runnr will xpnd wn running a maraton, aording to t Clvland Clini Cntr for Consumr Halt. 49. Pitur t Problm: Trmodynami systms ang tir trmal nrgy wn at flows and wn work is don. Stratgy: Us t first law of trmodynamis to find t at flow Q =Δ E+ W for a systm. Solution: 1. (a) Calulat Q: Q =Δ E+ W = 50 J + 50 J = 100 J =Δ + = 50 J + 50 J = 100 J 2. (b) Calulat Q: Q E W ( ) ( ). () Calulat Q: Q =Δ E+ W = 150 J + 50 J = 200 J Insigt: In part () t 200 J of at nrgy flows into t systm, providing for t 50 J of work don by t systm and tn inrasing t systm s trmal nrgy by 150 J. 50. Pitur t Problm: A at ngin dos work as it xtrats at from t ot rsrvoir and rjts at to t old rsrvoir. Stratgy: Calulat t ffiiny by dividing t work don by t nrgy input, and tn us t quation for onsrvation of nrgy alulat Q. Solution: 1. (a) Calulat t ffiiny: 2. (b) Rarrang t quation for nrgy onsrvation to find Q : W 160 J = = = 0.21 = 21% Q 770 J W = Q Q Q = Q W = 770 J 160 J = 610 J 770 J Insigt: An ffiiny of 21% implis tat 79% of t input nrgy is xaustd into t old rsrvoir. Wil tis may sm wastful, it is a typial ffiiny for modrn automobils. Eltri ars, owvr, do not us at ngins and ar not limitd by t sond law of trmodynamis. Q 160 J Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr

11 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 51. Pitur t Problm: A at ngin dos work as it xtrats at from t ot rsrvoir and rjts at to t old rsrvoir. Stratgy: Us t quation for nrgy onsrvation to alulat W and tn divid W by t at input Q to find t ffiiny. Solution: 1. Calulat t work W = Q Q = 570 J 440 J = 10 J from nrgy onsrvation: 2. Divid W by Q to find t ffiiny: W 10 J = = = 0.2 = 2% Q 570 J 570 J 440 J Insigt: Drasing Q wil kping Q onstant will always inras t work don and inras t ffiiny. 52. Pitur t Problm: A at ngin produs work in a yl wr it xausts 2/ of t 2 input at to t old rsrvoir ( Q = Q ). Stratgy: Substitut t givn valus of Q and Q to alulat t ffiiny of t at ngin. 2 W Q Q Q Q 1 Solution: Us t ffiiny quation: = = = 1 = 1 = Q Q Q Q Insigt: In an idal ngin, t ratio of at xaustd to at input will always b qual to t ratio of t tmpratur of old rsrvoir to t tmpratur of t ot rsrvoir, as in tis as Q Q = T T = Pitur t Problm: A at ngin produs work in a yl wr it xausts 2/ of t 2 input at to t old rsrvoir ( Q = Q ). Stratgy: Substitut t givn valus of Q and Q to alulat t ffiiny of t at ngin. Tn solv t ffiiny quation for t work don by t ngin. 2 W Q Q Q Q 1 Solution: 1. Us t ffiiny quation: = = = 1 = 1 = Q Q Q Q W 1 = = = 280 J = 9 J Q 2. Solv t ffiiny quation for W: W Q ( ) Insigt: In an idal ngin, t ratio of at xaustd to at input will always b qual to t ratio of t tmpratur of old rsrvoir to t tmpratur of t ot rsrvoir, as in tis as Q Q = T T = Pitur t Problm: In a basktball gam, t playr dos work and givs off at in t form of prspiration. Stratgy: Us t first law of trmodynamis to find t ang in trmal nrgy. T playr s work is positiv baus s dos work on r surroundings, and r at loss is du to t latnt at of vaporization of t prspiration. Solution: 1. (a) Writ t first law of trmodynamis using t latnt at of vaporization: Δ E = Q W = mlv W 2. Entr t givn valus: E ( )( ) kg J/kg J 492 kj Δ = = Insigt: Convrting t answr to nutritional aloris (Cal), w find 492 kj / Cal/kJ = 118 Cal. By omparison tr ar about 150 Cal in a 1.0-oz bag of potato ips. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr

12 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 55. Pitur t Problm: Tr diffrnt prosss at on a systm, rsulting in diffrnt final stats. Stratgy: Us t first law of trmodynamis to solv for t unknown quantity in a pross. Solution: 1. (a) Apply t first law dirtly: Δ E = Q W = 77 J ( 42 J) = 119 J 2. (b) Apply t first law dirtly: Δ E = Q W = 77 J 42 J = 5 J. () Solv t first law for Q: Q =Δ E+ W = 120 J J = 0 Insigt: Consrvation of nrgy rquirs tat t nt nrgy flow (Q and W) into t systm must qual t ang in intrnal nrgy, rgardlss of t pross by wi t nrgy xang ours. 56. In a onstant-volum pross no work is don and W = In an isotrmal pross t tmpratur dos not ang, and nitr dos t trmal nrgy, wi implis tat Δ E is zro. Tis is stritly tru only for idal gass. For instan, during t boiling of a liquid to a vapor, wn t bavior of t substan is not wll dsribd by t idal gas law, t tmpratur dos not ang but t trmal nrgy inrass du to t latnt at of vaporization. 58. In an adiabati pross tr is no at xang wit t surroundings and Q = T work don in any pross is qual to t orrsponding ara undr t urv in a prssur-volum grap. In a onstant-prssur pross tis ara is rtangular in sap. 60. Ys. T first law of trmodynamis stats tat t trmal nrgy in a systm an ang by itr work or at flow. Eitr on of ts an our at onstant prssur. For instan, if you rmov a up of ot off from t mirowav ovn and st it on t tabl, no work is don (t volum rmains onstant) but trmal nrgy flows out of t ot off and into t ool surroundings. Tis nrgy flow ours at onstant prssur. 61. T work don by a gas as it xpands at onstant prssur is qual to t prssur multiplid by t ang in volum. If t prssur of t gas is inrasd but t volum ang rmains t sam, t work don by t gas will inras. 62. Pitur t Problm: A fluid dos work on its surroundings as it xpands at onstant prssur. Stratgy: T work don by an xpanding fluid at onstant prssur is qual to t prssur multiplid by t ang in volum. W = PΔ V = Pa 0.42 m = 51,000 J = 51 kj Solution: Calulat t work: ( )( ) Insigt: T ara undr a PV plot is always qual to t work don by t systm, indpndnt of t typ of systm. 6. Pitur t Problm: A gas wit initial volum V i xpands at onstant prssur to twi its initial volum. Stratgy: Us t ara undr t PV plot to find t work don by t gas. Solution: 1. St t work qual to t prssur tims volum: ( f i) ( 2 ) W = P V V = P Vi Vi W = PV 2. Substitut t numri valus: ( )( ) i W = Pa 0.66 m = 92,000 J = 92 kj Insigt: T pross in tis problm orrsponds to t rigt-and portion of t diagram abov (xpansion from V i to 2V i ). Trmodynami work is positiv wn t volum inrass and ngativ wn t volum drass. P Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr

13 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 64. Pitur t Problm: A gas dos work on its surroundings as it xpands at onstant prssur. Stratgy: T work don by an xpanding gas at onstant prssur is qual to t prssur multiplid by t ang in volum. Solv tis xprssion for t ang in volum. W 82 J 4 Solution: Find t ang in volum: W = PΔV Δ V = = = m P Pa Insigt: Tis volum is quivalnt to 40 m, lss tan a pint in t Englis systm of units. 65. Pitur t Problm: Work is don on a gas at onstant prssur. Stratgy: T work don on a gas at onstant prssur is qual to t prssur multiplid by t ang in volum. Solv tis xprssion for t ang in volum. Solution: 1. (a) Work don on a gas is ngativ baus nrgy ntrs t systm. T work is also qual to PΔ V. Baus P is always positiv, t only way for t work to b ngativ is for Δ V to b ngativ, wi implis tat t volum of t gas will dras if work is don on it. W 62 J 4 2. (b) Find t ang in volum: W = PΔV Δ V = = = m P Pa Insigt: Tis volum is quivalnt to 540 m, a littl bit mor tan a pint in t Englis systm of units. 66. Pitur t Problm: A gas dos work on its surroundings as it xpands at onstant prssur. Stratgy: T work don by an xpanding gas at onstant prssur is qual to t prssur multiplid by t ang in volum. Solv tis xprssion for t prssur. W 22 J Solution: Find t prssur: W = PΔV P = = = 29 Pa ΔV 0.75 m Insigt: Tis is an xtrmly low prssur, only of atmospri prssur. To ra tis prssur in our atmospr you would av to limb to 4,900 m (114,500 ft) or almost four tims t igt of Mount Evrst. 67. Pitur t Problm: A systm tat is trmally isolatd from its surroundings undrgos an adiabati pross in wi its trmal nrgy inrass. Stratgy: Us t first law of trmodynamis to alulat t work don during an adiabati pross ( Q = 0 ). Solution: 1. Solv t first law for W, stting Q = 0: Δ E = Q W = 0 W W = ΔE 2. (a) Baus t trmal nrgy inrasd ( Δ E > 0 ) t work must b ngativ, wi mans tat it t work is don on t systm.. (b) Substitut t numrial valus: W E ( ) = Δ = 890 J = 890 J Insigt: Wn no at an ntr or lav a systm, any ang in intrnal nrgy is du to t work don on t systm or by t systm. 68. Pitur t Problm: A systm xpands at onstant prssur. Stratgy: Us t first law of trmodynamis to find t at absorbd Solution: 1. Solv t first law for at: Q =Δ E+ W =Δ E+ PΔ V 2. (a) Find Q for E 65 J: Δ = Q = 65 J + ( Pa)( 0.75 m ) = 94 kj; into t gas Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr. 11 1

14 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr. (b) Find Q for E 1850 J: Q = 1850 J Pa 0.75 m = 92 kj; into t gas Δ = ( ) Insigt: In ordr for at to flow out of t gas, t intrnal nrgy would nd to dras by at last 9.8 kj, wi is qual to t amount of work don by t gas. 69. No. T dras in t room s ntropy is a onsqun of t dlibrat work tat you did to organiz it. A arful analysis of t nrgy flow in your body rvals tat t inras in ntropy produd by t digstion of your food, and t xrtion of your musls, and t rlas of your body at is largr tan t dras of ntropy of t mssy room. T ntropy of t univrs as inrasd, in agrmnt wit t sond law of trmodynamis. 70. Pitur t Problm: An idal at ngin oprats btwn a ot rsrvoir at tmpratur T and a old rsrvoir at t tmpratur T. Stratgy: Us t xprssion for t ffiiny of an idal at ngin to answr t onptual qustions. Solution: T ffiiny of an idal at ngin ( max = 1 T /T ) dpnds on t ratio of absolut tmpraturs T and T. Doubling bot tmpraturs lavs tis ratio unangd. W onlud tat if bot Klvin tmpraturs ar doubld, t ffiiny of t ngin will stay t sam. Insigt: T bst way to inras t ffiiny of an idal at ngin is to inras t tmpratur diffrn btwn t two rsrvoirs. In ral lif t old rsrvoir is usually t nvironmnt (nar 00 K) and annot b angd, so t bst option is to inras t tmpratur of t ot rsrvoir. 71. Pitur t Problm: An idal at ngin oprats btwn a ot rsrvoir at tmpratur T and a old rsrvoir at t tmpratur T. Stratgy: Us t xprssion for t ffiiny of an idal at ngin to answr t onptual qustions. Solution: Adding t sam tmpratur to bot T and T mans tat t ratio T /T will av a valu tat is losr to 1. Trfor, t ffiiny of t ngin will dras if bot tmpraturs ar inrasd by 50 K. Insigt: For xampl, t maximum ffiiny of a at ngin oprating btwn 00 K and 500 K is max = 1 00 K 500 K = If bot tmpraturs ar inrasd by 50 K, tn max = 1 50 K 550 K = Pitur t Problm: You rub your ands togtr and frition onvrts t manial nrgy into trmal nrgy. Stratgy: Us t dfinition of ntropy ang to answr t onptual qustion. Solution: 1. (a) T dfinition of ntropy ang Δ S = Q T indiats tat wnvr at is transfrrd tr is a orrsponding ntropy ang. In tis as t manial nrgy of t ands is onvrtd into trmal nrgy Q tat is dpositd into t ands, inrasing tir ntropy. No at is subtratd from anywr, so w onlud tat t ntropy of t univrs will inras if you rub your ands togtr. 2. (b) T bst xplanation is C. T at produd by t rubbing raiss t tmpratur of t ands and t air, wi inrass t ntropy. Statmnts A and B ar bot fals. Insigt: All su fritional prosss produ an inras in t ntropy of t univrs, baus low-ntropy manial nrgy is onvrtd into ig-ntropy trmal nrgy. 7. Pitur t Problm: T ot and old rsrvoir tmpraturs of four diffrnt at ngins ar givn. Stratgy: T ffiiny of an idal at ngin an b found by alulating max = 1 T T. Us tis xprssion to find t maximum ffiinis of t four ngins and tn rank tm. Solution: 1. Calulat t maximum ffiiny of a at ngin: max, A max, C T, A 400 K T, B 400 K = 1 = 1 = 0.50 max, B = 1 = 1 = 0. T, A 800 K T, B 600 K T,C 800 K T, D 800 K = 1 = 1 = 0. max, D = 1 = 1 = 0.20 T 1200 K T 1000 K,C, D Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr

15 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 2. By omparing t ffiinis w arriv at t ranking D < B = C < A. Insigt: Not tat igr ffiinis ar assoiatd wit lowr old rsrvoir tmpraturs. For instan, ngins A and C a av a 400 K tmpratur diffrn, and ngins B and D a av a 200 K tmpratur diffrn, but in a as t ngin wit t lowr old rsrvoir tmpratur as t igr ffiiny. 74. Pitur t Problm: A at ngin dos work as it xtrats at from t ot rsrvoir and rjts at to t old rsrvoir. Stratgy: Calulat t ffiiny by dividing t work don by t nrgy input Solution: Calulat t ffiiny: W 20 J = = = 0.8 = 8% Q 610 J Insigt: An ffiiny of 8% implis tat 62% of t input nrgy is xaustd into t old rsrvoir. 610 J Q 20 J 75. Pitur t Problm: A at ngin dos work as it xtrats at from t ot rsrvoir and rjts at to t old rsrvoir. Stratgy: Us t quation for onsrvation of nrgy to alulat Q, and tn alulat t ffiiny by dividing t work don by t nrgy input. Solution: 1. (a) Rarrang t quation W = Q Q for nrgy onsrvation to find Q : Q = Q W = 780 J 110 J = 670 J 2. (b) Calulat t ffiiny: W 110 J = = = 0.14 = 14% Q 780 J 780 J Q 110 J Insigt: An ffiiny of 14% implis tat 86% of t input nrgy is xaustd into t old rsrvoir. Tis is not a vry ffiint at ngin! 76. Pitur t Problm: A nular powr plant dos work at a rat of 250 MW as it xtrats at from t ot rsrvoir at a rat of 85 MW and rjts at to t old rsrvoir. Stratgy: Us t quation for onsrvation of nrgy to alulat Q, and tn alulat t ffiiny by dividing t work don by t nrgy input. Solution: 1. (a) Rarrang t quation for nrgy onsrvation to find Q, dividing a Q Q W Q = Q W = trm by tim to rflt tat powr is bing t t t onsidrd instad of nrgy: Q 2. Substitut t numri valus: t. (b) Calulat t ffiiny = 85 MW 250 MW = 585 MW W W t 250 MW = = = = Q Q t 85 MW Insigt: Typially, for powr plants it is t rat of at flow and powr output tat is important. As sown in tis problm, t sam quations usd for at and work an b usd to dtrmin at flow rats and powr output. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr

16 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 77. Pitur t Problm: A oal-burning powr plant produs powr as it xtrats at from a ot tmpratur rsrvoir and rjts at to a old tmpratur rsrvoir. Stratgy: Combin t ffiiny quation and t nrgy onsrvation quation to solv for t rat at wi at is rjtd to t old rsrvoir. in trms of t ffiiny and powr output. Tn us t ffiiny quation to solv for t rat tat at must b supplid to t powr plant. Solution: 1. (a) Substitut Q = W + Q into = W Q, rarrang, and subtrat W from bot sids of t quation to find Q : W W = = Q W + Q W 1 W + Q = Q = W 1 Q W 1 1 = 1 = 550 MW 1 = 1.2 GW t t Divid by t tim to find t xaust rat: ( ). (b) Writ t ffiiny quation as a Q Wt 550 MW = = = 1.7 GW rat quation and solv for Q t : t 0.2 Insigt: A railroad ar olds about 100 tons of oal, wi an rlas about J. Su a railroad ar an provid 12 9 t = Q P = J J/s = 1550 s or only 26 minuts! ful to tis powr plant for ( ) ( ) 78. Pitur t Problm: Hat is addd to watr at its boiling point, onvrting t watr ntirly to stam. Stratgy: Us t latnt at of vaporization of watr to alulat t at addd to t watr. Tn alulat t ang in ntropy from Δ S = Q T. Solution: Calulat t ang in ntropy: Q T ml ( 1.85 kg)( J/kg) v 4 Δ S = = = = J/K = 11.2 kj/k T K Insigt: T stam as a igr ntropy tan liquid watr baus t random motions of t vapor moluls ar mor disordrd tan tos of t liquid watr moluls. 79. Pitur t Problm: A at ngin produs 2700 J of work as it xtrats at from a ot tmpratur rsrvoir and rjts at to a old tmpratur rsrvoir. Stratgy: Us t ffiiny quation to alulat onsrvation of nrgy to alulat Q : Q and tn us t quation for Solution: 1. (a) Solv t ffiiny quation for Q : W Q = 2. Substitut t givn valus: 2700 J Q = = 15 kj (b): Solv t nrgy onsrvation quation for Q : Q = Q W = J 2700 J = 12 kj 4. () Higr ffiiny mans lss at input is ndd to produ t sam work. Consquntly, lss at is lost to t surroundings. T answrs to part (a) will dras. Insigt: As an xampl of igr ffiiny, if = 0.24 and W = 2700 J, tn Q = 10.0 kj and Q = 7.6 kj. 80. Pitur t Problm: A at ngin xtrats at from a ot tmpratur rsrvoir and rjts at to a old tmpratur rsrvoir. Stratgy: T ffiiny of an idal at ngin dpnds upon t absolut tmpraturs of its ot and old rsrvoirs. Us Carnot s torm to dtrmin t tmpratur of t ot rsrvoir wn t ffiiny is 21%. Tn us Carnot s torm again to find t old rsrvoir tmpratur tat orrsponds to an ffiiny of 25%. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr

17 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr Solution: 1. Us Carnot s torm to dtrmin t tmpratur of t ot rsrvoir: 2. Us Carnot s torm again to dtrmin t tmpratur of t old rsrvoir tat T max T T = = 1 1 T T T = = = 1 max max 265 K 5 K 1 1 T T orrsponds to an ffiiny of 25%: T T ( ) ( )( ) max T T = = max max = 1 = 5 K = 250 K Insigt: Not tat t old rsrvoir tmpratur must b rdud in ordr to mak t ngin mor ffiint. 81. Pitur t Problm: T ffiiny of an idal at ngin is inrasd by lowring t old tmpratur rsrvoir. Stratgy: Us Carnot s torm to solv for t tmpratur of t old tmpratur rsrvoir using t initial ffiiny, tn rpat t alulation using t nw ffiiny. Solution: 1. (a) Solv Carnot s torm for T = T 1 max = 545 K = 82 K 2. (b) T ffiiny of a at ngin inrass as t diffrn in tmpratur of t ot and old rsrvoirs inrass. Trfor, t tmpratur of t low tmpratur rsrvoir must b drasd. T : ( ) ( )( ). () Apply Carnot s torm wit t nw ffiiny: T = ( 545 K)( ) = 27 K Insigt: T ffiiny of an idal at ngin is inrasd wn t tmpratur diffrn btwn t two rsrvoirs inrass. Wn t ot tmpratur rsrvoir is fixd, t ffiiny an b inrasd by lowring t tmpratur of t old rsrvoir. 82. Pitur t Problm: An idal at ngin prforms 2200 J of work as it xtrats 2500 J of at from a ot tmpratur rsrvoir and rjts at to a old tmpratur rsrvoir. Stratgy: Us t ffiiny quation to alulat, and tn us t quation for nrgy onsrvation to find Q, and Carnot s torm to find t ratio of rsrvoir tmpraturs. Solution: 1. (a) Apply t W 2200 J = = = 0.88 ffiiny quation: Q 2500 J 2. (b) Solv Q = W + Q for Q : Q = Q W = 2500 J 2200 J = 00 J. () Solv Carnot s torm T T 1 1 max 1 8. for tmpratur ratio: = T T = 1 = max = Insigt: A at ngin wit 88% ffiiny would nd to av t ot tmpratur rsrvoir at last 8. tims ottr tan t old tmpratur rsrvoir. For instan, if t old rsrvoir is at room tmpratur (00 K) t ot tmpratur rsrvoir would av to b at last 2500 K, suffiintly ot to mlt stl! 8. Pitur t Problm: As at flows out of a ous, t ntropy of t ous drass and t ntropy of t outsid inrass. Stratgy: Us Δ S = Q T to sum t ntropy angs for insid and outsid t ous. T rsulting quation an b dividd by tim in ordr to dtrmin t rat of ntropy ang. Solution: Sum t insid and outsid angs ΔS Q t Q t = in ntropy, and divid a trm by t tim: + t T insid T outsid 25,000 W 25,000 W = + = 12 J/K/s K K Insigt: Altoug t ang in ntropy of t insid was ngativ, t nt ang in ntropy is positiv. T total ntropy of t univrs itr stays t sam or inrass during any pross, and it always inrass wn trmal nrgy is transfrrd from a warm rgion to a old rgion. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr

18 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 84. Pitur t Problm: Wil dsnding at onstant spd, a parautist s gravitational potntial nrgy is onvrtd to trmal nrgy, rsulting in an inras in ntropy. Stratgy: T paraut onvrts t parautist s manial nrgy into trmal nrgy by mans of frition. Us Δ S = Q T to alulat t ang in ntropy, ltting Q qual t ang in gravitational potntial nrgy. Solution: 1. St t at in t ntropy quation qual to t ang in gravitational potntial nrgy: 2. Substitut t numrial valus: Q ΔPE mg Δ S = = = T T T 2 ( )( )( ) 88 kg 9.81 m/s 60 m Δ S = = 1100 J/K = 0.11 kj/k K Insigt: In t absn of air rsistan, t parautist s gravitational potntial nrgy would b onvrtd to kinti nrgy, not at, wit no inras in ntropy. Of ours, t paraut would also b uslss in tat situation! 85. Tis would b a violation of t sond law of trmodynamis, wi stats tat at always flows from a igtmpratur objt to a low-tmpratur objt. If at wr to flow spontanously btwn objts of qual tmpratur, t rsult would b objts at diffrnt tmpraturs. Ts objts ould tn b usd to run a at ngin until ty wr again at t sam tmpratur, aftr wi t pross ould b rpatd indfinitly. 86. T first law of trmodynamis stats tat t trmal nrgy in a systm an ang by itr work or at flow. In tis as t manial work you do to rub your ands togtr inrass t trmal nrgy of your ands by mans of frition. 87. T law of trmodynamis most prtinnt to tis situation is t sond law, wi stats tat pysial prosss mov in t dirtion of inrasing disordr. To dras t disordr in on rgion of spa (Humpty Dumpty) rquirs work to b don, and a largr inras in disordr in anotr rgion of spa (all t king s orss and all t king s mn). Humpty Dumpty will nvr spontanously rassmbl; putting im bak togtr again rquirs grat ffort. 88. No at is xangd in an adiabati pross. 89. Pitur t Problm: A gas follows t pross from point A to point B in t prssur-volum grap sown at t rigt. Stratgy: Find t nt work don by t systm by masuring t ara undr t urv in t PV plot. Tis ara is sadd in purpl. Rall tat t ara of a trapzoid is t bas multiplid by t avrag of t igts 1 A = + b of t sids, or ( ) Solution: Find t ara of t trapzoid on t PV plot: ( 4 1 m ) 1 2 ( kpa) W = + = 00 kj Insigt: Additional information about t gas, su as t tmpratur at point A or point B, would b rquird in ordr to find t at flow or t ang in trmal nrgy during tis pross. 90. Rports will vary. In a disl ngin t adiabati omprssion ratio of t piston is suffiint to rais t tmpratur of t air-ful mixtur abov t ignition point. Typial disl omprssion ratios ar from 14:1 to 22:1. Advantag: Disl ngins ar mor ffiint baus ty oprat at igr omprssion ratios and ombustion tmpraturs tan non-disl ngins. Disadvantags: Disl ngins ar loudr; disl ful oftn osts mor tan gasolin; disl ngins mit mor partiulats. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr

19 Captr 11: Trmodynamis Parson Pysis by Jams S. Walkr 91. Wn you rid your biyl down a stp ill wit no frition, your gravitational potntial nrgy is onvrtd into kinti nrgy and you gratly inras your spd. If you rid down a stp ill at onstant spd, you an onlud tat frition is onvrting your manial nrgy into trmal nrgy. Tis frition is primarily du to t air, but tr is also frition btwn t tirs and t road, frition in t axls of t biyl, and possibly frition du to braking ndd to maintain a onstant spd. 92. Pitur t Problm: An OTEC (Oan Trmal Enrgy Convrsion) at ngin produs work by xtrating at from t surfa of t oan and rjting at to t oldr, dp-watr of t oan. Stratgy: Us Carnot s torm to dtrmin t maximum ffiiny. Rmmbr to onvrt t tmpratur from dgrs Clsius to klvins. Solution Insrt t givn tmpraturs (in klvins) into Carnot s torm. T alulatd answr orrsponds to oi A. max ( K) ( K) T = = = = % T Insigt: Six prnt ffiiny mans tat for vry 100 Jouls of at xtratd from t watr only 6 Jouls of work an b produd. 9. Pitur t Problm: During t opration of an OTEC at ngin, 1500 kg of watr at 22 C is oold to 4.0 C. Stratgy: Us t spifi at quation Q = mδ T to dtrmin t at rlasd by t warm watr. ( )( )( ) 8 Solution: Calulat t at rlasd. T alulatd answr orrsponds to oi B. Q = mδ T = 1500 kg 4186 J/kg/C C = J Insigt: If tis mu nrgy wr transfrrd vry sond, and 6.1% of t nrgy flow wr onvrtd into work, t output of tis at ngin would b 6.9 MW. Not tat 1.5 mtri tons of watr ar ndd to transfr lss nrgy tan wat would b rlasd by burning a gallon (2.8 kg) of gasolin. 94. Pitur t Problm: An OTEC (Oan Trmal Enrgy Convrsion) at ngin produs work by xtrating at from t surfa of t oan and rjting at to t oldr, dp-watr of t oan. Stratgy: Us Carnot s torm to dtrmin t maximum ffiiny. Rmmbr to onvrt t tmpratur from Clsius to Klvin. Solution Insrt t givn tmpraturs (in klvins) into Carnot s torm. T alulatd answr orrsponds to oi A. max ( K) ( K) T = = = = % T Insigt: If t rat of ooling wr t sam as abov (1500 kg of watr anging from 22 C to 2.0 C vry sond) t powr output would tn b 8.5 MW. A dtaild analysis would b rquird to did if t xtra 1.6 MW of output would adquatly ompnsat for t ost rquird to oprat in t dpr 2.0- C watr. Copyrigt 2014 Parson Eduation, In. All rigts rsrvd. Tis matrial is prottd undr all opyrigt laws as ty urrntly xist. No portion of tis matrial may b rprodud, in any form or by any mans, witout prmission in writing from t publisr