15 - 455 CHAPTER to THERMDDTNAMICS s as BflltllEPTS...

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Unformatted text preview: 455 CHAPTER to THERMDDTNAMICS s as BflltllEPTS '7" Note to Instructors: The numbering of the questions shown here reflects tltefacr that they are only a representative subset afrhe total number --j available airline. However: all afrire questions are avatiahieflrr assignment via an aatr'ae homelrvarir martagerrtear program Ettc'fl' as WileyPLUS or - r- - Section 15.3 The First Law of Thermodynamics Section 15.5 Heat Engines 1. The first law of thertnodynarnics states that the change so in the 13. a heat engine takesheat Q“ from a hot reservoir and uses u t-. intemai energy of a system is given by dbl = Q—W, where Q is this energy to perform weir]; W.Assuming that Q" eannothee’ the heat and W is the work. Both {2 and Wcan be positive or negative how can the efficiency of the engine be improved? {a} i - ': numbers. Q is a positive number if . and W is a positive work W; the heat QC rejected to the coid reservoir increases a. number if . la} the system loses heat; work is done by salt. {h} Increase the work W; the heat Q: rejected totheeolrl" the system (It) the system loses heat; work is done an the system voir remains unchanged. [c] Increase the work W; the _ {c} the system gains heat; work is done by the system {t1} the sys— rejected to the cold reservoir decreases as a resuit. {d} I - n- tem gains heat; work is done an the system work W; the heat {2: rejected to the cold reservoir remains one Swan“ [54 Thermal mm to} Decrease the work W: the heat 12.;- rejected In the cold .- . decreases as a result. 4. The drawing shows the es- pansion of three ideal gases. Rank the gases according to the work they do. iargest to smallest. {a} a. B. C {h} a and E {a tie]. C {e} H and C ta tie). a {ti} B, C. a {e} C, at, B IS. The pressure—volume graph shows three paths in which a gas expands from an initial state A to A a final state E. The change flUAHE in intemal energy is the same for each of the paths. Bank the paths according to the heat 1;? added to the gas. largest to smallest. to] l. 2. 3 [b] l. 3. 2 {E} 3’ L 3 {d} 3‘ L 2 {E} 3! 2‘ 1 Section 15.10 Refrigerator-man Conditioners. Section 15.5 Thermal Processes Using an Ideal Gas and Heat DE . . . it. a r‘ - r ' ' E An Ideal mflnflmmm gag expands lfiflmmmy I:er A m E! as the re rtgerator operates for a certatn time. and the work IE: graph shotvs. What can he said ahout this prtitress'i' {a} The gas does ma Emma] magi dunng “1'5"” '5 W = “i [in J” "ham? about the heat delivered to the room containing the ref keg" no work. [bi No heat enters or leaves ' " A . . 1 _ _,_i the £351 {c} The first law fir [harm-l} mmerm {a} The heat delivered to the room ts less titan lflfli} i. {b} “1 Section 15.9 Carnot’s Principle and the Cantor Engine 15. The three Cantot engines shown in the drawing operate i. and cold reservoirs whose temperature differences are lflfl K. ' :.I5._§. 1:. efficiencies of the engines. largest tosmallest. (and! engines -- g: sauteetficiency. tibia. B. [3 {ct list. C [d] C. that {e}fl-_ Pressure Pressure Volume dynamics mes hm apply man ifimhflrfi g / delivered to the room ts equal to thrill} l. {e} The heat dei -—-;.;__ . . a the room is greater than Jena 1. - mal process. {d} The tdeal gas law is g not valid during an isothermal process. Et Section 15.11 Entropy {E} “If”: '5 "‘3' Changf '“ if” Imam” u I 19. Heat is transferred from the sun to the earth via electro energy “Hm 535' “um waves {see Chapter 24}. Because of this transfer. the e '- 1d. a monatomic ideal gas is thermally insulated. so no heat can flow the sun . the entropy of the earih . between it and its surroundings. Is it possible for the temperature of the entropy of the sun-cards system —. {a} increases. 1+ gas to rise? {a} Yes. The temperature can rise if work is done by the gas. decreases {b} decreases, increases, increases {e} inc ' {bl Not The only way that the temperattue can rise is if heat is added to creases. increases {d} increases. decreases. increases {at I e'fi": the gas. {cl 1t’es. The temperature can rise if work is done an the gas. increases, decreases as “filcyPLUS or Wehrisriga. and those marked with the icon @ are presented in WileyF'LtJS using a guided tutorial format that provides enhanced interarn'vt'ryt See Preface firr additional details. 55m Solution is in the Student Solutions Manual. www Solution is available onllne at www.mleymonticollegeteatnell i This "m" mpmmfi ‘1 hmmfldim} “Ppflmhflfl' Baffin“ [5'3 The first Law at TherdeFMifi energy decreases by 4.2 Is: lfl“ 1. Determine each of es: 1. in moving out of a dormitory at the end of the semester. a lowing quantities [including the algebraic sign}: in} H" l'='- student does 1.6 K 104 .l of work. In the process. his internal to} Q ' PFtnEtLEtna 46? W' p"; '. ht a game nf tenth-“ill nutdnnrs en a cnld day, a player will be- 13. The pressure and sni- E— - " " gin tn feel exhausted sitar using apptexintately 31] at HP] ume cf a gas are changed .Tfla: 1n5 gm,- may. in» I: energy. {a} lI‘Etne player. dressed tnn lightly fur the alnng the path AREA. ur Wetssssr _I' , has tn lease the game after lnsing as 3r: 1&5 J at heat. Hnw Using the data shewn in the 3- earl: has he dune? {b} Annther player, wearing clauses that graph, detennine the wnrlt ;5 letter preteetinn against heat less, is able tn remain in the game dune {including the aige- g t uses ! w L, tn dn 2.] K H]: J at wnrit. What is the magnitude ed" the bruit: sign] in each segment E an}: mfi the _iI-: hehas Inst? {if the path: {E} A If! B. A system dues 164 1 at war}: en its enyirnnruent and gains “’1' B “1' Cr and {‘3} Cm"- .Iifij: in the pmeess. Find the change in the internal energy at “L Refflr m Mulliplb .' system and {hi the enyirnnrnent. Campy Example 3 m see A systeIn dues 4.3 is: Ht" 1 ni' wnrk, and lb 3*: it!" .i nf heat hnw the enucepts pertinent 3-5 3‘ 13—3 513 3"- 19—3 system during the precess. Find the change in the inter— In this prnblem are used. autumn, m3 :5 r a at the sysmm. The pressure at a gas re- Fmbfem r3 _;.'_ 1'lr'hen nne gallnn nf gasniine is burned in a car engine, Tum-“5 “Human! Whflfl [ht _ I malnfimflmflj energy is Emmi SHFFDEE that I'm 3,; ms 1 temperature, 1trnlume, and Internal energy. at the gas increase by [stress flaws directly into the surrnundings {engine black and +51“ C”- 1=40 ii “T3 [113* and 939 L Frsssflrslr- The mass at" the sea . sfitflm} in “1: fan“ flf hBaL ELI-J E J Ufuflflz IS 24.0 g, Ell-[l I125 Spflfllfifl hEflI Cflpflfiliy l5 *CDL DEIETI'HlflE {it the ear gu nne mile, hnw many miles can the car travel nn am: the pressure. 535? 15.. arm A system gains 15m 1 cf heat, while the internal energy at --;::g--- rnnles at an ideal menatnrnie gas are at a temperature at the system increases by 45m” and the 1Innlume deereasm by new n13. “than, 2433 J nf heat is added tn the gas, and 962 .l nf wnrit is Assume that the pressure is cnnstant and find its value. '-::.'. * 1 s _ . _ ' it' What H m: final Emmi-3mm “F “It gas *lfi. A piece at aluminum has a 1rnlunie nt' Isl is: ill—3 m3. The cnefii- l" “Emifiingr a wag“ “HF! 195:5 “JED kg {if wamr ihm‘fgh cient nl' 1rnlume expansinn int aluminum is ,3 = 69 It: lfl'fi HID)" '. i- erapuratren, the heat required tn eyapnrate the water Wmlflg The temperature at this abject is raised treat 20 tn 32ft 51:. Haw etisht 'ifiEF‘E deF- The Win-1‘ dflflfi l“ “fling Weight-“i is much war}: is dune by the expanding aluminum if the air pressure is it It? .l. ta} Assuming that the latent heat uf yapcriaatinn at" H}! y; mi Pa? ram is 2.42 E 10" .h’kg, find the change in the internal energy _ _ I i I -I_I fiflen {g} Hamming the minimum number flf "um, * 11'. earn wwwA mnnatcmtc ideal gas expands tsebarreatly. Using the 'T's . ' nf fwd [1 nunitiflnm camfie = 41 gg n that must ht first law at therrundynarnics, prnye that the heat :2 is pasture, an that In mplam The MES fir imfimal Energy it is impossible fnr heat tn flew nut nf the gas. “'13. Refer tn the drawing that ancnutpanies Prnblern 91. 1't‘lt’hen a sys- "f- '- :1“ manual Pm tem changes hem A tn 5 alnng the path shnwn en the pressure-versus- ynlutrte graph. it gains 2TH” ni' heat. What is the change in the W5 Imhflnc heanng, during which It gains 547i} 1 nl‘ inmmal {mag}, Dru-lg 53,531“? a pressure nf 3.45 is 105 Pa. Fnllnwing this, it experi- .'!;_'_: isuharic enrnpressinn that is alsn adiabatic, in which its ynl— “19. 1Water is heated in art npen pan where the air pressure is use at— §,-r-r-=~"" by E34 Its ill—3 in]. Find the tntal change in the ntnsphet'e. The water remains a liquid, which expands by a small a at" the gas fer this twu-step preeess. Be sure tn include amnunt as it is heated. Determine the ratie ef the werit dune by the =I- sign t+ er -} cf the tntal change in the internal energy. water tn the heat absnrbed by the water. 3.21-Eflllbt31' nfie is fired, the expanding gas item the Seth.“ 155 manual 1, Using an Ida] GE .. _.- = - t‘ tier creates a pressure behind the bullet. This pressure _ El fume that Flights the bullet [Waugh fl“: th The baml 2t]. Fire males at" a rnnnatnmic ideal gas expand adiabatically, and its .- “I : a. = Egg 3,; [gr 3 kg) has 3 Speed gr 3?” mfg afifir P33? dnne {including the algebraic sign} by the gas, and {It} the change ""'."-'.-I this barrel. Ignnre fi-ictinn and determine the average m “5 '"mmai “erg-'1'" 3i” “1‘ Expanding 335- 21. Illll Three rnnles at an ideal gas are cnrnpressed item 5.5 Is: IIIII‘I system gains flat} J at heat at a eenstant pressure at tu 2.5 a: hit"2 m3. During the enmpressiun, Ex] a: lit” 1 nt wart: is ' i" ' Fa. and its internal energy increases by 3991]]. What is the dune en the gas, and heat is returned tn keep the temperature at" the : sulume ef the system, and is it an increase er a decrease? gas cunstant at all times. Find {a} AU, {b} Q, and {c} the temper— white expanding under isnbaric cnnditinns, dnes arse J at slurs at the sea- unsure “f "if: E35 is “5 3": HF Paw 3"" “5 initial “alum 22. a Three males at nenn expand isntherrnally tn 1125!} frnln its “11- What 15 “‘3 final mlume flf “13 335? 0.1m n13. late the gas finws 4.75 is: lllr‘ .l nibeat. Assuming that seen 31 r n .- at a gas is changed ' is an ideal gas, find its temperamre. "-+ ljl'tt't'r bIEI‘WEflI't A and I E. DD- Ilflt flE-Elll'l‘lfl that l 'r_ _:'_':';_ __ . 3;}: ii} I :1: lalineisanisetherm urthat "_ " "r.."f*:"' , tn} Find the magni- l— ? '1' I I r' 1 L fur the WEB. flfld 2g” 194 24. The pressure nt'a mnnatnrnie idenl gas {-y = 3;} dnubles during an ' whether the want is adiabatic cempressinn. What is the ratie at the final uniume tn the ini- 2.n a»: 1n' 3 - tial ynlu nte'.JI 23. The temperature at” a munatemic ideal gas remains ennstant dur— ing a prncess in which 47ou nf heat flnws nut nt' the gas. Hnw much wnrk {including the prnper + nr — sign} is dune? 453 eHhs-rtsn 1e THERMDDvHAMIcs 25. earn A menatemic ideal gas has an initial temperature at‘ 4fl5 K. “‘32. Beginning with a pressure at 2.21:] it IEF Pa and a - This gas eitpands and dees the same ameunt el' werlt whether the «6.34 it: ltl‘fl m”, an ideal menatemic gas {y = undergees espansien is adiabatic er isethermal. When the eitpansien is adiau batic eitpansinn such that its final pressure is 3.1.5 It: lll" Pa. 1'5_ batic. the final temperature ef the gas is 245 K. What is the ratie el' native precess leading tn the same final state begins with an the final tn the initial velume when the eitpansien is isethermal? ceeling tn the final pressure, fellewed by an isebaric espan final velume. Hew much mere werlt dnes the gas de in the precess than in lhe alternative precess? 26. Heat is added isethennally lb 2.5 mei at a menatemic ideal gas. The temperature ef the gas is 43!} K. Hew much heat must be added I in make the velume ef the gas deuble? i“F33. item The drawing shuws an adiabatically iselated ---.—.i.___ divided initially inte twe identical parts by an adiabatic m Beth sides centain ene mele el' a menatemic ideal gas {y = with the initial temperature being 525 K en the left and 2?5 K en the right. The pani- tien is then aliewed te meve slewly [i.e.. quasi—statically) tti the right. until the pressures en each side at the partir . . lien are the same. Find the final tempers #23. @ An ideal gas ts taken threugh the three precesses murfl Emmi: [allefland {mfighl‘ {$43. B-t-C.andC—*A] shewn in the drawing. In gen— Sectien 15.15 Specific Heat Capacities “'31- fl“ Each [amass [hi-i inler‘ 34. Three nieles at a menatemic ideal gas are heated at as nal energy U ef the gas can - ume ef 1.5fl n13.Thc amtiurtl efbeat added is 5.24 it: ['33]. l shims-t bflflflilfifl lit-“ill Q ‘33“ be is the change in the temperature cf the gas? lb} Find the vi. , “(mm t“ “1' mm”??? fmm “it its intental energy. {c} Determine the change in pressure. - I 3:: Efrjnpfhifln E: daft: 35. earn The temperature ef 2.5 mel ef a menatemic -. : i: g g ” 35d K. The internal energy til this gas is deubied by the :.i-i‘i'_ three recesses shewn in the “Hume . . . - P heat. Hew much heat is needed when tt ts added at {a} c is. drawin . fill in the five missin entries in the l‘ellewin table. 3‘ g g urne and {h} eenstant pressure? EDGE” ‘5“ Q W 315. A menatemic ideal gas in a rigid centainer is heated In'-_ yr _1.. g {h} + 551 J (a) tti 279 K. by adding ssee J at heat. Hew many males at gas . . I) J a u-i c +sstis J {c} mass .1 ‘“ “1? “mm” ._ C —* A [d] {E} Fg-yqfl ] 37- 55m Heat is added te lWfl identical samples efa will; gas. in the first sample the heat is added while the velume , , _ is itept eenstant. and the heat causes the temperature te dse “’29. earn The drawing refers te ene mele ef a menatemic ideal gas In the Ecflmd gamma an idfimiwl amflum Dr heat it: addfld I and shews a precess that has feet steps. twe isebaric (A te H. C te D} pmsfium mm “m [ht mlume) m. “E gas is kept WHEEL 5p and twe isecherte [B tti t2“. fl tn A}. ICempletc the feilewtng table by much dues the tampflflmre {If [his Hamfile incmflfifi? - calculat' AU. W. and incind'n the a] ebric sitns fer e' h [if mg 91: I g E d b J “L 33. @ Under certslantrveltlrne cenditiens. 35th?! .1 ef the feur steps. . tn Le meles ef an tdeal gas. As a result, the temperature el' creases by ?5 K. Hew much heat weuld he required te cause u.- temperature change under eenstant—pressure cenditieas? flit" :4 Hit 3 same anything abeut whether the gas is menatemic. dist ' *27. Refer te Interactive Selutien 15.2? at www.wiley.cem!cellegei’ cutnell fer help in selvirig this preblem. A diesel engine dees net use spark plugs te ignite the fuel and air in the cylinders. Instead. the tern— perature required te ignite the fuel eccurs because the pistens cem- press the air in the cylinders. Suppese that air at an initial temperature at 1] “C is cetnpressed adiabaticaily te a temperature ef ass “C. Assume the air Id be an ideal gas fer which 'y = Find the cempres- sien ratie. which is the mile ef the initial velume tn the final velume. 52bit - II‘“-Eflfl.ifil-li isetherm _ . , . c 3 m C 39. Heat {2 is added la a menatemic ideal gas at eenstant.__ ADiZm-lt 'sethertn . . " -+. 2003p Emthem.‘ C in L) As a result. the gas dees werlt W. and the men QIW. I- 9 1'1? d aall]. A menatemic ideal gas expands at eenstant pressure. iii; Pemfinlege til” the heat being supplied te the gas is used In i . internal energy ef the gas? {b} What percentage is used the werlt et' eitpansien? *4]. Suppese that 3] .4 .1 cf heat is added le an ideal gaaTl'iEfl - :. at a eenstant pressure at laid it: lill‘l Fa while changing its i- “:7. Still it: ill"? te Elli] it lil'"1 mi. The gas is net menatemic. seam Cs = 1:1? dtfl net aPPlIi’. {it} Determine the citng in “it "i *3]. The pressure and velume _ _ . _ 1 -. . _ m. an idea: mflnflmmic gm; E ergy ef the gas. [Iii Calculate tts melar specthe heat capacity change freni it tti ti te C. as the drawmg shews. The 11LIfllnmmlsi, _ curved line between A and C . i5 A11 ififllht‘fifl. {a} DEEP _ “‘43. fine mele el' neen. a menatemic gas. starts but at ca --I='_..jg. mine the tetal heat fer the '1 “if _' we” standard temperature and pressure. The gas is heated at i; t; preeess and {bi state whether . unte until its pressure is tripled. then further heated at it :‘Hi j_' the flew ef heat is inte er ant {11233 J sure until its velume is deuhled. Assume that neen behavesas ef the gas. velume. m gas. Fer the entire precess. find the heat added tn the gas. 1ileltirne *30. ® A menatemic ideal gas (1: = if} is centained within a per— lectly insulated cylinder that is fitted with a mevahie pisten. The ini- tial pressure at the gas is [.50 2a: ll'lir Pa. The pisten is pushed sti as te cempress the gas. with the result that the Kelvin temperature deuhles. 1|What is the final pressure el‘ the gas? till. A menatemic ideal gas is heated while at a eenstant vb Lilli it lt’l‘i m3. using a ten-watt heater. The pressure f' creases by 52:} it Ill“1 Pa. Hew leng was the heater en? ' :.- 15.3 Heat Engines Heat engines taire input energy in the fnrrn nf heat. use snme nf that energy tn dn wnrlt. and exhaust the remainder. Eff-Ell y. a persnn can be viewed as a heat engine that takes an input al energy. uses snnte nf it In dn wnrir. and gives ntf the rest 'I Suppnse that a trained athiete can functinn as a heat engine _ _I _ _ El efliciency nf {H l. {a} What is the magnitude nf the internal [it that the athlete uses in nrder tn dn 5.! I. 10*] nf wnrir‘i' i' r: nnine the magnitude cf the heat the athlete gives nff. 51:3" -- Multiple-Cnncept Example If: deals with the cnncems that --':'i"m-- s tin this prnblem. In dning lfi 600 J nf wnrit. an engine "ii. nf heat. What is the etficiency cf the engine? :.lawnmnwer engine with an efficiency nf £122 rejects sane .i nf ' secnnd. What is the magnitude nf the wnrit that the engine -I u nae secnnd? 5g. tn a tune-up. the efficiency nf an autnmnbile engine in- 5.13%. Per an input heat nf i3ilfl .i. hnw much mnre wnrlr _' 'it engine prnduce after the tune-up than befnre'? _"'--'_ ® A 52-kg mnuntain climber. starting frnm rest. ciimbs a .‘ vertical distance nf are m. At aia tnp. she is again at teat. in her bndyr generates 4.] 3r: lfl‘i'l nf energy via metabnlic In ran. her bndy acts like a heat engine. the efficiency nf .5: given by Equatittn i5.“ as e = IWHQi—ii. When: iwi i5 [ha :_t:;..:.i-- at“ the wnrir she dnes and ligand is the magnitude cf the in- Find her efficiency as a heat engine. - mew Due tn design changes. the efficiency nf an engine in- fmnt [1.23 tn I142. Fnr the same input heat IQHI, these changes -§_: the wnrlt dnne by the mere efficient engine and reduce the £523 3tIfheat rejected tn the cnld reservnir. Find the ratin nf the heat 51-: tn the cnld reservnir fnr the imprnved engine tn that fnr the ' _.engine. -'engine has an efficiency e... The engine talres input heat nf 5:5;3H' IflHI frnm a hnt reservnir and delivers wnrlt nf magnitude 13' :‘hflfli rejected by this engine is used as input heat fer a sec- ;u which has an efficiency a; and delivers wnrit nf magni- The nverall efficiency nf this twn-engine device is the nf the tntai wnrk delivered {JWII + [WEI] divided by the flir- IQH! nf the input heat. Find an expressinn fnr the nverail 3w. e in terms nfe. and e3. . 15.9 |lilarnnt's Principle and the Garnet Engine Lyn n - nf its cnld reservnir is 2T5 it. Assuming that the temper- i " hnt reservnir remains the same. what must be the temper- .='-u- cnid reservnir in nrder tn increase the efficiency tn 32.0%? -=."_'-thnusand jnules nf heat is put intn a Camnt engine whnse .I reservnirs have temperatures nf 5m and 2th] K. respec- . much heat is cnnverted intn wnrit‘?r |Camel engine has an efficiency nf thitltl. and the tempen i.- cnid reservnir is 3T3 K. {a} Determine the temperature .- ir. is} it sssn 1 cf heat is rejected tn the cnld reser— arnnunt nf heat is put intn the engine? m engine nperates with a large bnt reservnir and a much i reservnir. As a result. the temperature nf the bet reservnir ._ rant whiie the temperature nf the cnld reservnir sinwly _ temperature change decreases the efficiency cf the en- 'i'i't from (MS. Find the ratin cf the final temperature cf the . tn its initial temperature. {:15 au- dnes IE Silt} .i nf wnrk and rejects 1555!?! J nf heat intn '-,j:_;,-_:.«' ir whnse temperature is 235 K. What wnuld be the .' 5;; 'ble mmperature nf the hnt reservnir? "in at engine nperates with an efficiency nt' Elflh when the *‘t‘il. earn The drawing (nnt tn scale} shnws PRDELEMS 439 Eli. @ Carnnt engine A has an efficiency ni‘ nan. and Carnnt en- gine B has an efficiency nf 0.31]. Beth engines utilise the same hnt reservnir. which has a temperature nf nit} K and delivers [Edit .I nf heat tn each engine. Find the magnitude nf the wnrir prnduced by each engine and the temperatures nf the cnld reservnirs that they use. 5?. Concept Simulattan 15.1 at unvwmiieymnmfcnllegefcutnell il- lustrates the cnncepts pertinent tn this prnbiem. A Carnnt engine np- erates between temperatures nf see and 350 K. Tn imprnve the efficiency nf the engine. it is decided either tn raise the temperature cf the hnt reservnir by 40 K nr tn lnwer the temperature cf the cnld reservnir by 4t] K. Which change gives the greatest imprnvement‘i Justify ynur answer by calculating the efiiciency in each case. *58. The hnt reservnir fer a l['a'arnnt engine has a temperature nf 3910 K. while the cnld reservnir has a temperature nf srn K. The heat input fnr this engine is 43th} .1. The Ib'r'fl-K reservnir alsn serves as the hnt reservnir fer a secnnd Carnnt engine. This secnnd engine uses the re- jected heat cf the first engine as input and extracts additinnai wnrk frnm it. The rejected heat frnm the secnnd engine gnes intn a reser- vnir that has a temperature nf 420 K. Find the tnfal wnrlt delivered by the ttvn engines. 1'59. item A pnwer plant taps steam superheated by gendterinai energy tn Stlfi K [the temperature cf the bet reservnir} and uses the steam tn tin wnrit in taming the turbine nf an electric generatnr.‘ The steam is then cnnverted baclt intn water in a cnndenser at 323 K. [the tempera~ ture nf the cnld reservnir). after which the water is pumped bacir dnwn intn the earth where it is heated again. The nntput pnwer (wnrir per unit time} nf the plant is 34 Dill} Irilnwatts. Determine {a} the maximum efficiency at which this plant can nperate and {b} the minimum arnnunt nf rejected heat that must be remeved frnm the cnndenser every twenty-fnur hnurs. *titt. Snppnse that the gasnline in a car engine burns at 63! “C. while the exhaust temperature [the temperature nf the cnld reservth is [39 “C and the nutdnnr temperature is 2? “C. Assume that the engine can be treated as a Camnt engine (a grnss nversimplificatien}. In an attempt tn increase mileage perfnrmance. an inventnr builds a secnnd engine that functinns between the exhaust and nutdnnr temperatures and uses the exhaust heat tn prnduce additinnai wnrtt. Assume that the in— ventnr's engine can alsn be treated as a Carnnt engine. Determine the ratin nf the tntai wnrlt prnduced by bnth engines tn that prnduced by the first engine alnne. the way in which the pres— sure and vnlume change fnr an ideal gas that is used as the wnrking substance in a lCarnnt dhgine. The gas begins at pnint a {pressure = Pa. vnlnme = VI) and expands isnthermaliy at temperature TH until pnint b (pressure = Pg. vnlume = Vb} is reached. During this expan- sinn. the input heat nf magnitude IQHI enters the gas frnm the hnt Pressure —~II- isntnerm temperature = TH Isntherm temp-stature 2 T1:- 4?“ cHAFTEH 15 THERMDDTHAMICE reseweir cf the engine. Then, frem point h tn pcint c (pressure = PE, *7}. Elm Review Cenceptual Example 9 hetbre attempting this - t-E'. velume = ital, the gas expands adiabaticaily. Next, the gas is lem. h. windew air cenditiener has an average ceefficient et' perfn- rt cempressed iscthertnally at temperature Te frem peint c in peint d ance cf it]. This unit has been placed en the fleet by the bed1 {pressure = P". velurne = ltd]. During this cempressien, heat ef mag— futile attempt te cue] the hedreem. During this attempt In it lfl‘l; nitude IQt-I is rejected te the celd reserveir ef the engine. Finally. the heat is pulled in the fmnt ef the unit. The mum is sealed and en t='_ : r gas is cempresscd adiabatically t’rern peint d te paint a. where the gas 33th] mel ef air. Assuming that the melar specific heat capacity aft-i; is back in its initial state. The everall precess a te b it} c te d is called air is C..- = git, determine the rise in temperature caused by t- : u :_.E a lClarinet cycle. Pruve fer this cycle that Iflelt iQHI = TCA'TH. the air cenditiener in this manner. “til. A nuclear-fueled eiectric pewer ptant utilizes a se—called “beil— “31 lfltflt‘itflw LfllffliflEtWfil'fl 15-1 at mtflfli'mmueflfl' ' "' ing water reacter." In this type ct" reacter. nuclear energy causes wa- Ehplfltfla Hm“! flPPWflCh it} Pmbteme such as this. Twe itilegrams cf utiliz- ter under pressure in bell at 235 {’C [the temperature ef the hut uid water at [l “C is put inte the freezer cernpartment {If a CHEW-'1 If" reserveir}. After the steam tie-es the werk ei turning the turbine at an friserater. The temperature at the eempartmeat ie -15 “C. and HT? electric generate-r, the steam is cenverted back inte water in a een- temperature flf the Hither-I i5 27 “(3- If the 431351 (If Elfififlififli Bflfll’flg ii denser at 4t} “C {the temperature at the ccld reserveir]. Te keep the ten cents per kiluwatt -heur. hew much dees it cest te make ttve j; cendenser at 4t] “C. the rejected heat must be carried away by seme slams at ice at '3 “C? meansn—fer example, by water item a river. The plant eperates at e73_ Hm m A gamut magenta]. “Hugh” hgflt fmm its ,I..-j_'_: threetfeurths ei its Carnet efficiency. and the electrical eutput pewer tgtj ac] m the mum at, eutside (2.1g Ty {a} Find the teeth t-_. ef the plant is [.2 .‘a It)? watts. a river with a water flew rate at Df Peyyflrmanee [If the mffiggyflmg th} Determine the magnittth=' Lil it lit"s kgtts is available in remeve the rejected heat frem the the; minimum wflrk needed m cm] 51m kg hf water {mm 2m]? plant. Find the number ef Celsius degrees by which the temperature fifl at: when it '15 ghee-d in the refrigerate“ " ef the river rises. 1 “T4. A |Camel engine uses het and ceid reserveirs that have t._'.- peratures ei' [£34 and 342 K, respectively. The input heat fer Sectien 15.10 Reirigerninrs, J-'-i..ir Cnnditiuners, engine is IQHI. The werlt delivered by the engine is used In t a and Heat Pumps ate a Camut heat pump. The pump remeves heat frem the ,4": reserveir and puts it inte a hut reserveir at a temperature .T'. '1' ameunt ei" heat remeved frem the 842-191 reserveir is alse the temperature T‘. til earn w The temperatures indeers and eutdeers are 299 and 312 K. respectively. A Carnot air cenditiener depesits 6.12 it 105 .l ui' heat nutrients. Hew much heat is remeved frem the heuse‘? 64. ® The inside {if a Carpet refrigeratcr is maintained at a temper“ ature cf arr K, white the temperature in the kitchen is see K. Using Beaten 15-11 Entrees 250D .I et werk. hevv much heat can this refrigerater remeve trem its as. Ceneitler three engine; that eeeh use lest} J er heat hem are inside cempartment'i' reserveir {temperature = 55D K}. These three engines reject bee-3;; celcl reserveir {temperature = 33C! K}. Engine I rejects 1 lit” at I; Engine II rejects 9% J et‘ heat. Engine III rejects see .I et' heat.- ei the engines eperates reversibly, and twe nperate irre .1lii lid. @ Twe Carpet air cenditieners. h. and B. are remeving heat Hewever. cf the twe irreversible engines: ene vielates the frem different reems. The eutside temperature is the same fer beth fly mmfigynamics and mum that exist Fm etteh ef the teams 30% K- The team serviced hr unit e is kept at a temperature tennine the total entrepy change {if the universe, which is the t “f 294-“ Kt While ‘1'“? {mm SEWiEFd hi“ “Hit 3 is 1051’" 31391-0 K The the entrepy changes at the hut and celd reserveirs. tJn the --: i133"- rEmDVEd fmm 51m” Tmm ‘5 433a 1- Fm" bum “miss find fl“ yeur calculatiens, identify which engine eperates reversibly, - “1 mhflimd’e Eff “1'3 “Kirk Equimd and it“? mflBflimdfl [if “it him 55' eperates irreversibly and ceuld exist. and which eperatesi - -- Pusiifld “Uifiidfl- and ceuld net exist. 67. A. CHI-HUT refrigerater i5 “Std in E kthhErl in the tempera- Tfil Heat Q flflwg gmntflneflugly fi'Dm fl mflnflir at K 'II ture is kept at 3m K. This refi'igeratcr uses 24] I cf werk te- remcve reserveir that has a jewet- tempetttture y: Emugfl ef the the, _ t 25d] 1 et‘ heat item the feed inside. What is the temperature inside flaw. thin}. Pet-tent hf? Q is muggy-Ed unavailable ft". warp . ,,;-_.-. “'13 rEfrigi-‘rmmr? Garnet engine eperates between the reserveir at temperature T tifl. A heat pump remeves 2091] J et' heat t'rem the eutdeers and de— 'FSFWDiT at 243 K‘ Find thfl mmifimur‘i T“ livers iii-ti} 1 cf heat te the inside ei‘ a heuse. {it} flew much werk Tr. sen-t Find the change in entrepy cf the Htfl melecuies -_ fleet the heat pump need? thi “stat it the eeeffieient at nerfene- {a} three itilegrams er ice melts inte water at are K see {I1}!- an'I [if the heat Pump? kilegran'ts cf water changes inte steam at 373 Iii. {cl (in the ef the answers te parts {a} and {b}, discuss which change t—_' mere diserder in the cellectien ef Hyfl melecules. - 65. at refrigerater eperates between temperatures cf 2% and 2T5 K. What weuld be its maximum ceefiicient ei' pet-termance':I I59. a Carpet heat pump eperates between an euttteer temperature at 2&5 K and an indeer temperature ef 298 K. Find its ceefficient et‘ perfermance. rs. er a celd day. 24 see J at heat leaks eut et' a heuse. side temperature is 2i “C, and the eutside temperature is -t What is the increase in the entrepy cf the universe that Iii less preduces? “it. The wattage et' a cemmercial ice maker is 225 W and is the rate at which it dries werlt. The ice maker eperates just like a refrigera- ter er an air cenditiener and has a ceefficient cf perfermance cf see. The water geing inte the unit has a temperature et' 11th “C, and *fl. Refer te Interactive autumn 1539 at wwwmrileyme n n i: the ice maker preduces ice cubes at tit} “C. Ignering the wrath cutnell to review a methcd by which this pruhlem can he needed te keep stered ice frem melting. find the maximum amuunt {a} After hilt} kg at“ water at Bit} “C is mixed in a perfect {in kg) ef ice that the unit can preduce in ene day ef centinueus with 3th} kg at ice at [it] "C, the mixture is allewed te reach -n=,-._ alteration. riuni. When heat is added in in remeved frern a selid er til-’1'- “17.. and specific heat ca- - ' ' I -' 'ELethechange in entrepy be sbuwn te be flS= ' 'p'Ti). where T.- and TE flit initial and final Kelvin [ii-r: res. Using this eit- and the change in ED- l‘bt melting. find the in entrepy tbat eccurs. iii: the entrepy ef the increase at decrease Itflfittii hi the mixing 2"-:- Give yeur reasening "in whether yeur answer 39'." {a} is censistent with -. erbere. _": Hews frem a reser- ass It tn a reserveir at _'= mutt FHflBLEMS rnele at" a menatemic ideal gas expands adiabatically tilt] J et‘ werlt. By hew many kelvins dues its temperature whether the change is an increase er a decrease. ._,| flnevhalt' mule at” a menatemic ideal gas abserbs i200 J at iii: 25011)] et‘ werlt is dene by the gas. {a} What is the tempera ne- ef the gas? [bi Is the change an increase er a decrease? __Ipie-Cencept Example s deals with the same cencepts as a dees. What is the efficiency ef a heat engine that uses an -."-:I uf 5.6 H [‘3‘1 J and rejects 1.3 at It)? J ef heat?I r a centained in a chamber such as that in Figure 15.4. the reginn eutside the chamber is evacuated and the tetal black and the mevable pisten is [35 ltg. When Eflfifl J at ii- inte the gas. the internal energy at the gas increases by - Ir: is the distance s threugb which the pisten rises? . _i_:u-' i has an efficiency ef {HS and requires ssce J ef input r a certain amennt et" WDTK. Engine 2 has an efficiency - performs the same ameunt ef Wfll'i-C. Hew much input heat and engine require? proeess eccurs in which the entrepy ef a system increases ' During the precess. the energy that beeemes unavailable rk is acre- {a} Is this precess reversible er irreversible? lessening. {b} Determine the change in the entrepy ef the 2.45;! tipie-Cencept Example ltJ te review the cencepts that are "ii'Ziu this prebient. The water in a deep undergreund well is celd reserveir ef a Camel heat pump that maintains the “in of a heuse at 311]] K. Te depesit la EDD J ef heat in the -':Iteat pump requires Ebb] ef werl-t. Determine the temper- well water. " air cenditiener maintains the temperature in a heuse at day when the temperature eutside is lit] K. What is the f _ uf perfennance ef the air cenditiener? neetTIcintAL PRDELEMS Ht 2?3 K thteugh a b.35-m cepper red with a cresswsectienat area ef 9.4 it Hi“ In2 {see the drawing]. The heat than leaves the 2?3-K reserveir and enters a Carnet engine. which uses part ef this heat te de werk and rejects the remainder in a third reserveir at l?3 K. Hew much at the heat leaving the 3?}K reserveir is rendered an- available fer deing werk in a peried ef it] min? a; *3]. @ An irreversible engine uperates between temperatures ef 352 and 314 K. it absurbs 1235 J at heat frem the bet reserveir and dues 254 J ef werlt. {a} What is the change £3..an in the entrepy ef the universe asseciated with the eperatien ef this engine? {is} If the engine were reversible. what weuld be the magnitude IWI ef the WDI'K it weuld have dene. assuming that it eperated between the same temperatures and abserbed the same heat as the irreversible engine? [c] Using the results at parts {a} and (bi. find the difference between the werit preduced by the re- versible and irreversible engines. 5H]. A Carnet engine has an efficiency ei' DAD. The Kelvin tempera- ture at its bet reserveir is quadrupled. and the Kelvin temperature ef its ceid reserveir is deubled. What is the efficiency that resuits frent these changes? 9]. learn in} Using the data presented in the accempanying pressure-versus-vetunte graph. estimate the magnitude ef the werlt dene when the system changes frum A re 3 tn 1': aleng the path sbewn. (b) Detennine whether the werit is dene by the system er en the system and. hence. whether the werit is pes- itive er negative. .. - . ......i. 1 . '3 |v I I] IJITIE' a.ea1e"3m3 $92. Refer tn the drawing in Preblem [2. where the curve between A and B is new an isetberm. em ideal gas begins at A and is changed aleng the heriaental line frent A te C and then aleng the vertical line item If te E. ta} Find the heat fer die precess ACE and {b} deter" mine whether it flews inte er eut ef the gas. *93. earn Suppese a menatemic ideal gas is centained within a verti— cal cyiinder that is fitted with a mevable pisten. The pisten is Frictien— less and has a negligible mass. The areaef the pisten is 3.14 a: til—1’ mi. and the pressure eutside the cylinder is Ltd] at it?1 Pa. Heat (2fl93 J J is remeved frern the gas. Threugb what distance dees the pisten tirep? "=94. An air cenditiener Iteeps the inside et' a hnuse at a temperature ei l'ElJfl “C when the eutdeer temperature is 33.0 "C. Heat. leaking inte the heuse at the rate ef ID EDDjeules per secend. is remeved by the air cenditiener. Assuming that the air cenditiener is a |Carpet air cenditiener. what is the werit per secend that must be dene by ,the electrical energy in erder te keep the inside temperature censtant? ...
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15 - 455 CHAPTER to THERMDDTNAMICS s as BflltllEPTS...

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