Physics 41 Chapter 22 HW Serway 7 th Edition

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1 yss 41 apter H Serway 7 t Edton oneptual uestons: 1,, 8, 1 roblems: 9, 1, 0,, 7, 9, 48, 54, 55 oneptual uestons: 1,, 8, 1 1 Frst, te effeny of te automoble engne annot exeed te arnot effeny: t s lmted by te temperature of burnng fuel and te temperature of te envronment nto w te exaust s dumped Seond, te engne blok annot be allowed to go over a ertan temperature rd, any pratal engne as frton, nomplete burnng of fuel, and lmts set by tmng and energy transfer by eat ger steam temperature means tat more energy an be extrated from te steam For a onstant temperature eat snk at, and steam at, te effeny of te power plant goes as 1 and s maxmzed for a g 8 (a) en te two sdes of te semondutor are at dfferent temperatures, an eletr potental (voltage) s generated aross te materal, w an drve eletr urrent troug an external rut e two ups at 50 ontan te same amount of nternal energy as te par of ot and old ups ut no energy flows by eat troug te onverter brdgng between tem and no voltage s generated aross te semondutors eat engne must put out exaust energy by eat e old up provdes a snk to absorb output or wasted energy by eat, w as nowere to go between two ups of equally warm water 1 (a) For an expandng deal gas at onstant temperature, te nternal energy stays onstant e gas must absorb by eat te same amount of energy tat t puts out by work en ts entropy ange s ΔS Δ nr ln 1 For a reversble adabat expanson Δ 0, and Δ S 0 n deal gas undergong an rreversble adabat expanson an ave any postve value for ΔS up to te value gven n part (a) roblems: 9, 1, 0,, 4, 7, 9, 48, 54, K (a) 14 K Δ e 14 67% J, eng eng J 588 k Δt 1 s

2 1 n deal gas s taken troug a arnot yle e sotermal expanson ours at 50, and te sotermal ompresson takes plae at 500 e gas takes n 1 00 J of energy from te ot reservor durng te sotermal expanson Fnd (a) te energy expelled to te old reservor n ea yle and te net work done by te gas n ea yle 1 Isotermal expanson at 5 K Isotermal ompresson at K Gas absorbs 1 00 J durng expanson (a) 100 J 74 J 1 5 eng J 459 J O Δ 89 arnot refrg J per 1 J energy removed by eat Seton 5 Gasolne and esel Engnes 7 In a ylnder of an automoble engne, just after ombuston, te gas s onfned to a volume of 500 m and as an ntal pressure of a e pston moves outward to a fnal volume of 00 m and te gas expands wtout energy loss by eat (a) If 140 for te gas, wat s te fnal pressure? How mu work s done by te gas n expandng? (a) f f m f ( a) 44 ka f 00 m d Integratng, m ( 50 )( a)( m ) 1 f 00 m J

3 f 9 Δ S nrln Rln 576 J K ere s no ange n temperature for an deal gas FIG 9 0 (a) Frst, onsder te adabat proess : so lso or L ka 71 ka 150 L nr nr Now, onsder te sotermal proess : K 549 K K ka 100 L 40 L 150 L Next, onsder te adabat proess : 445 ka ut, from above lso onsderng te sotermal proess, 1 Hene, 1 w redues to 100 L Fnally, ka 875 ka 160 L State (ka) (L) (K) For te sotermal proess : Δ Ent n Δ L 40 L 150 L 160 L 160 ln 4 mol 814 J mol K 70 K ln kj 100 so nr For te adabat proess : 0 Δ Ent n ( ) 4 mol ( 814 J mol K ) ( ) K 498 kj and +Δ E nt 0+ ( 498 kj) 498 kj

4 For te sotermal proess : Δ Ent n Δ ln 4 mol 814 J mol K 549 K ln 50 kj 40 and nr Fnally, for te adabat proess : 0 Δ Ent n ( ) 4 mol ( 814 J mol K ) ( ) K kj and +Δ Ent kj kj roess (kj) (kj) Δ Ent (kj) e work done by te engne s te negatve of te work nput e output work gven by te work olumn n te table wt all sgns reversed eng s () eng 156 kj e 07 or 7% 658 kj 549 e or 7% 70 O 0100O 4 arnot yle or arnot effeny arnot yle 9 K K 68 K FIG 4 us, 117 joules of energy enter te room by eat for ea joule of w ork done

5 5 n deal refrgerator or deal eat pump s equvalent to a arnot engne runnng n reverse at s, energy s taken n from a old reservor and energy s rejeted to a ot reservor (a) Sow tat te work tat must be suppled to run te refrgerator or eat pump s Sow tat te oeffent of performane of te deal refrgerator s O 5 (a) For a omplete yle, Δ Ent 0 and ( ) 1 e ave already sown tat for a arnot yle (and only for a arnot yle) erefore, e ave te defnton of te oeffent of performane for a refrgerator, O 1000 J 48 Δ Sot 600 K Usng te result from part (a), ts beomes O J Δ Sold 50 K (a) Δ S Δ S +Δ S U ot old 0476 J K e eng e J 417 J () net 417 J 50 J 167 J 1Δ S U 50 K 0476 J K 167 J

6 *54 (a) For te sotermal proess, te work on te gas s ln ( a)( m ) ln J were we ave used and atm a 100 L m FIG 54 Δ a m J 0 and eng J 410 kj Sne s an sotermal proess, Δ Ent, 0 and For an deal monatom gas, R and J 5R nr R R 5 lso, nr R R 5 n Δ 100 R kj R so te total energy absorbed by eat s kj+ 608 kj 14 kj 5 5 n Δ nrδ Δ () J 101 kj (d) eng eng e J J or 89% (e) arnot engne operatng between ot 5060/R and old 1010/R as effeny 1 / 1 1/5 800% e tree-proess engne onsdered n ts problem as mu lower effeny

7 *55 t pont, nr and n 100 mol t pont, nr so t pont, ( )( ) 6 nr and t pont, ( ) nr so e eat for ea step n te yle s R 5R found usng and : FIG 55 n nr n 6 750nR n 6 6nR n 50nR (a) erefore, enterng + 105nR leavng + 850nR () tual effeny, e 0190 (d) arnot effeny, e e arnot effeny s mu ger

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