CHAPTER 14: Heat. Answers to Questions

Transcription

1 CHAPER : Hea Answers uesins. he wrk ges priarily in increasing he eperaure f he range juice, by increasing he average kineic energy f he lecules cprising he range juice.. When a h bjec wars a cler bjec, energy is ransferred fr he h bjec he cld bjec. eperaure des NO flw. he eperaure changes f he w bjecs are n necessarily equal in agniude. Under cerain circusances, hey can be equal in agniude, hwever. In an ideal case, he aun f hea ls by he warer bjec is he sae as he aun f hea gained by he cler bjec.. (a) Inernal energy depends n bh he nuber f lecules f aerial and he eperaure f he aerial. Hea will flw naurally fr he bjec wih he higher eperaure he bjec wih he lwer eperaure. he bjec wih he high eperaure ay r ay n be he bjec wih he higher inernal energy. (b) he w bjecs ay cnsis f ne wih a higher eperaure and saller nuber f lecules, and he her wih a lwer eperaure and a larger nuber f lecules. In ha case i is pssible fr bh bjecs have he sae inernal energy, bu hea will sill flw fr he bjec wih he higher eperaure he ne wih he lwer eperaure.. he waer will ca he plans, and s he waer, n he plan, is in cnac wih he cld air. hus as he air cls, he waer cls befre he plan des he waer insulaes he plan. As he waer cls, i releases energy, and raises he eperaure f is surrundings, which includes he plan. Paricularly if he waer freezes, relaively large auns f hea are released due he relaively large hea f fusin fr waer. 5. Because he specific hea f waer is quie large, i can cnain a relaively large aun f heral energy per uni ass wih a relaively sall increase in eperaure. Since he waer is a liquid, i is relaively easy ranspr fr ne lcain anher, and s large quaniies f energy can be ved fr ne place anher wih relaive sipliciy by waer. 6. he echanis f evaprain f he waer fr he is clh jacke requires energy (he laen hea f vaprizain), se f which will ce fr he inerir f he caneen. his reval f energy fr he inerir helps keep he inerir f he caneen cl. Als, he eal caneen is a gd heral cnducr, and s hea can ransfer fr he waer he clh jacke cl he waer. 7. Sea a 00 C cnains re heral energy han waer a 00 C. he difference is due he laen hea f vaprizain, which fr waer is quie high. As he sea uches he skin and cndenses, a large aun f energy is released, causing re severe burns. And he cndensed waer is sill a 00 C, and s re burning can ccur as ha waer cls. 8. Evaprain invlves waer lecules escaping he inerlecular bnds ha hld he waer geher in he liquid sae. I akes energy fr he lecules break hse bnds ( verce he bnding frces). his energy is he laen hea f vaprizain. he s energeic lecules (hse having he highes speed) are he nes ha will be able prvide he s energy (fr heir kineic energy) be able verce he bnding frces. he slwer ving lecules reain, lwering he average kineic energy and hus lwering he inernal energy and eperaure f he liquid. 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 0

2 Giancli Physics: Principles wih Applicains, 6 h Ediin 9. he paes will n ck faser if he waer is biling faser. he biling waer is he sae eperaure wheher i is biling fas r slw. 0. An rdinary fan des n cl he air direcly. I acually wars he air slighly, because he r used pwer he fan will exhaus se hea in he air, and he increase in average kineic energy f he air lecules caused by he fan blades pushing he eans he air eperaure increases slighly. he reasn fr using he fan is ha i keeps air ving. he huan bdy wars he air iediaely arund i, assuing he air is iniially cler han he bdy. If ha wared air says in cnac wih he bdy, hen he bdy will lse lile furher hea afer he air is wared. he fan, by circulaing he air, reves he heaed air fr clse he bdy and replaces i wih cler air. Likewise, he bdy is als cled by evaprain f waer fr he skin. As he relaive huidiy f he air clse he bdy increases, less waer can be evapraed, and cling by evaprain is decreased. he fan, by circulaing he air, reves he huid air fr clse he bdy and replaces i wih less huid air, s ha evaprain can cninue.. Even hugh he eperaure is high in he upper asphere, he densiy f gas paricles is very lw. here wuld be relaively very few cllisins f high-eperaure gas lecules wih he anial war i. Insead, he anial wuld radiae hea he rarified asphere. he eissiviy f he anial is uch greaer han ha f he rarified asphere, and s he anial will lse uch re energy by radiain han i can gain fr he asphere.. Snw, paricularly a very lw eperaures, has a lw heral cnduciviy because i has any iny air pckes rapped in is srucure i igh be described as fluffy. Since his fluffy snw has a lw heral cnduciviy, he snw will n cnduc uch hea away fr an bjec cvered in i.. We assue ha he we sand has been weed fairly recenly wih waer ha is cler han he sand s iniial eperaure. Waer has a higher hea capaciy han sand, and s fr equal asses f sand and waer, he sand will cl re han he waer wars as heir eperaures ve wards equilibriu. hus he we sand ay acually be cler han he dry sand. Als, if bh he we and dry sand are a a lwer eperaure han yur fee, he sand wih he waer in i is a beer heral cnducr and s hea will flw re rapidly fr yu in he we sand han in he dry sand, giving re f a sensain f having uched sehing cld.. An bjec wih high hea cnen des n have have a high eperaure. If a given aun f hea energy is ransferred in equal-ass saples f w subsances iniially a he sae eperaure, he subsance wih he lwer specific hea will have he higher final eperaure. Bu bh subsances wuld have he sae hea cnen relaive heir riginal sae. S an bjec wih high hea cnen igh be ade f aerial wih a very high specific hea, and herefre n necessarily be a a high eperaure. 5. A h-air furnace heas priarily by air cnvecin. A reurn pah (fen called a cld air reurn ) is necessary fr he cnvecive currens be able cpleely circulae. If he flw f air is blcked, hen he cnvecive currens and he heaing prcess will be inerruped. Heaing will be less efficien and less unifr if he cnvecive currens are prevened fr circulaing. 6. A ceiling fan akes re f a breeze when i is se blw he air dwn (usually called he frward direcin by fan anufacurers). his is he seing fr he suer, when he breeze will feel cling since i acceleraes evaprain fr he skin. In he winer, he fan shuld be se pull air up. his frces he warer air a he p f he r ve u wards he walls and dwn. he relcain f warer air keeps he r feeling warer, and here is less breeze effec n he ccupans f he r. 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he

3 Chaper Hea 7. When he garen is fluffed up, i will have he s air rapped in is srucure. he air has a lw heral cnduciviy, and he re he garen can be fluffed, he re air i will rap, aking i a beer insular. he lf value is siilar he R value f insulain, since he hicker he insulain, he higher he R value. he rae f heral cnducin is inversely prprinal he hickness f he cnducr, s a hick cnducr (high lf value) eans a lwer heral cnducin rae, and s a lwer rae f lsing bdy hea. 8. Fr all echaniss f cling, he rae f hea ransfer fr he h bjec he cld ne is dependen n surface area. he hea sink wih fins prvides uch re surface area han jus a slid piece f eal, and s here is re cling f he icrprcessr chip. A ajr echanis fr cling he hea sink is ha f cnvecin. Mre air is in cnac wih he finned hea sink han wuld be in cnac wih a slid piece f eal. here is fen a cling fan circulaing air arund ha hea sink as well, s ha heaed air can cninually be replaced wih cl air pre re cling. 9. When here is a eperaure difference in air, cnvecin currens arise. Since he eperaure f he land rises re rapidly han ha f he waer, he air abve he land will be warer han he air abve he waer. he war air abve he land will rise, and ha rising war air will be replaced by cler air fr ver he bdy f waer. he resul is a breeze fr he waer wards he land. 0. We assue ha he eperaure in he huse is higher han ha under he huse. hus hea will flw hrugh he flr u f he huse. If he huse sis direcly n he grund r n cncree, he hea flw will war he grund r cncree. Dir and cncree are relaively pr cnducrs f hea, and s he heral energy ha ges in he will say fr a relaively lng ie, allwing heir eperaure rise and hus reducing he hea lss hrugh he flr. If he flr is ver a crawlspace, hen he heral energy fr he flr will be heaing air insead f dir r cncree. If ha wared air ges ved away by wind currens r by cnvecin and replaced wih clder air, hen he eperaure difference beween he inside and uside will say large, and re energy will leave hrugh he flr, aking he inside f he huse cler.. Air is a prer cnducr f hea han waer by rughly a facr f 0, and s he rae f hea lss fr yur bdy he air is rughly 0 ies less han he rae f hea lss fr yur bdy he waer. hus yu lse hea quickly in he waer, and feel cld. Anher cnribuing facr is ha waer has a high hea capaciy, and s as hea leaves yur bdy and eners he waer, he eperaure rise fr he waer clse yur bdy is sall. Air has a saller hea capaciy, and s he eperaure rise fr he air clse yur bdy is larger. his reduces he eperaure difference beween yur bdy and he air, which reduces he rae f hea lss he air as well.. A hereer in he direc sunligh wuld gain heral energy (and hus shw a higher eperaure) due receiving radiain direcly fr he Sun. he eissiviy f air is sall, and s i des n gain as uch energy fr he Sun as he ercury and glass d. he hereer is reach is equilibriu eperaure by hea ransfer wih he air, in rder easure he air eperaure.. Preaure babies have underdevelped skin, and hey can lse a l f isure hrugh heir skin by evaprain. Fr a baby in a very war envirnen, like an incubar a 7 C, here will be a large evapraive effec. A significan increase in evaprain ccurs a incubar eperaures, and ha evaprain f isure fr he baby will cl he baby draaically. hus an incubar us have n nly a high eperaure bu als a high huidiy. Oher facrs igh include radiaive energy lss, bld vessels being clse he skin surface and s here is less insulain han a re aure baby, and lw fd cnsupin replace ls energy. 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he

4 Giancli Physics: Principles wih Applicains, 6 h Ediin. Shiny surfaces absrb very lile f he radiain ha is inciden n he hey reflec i back wards he surce. hus he liner is silvered reduce radiain energy ransfer (bh in and away fr he subsance in he hers). he (near) vacuu beween is w walls reduces he energy ransfer by cnducin. Vacuu is a very pr cnducr f hea. 5. he verall R-value f he wall plus windw is lwer han R and higher han R. he rae f hea ransfer hrugh he enire wall + windw area will increase, bu he al area and he eperaure A difference has n changed. hus, since, fr he rae increase eans he R- Reffecive value had drp fr is riginal value. Hwever, he rae f hea ransfer will be lwer han if he wall was ally glass, and s he final R-value us be higher han ha f he glass. 6. (a) () Venilain arund he edges is cling by cnvecin. () Cling hrugh he frae is cling by cnducin. () Cling hrugh he glass panes is cling by cnducin and radiain. (b) Heavy curains can reduce all hree hea lsses. he curains will preven air circulain arund he edges f he windws, hus reducing he cnvecin cling. he curains are re paque han he glass, prevening he elecragneic waves respnsible fr radiain hea ransfer fr reaching he glass. And he curains prvide anher layer f insulain beween he udrs and he war inerir f he r, lwering he rae f cnducin. 7. he heral cnduciviy f he wd is abu 000 ies less han ha f he aluinu. hus i akes a lng ie fr energy fr he wd flw in yur hand. Yur skin eperaure rises very slwly due cnac wih he wd cpared cnac wih he aluinu, and s he sensain f heaing is uch less. 8. he Earh cls priarily by radiain. he cluds ac as insulain in ha hey absrb energy fr he radiaing Earh, and reradiae se f i back he Earh, reducing he ne aun f radian energy lss. 9. he eergency blanke is shiny (having a lw eissiviy) s ha i reflecs a persn s radiaed energy back he, keeping he warer. Als, like any blanke, i can insulae and s reduce hea ransfer by cnducin. 0. Ciies siuaed n he cean have less eperaure exrees because he ceans are a hea reservir. Due cean currens, he eperaure f he cean in a lcale will be fairly cnsan during a seasn. In he winer, he cean eperaure reains abve freezing. hus if he air and land near he cean ge clder han he ceans, he ceans will release heral energy, deraing he eperaure f he nearby regin. Likewise, in he war seasns, he cean eperaures will be cler han he surrunding land ass, which heas up re easily han he waer. hen he ceans will absrb heral energy fr he surrunding areas, again deraing he eperaure. Sluins Prbles. he kcal is he hea needed raise kg f waer by C. Use he definiin find he hea needed. kcal 86 J kg 95 C 5 C.0 0 J kg C kcal 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he

5 Chaper Hea. he kcal is he hea needed raise kg f waer by C. Use ha definiin find he eperaure change. hen he final eperaure can be fund J kcal kg C 0.6C Final eperaure 0.6 C.0 kg 86 J kcal. (a) (b).86 0 J Cal.0 0 J Cal kwh 500 Cal.9 kwh 860 Cal (c) A 0 cens per day, he fd energy css $0.9 per day. I wuld be pracically ipssible feed yurself in he Unied Saes n his aun f ney.. Assue ha we are a he surface f he Earh s ha kg has a weigh f.0 lb. 0.5 kg 5 9 C kcal Bu lb F 0.5 kcal 86 J 0.5 kcal 055J kcal lb F kg C 5. he energy inpu is causing a cerain rise in eperaure, expressible as a nuber f Jules per hur per C. Cnver ha ass using he definiin f kcal J h kcal kg C. 0 kg h 5 C 86 J kcal 6. he waage raing is Jules per secnd. Ne ha L f waer has a ass f kg. kg kcal 86 J s.50 0 L 0C. 0 s.0 in L kg C kcal 50 J 7. he energy generaed by using he brakes us equal he car s iniial kineic energy, since is final kineic energy is 0. v s kcal. 0 kg 95 k h.0 0 kcal.6k h 86 J 0 8. he hea absrbed can be calculaed fr Eq. -. Ne ha L f waer has a ass f kg. c kg 6 6 L 86 J kg C 90 C 0 C.7 0 J L 9. he specific hea can be calculaed fr Eq J c c 5. kg.5 C 8.0 C 96 J kg C.0 0 J kg C 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he

6 Giancli Physics: Principles wih Applicains, 6 h Ediin 0. he hea absrbed by all hree subsances is given by Eq. -, c. hus he aun f ass can be fund as. he hea and eperaure change are he sae fr all hree c subsances. : : : : : : : : Cu Al HO c c c c c c Cu Al HO Cu Al HO : : 0.7 :.65 : he hea gained by he glass hereer us be equal he hea ls by he waer. c c glass glass eq i glass HO HO iho eq 5 g 0.0cal g C 9. C.6 C 5 g.00cal g C 9. C i HO i HO 0. C. he hea ls by he cpper us be equal he hea gained by he aluinu and he waer. c c c Cu Cu icu eq Al Al eq ial HO HO eq iho 0.5 kg 900J kg C 0.5 kg 90J kg C 85 C.0 C eq eq 0.85 kg 86J kg C eq 9. C. he hea ls by he hrseshe us be equal he hea gained by he irn p and he waer. Ne ha L f waer has a ass f kg. c c c she Fe ishe eq p Fe eq ip HO HO eq iho 0.0 kg 50J kg C 5.0 C 0.0 kg 50J kg C 5.0C 0.0C i she 86 C 90 C i she.5 kg 86 J kg C 5.0C 0.0C. he hea ls by he subsance us be equal he hea gained by he aluinu, waer, and glass. c c c c c x x ix eq Al Al eq ial HO HO eq iho glass glass eq iglass x c c c Al Al eq ial HO HO eq iho glass glass eq iglass x i x eq 0.05 kg 900 J kg C 0.65 kg 86 J kg C 0.07 kg 80 J kg C.5C.8 0 J kg C 0.5 kg 0 C 5.0 C 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 5

7 Chaper Hea 5. he hea us war bh he waer and he p 00 C. he hea is als he pwer ies he ie. P c c Al Al HO HO HO c c 0.6 kg 900 J kg C 0.75 kg 86J kg C 9C Al Al H O H O H O 5 s 7 in P 750 W 6. he hea released by he 5 gras f candy in he burning is equal he hea absrbed by he bb, calrieer, and waer. c c 5 bb cup Al HO HO 0.75 kg 0.6 kg 0. kcal kg C.00 kg.00 kcal kg C 5.5 C 5.0 C 88. kcal he hea released by 75 gras f he candy wuld be 5 ies ha released by he 5 gras kcal 0 kcal 0 Cal he hea ls by he irn us be he hea gained by he aluinu and he glycerin. c c c Fe Fe i Fe eq Al Al eq i Al gly gly eq i gly 0.90 kg 50 J kg C C kg 900 J kg C 8C 0.50 kg c 8C gly c gly. 0 J kg C 8. We assue ha all f he kineic energy f he haer ges in heaing he nail. KE 0 v c haer haer nail Fe 0 v 5.0 kg 6.5 s haer haer nail c Fe 0.0 kg 50J kg C 0. C.0 0 C 9. 65% f he riginal penial energy f he aluinu ges heaing he aluinu PE 0.65 gh c 0.65gh c Al Al Al Al s J kg C 0.C 0. (a) Since c and C, equae hese w expressins fr and slve fr C. c C C c (b) Fr.0 kg f waer: C c.0 kg 86 J kg C. 0 J C (c) Fr 5 kg f waer: C c 5 5 kg 86 J kg C.0 0 J C. he silver us be heaed he eling eperaure and hen eled. c L hea el fusin kg 0 J kg C 96 C 0 C 6.50 kg J kg J 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 6

8 Giancli Physics: Principles wih Applicains, 6 h Ediin. Assue ha he hea fr he persn is nly used evaprae he waer. Als, we use he hea f vaprizain a r eperaure (585 kcal/kg), since he persn s eperaure is clser r eperaure han 00 C. 80 kcal L 0.08 kg 0. kg 0 L vap L 585kcal kg vap. he xygen is all a he biling pin, s any hea added will cause xygen evaprae (as ppsed raising is eperaure). We assue ha all he hea ges he xygen, and nne he flask J L. kg vap L 5. 0 J kg vap. Assue ha all f he hea ls by he ice cube in cling he eperaure f he liquid nirgen is used bil he nirgen, and s nne is used raise he eperaure f he nirgen. he biling pin f he nirgen is 77 K 96 C. c L ice ice i ice f ice nirgen vap.0 0 kg 00 J kg C 0 C 96 C ice ice i ice f ice c nirgen L vap 00 0 J kg 6. 0 kg 5. he hea ls by he aluinu and 0 g f liquid waer us be equal he hea gained by he ice in waring in he slid sae, eling, and waring in he liquid sae. c c c L c Al Al ial eq HO HO iho eq ice ice el i ice fusin HO eq el kg 900J kg C.0C 0. kg 86J kg C.0C ice 5 00J kg C 8.5C. 0 J kg 86J kg C 7C kg 6. (a) he heaer us hea bh he biler and he waer a he sae ie. P c c Fe Fe HO HO c c 0 kg 50J kg C 80 kg 86 J kg C 8C Fe Fe HO HO 7 P 5. 0 J h 5.6h 5.6 h (b) Assue ha afer he waer sars bil, all he hea energy ges in biling he waer, and nne ges raising he eperaure f he irn r he sea. 5 L 80 kg.6 0 J kg HO vap HO vap 7 P L P 5. 0 J h hus he al ie is 5.6 h 6.07 h.7 h h 6.07 h 7. We assue ha he cyclis s energy is nly ging evaprain, n any heaing. hen he energy needed is equal he ass f he waer ies he laen hea f vaprizain fr waer. Ne ha L f waer has a ass f kg. Als, we use he hea f vaprizain a r eperaure (585 kcal/kg), since he cyclis s eperaure is clser r eperaure han 00 C. L 8.0 kg 585 kcal kg.7 0 kcal HO vap 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 7

9 Chaper Hea 8. he hea ls by he sea cndensing and hen cling 0 C us be equal he hea gained by he ice eling and hen waring 0 C. L c L c sea vap HO isea eq ice fus HO eq iice L c L c fus HO eq iice vap HO isea eq 5 sea ice kg.00 kg. 0 J kg 86J kg C 0C.6 0 J kg 86J kg C 80C 9. he hea ls by he aluinu and he waer us equal he hea needed el he ercury and war he ercury he equilibriu eperaure. c c L c Al Al ial eq HO HO iho eq Hg fusin Hg eq el c c L c Al Al i Al eq HO HO i HO eq fusin Hg eq el Hg 0.60 kg 900 J kg C 0.00 kg 86J kg C.80 C 5.06 C.00 kg 8J kg C 5.06 C 9.0 C. 0 J kg 0. Assue ha he kineic energy f he bulle was all cnvered in hea which eled he ice. v L bulle ice fusin v kg 50 s bulle ice 5 L fusin. 0 J kg kg 6.6 g. Assue ha all f he eled ice says a 0 C, s ha all he hea is used in eling ice, and nne in waring waer. he available hea is half f he riginal kineic energy v L skaer ice fusin skaer ice 5 L fusin v 5.0 kg 6. s. 0 J kg.7 0 kg.7 g. he kineic energy f he bulle is assued war he bulle and el i. v c L v c L Pb el i fusin 5 0J kg C 7 C 0 C J kg Pb el i fusin.6 0 s. he hea cnducin rae is given by Eq. -. ka l 60 C C 00J s C.0 0 8W Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 8

10 Giancli Physics: Principles wih Applicains, 6 h Ediin. he hea cnducin rae is given by Eq. -. ka l 5.0 C 5 C J s C W 5. (a) he pwer radiaed is given by Eq. -5. he eperaure f he ungsen is 7K 5K 98K. 8 e A W K K 95 W (b) he ne flw rae f energy is given by Eq. -6. he eperaure f he surrundings is 68 K. 8 e A W K K 68 K W 6. he disance can be calculaed fr he hea cnducin rae, given by Eq. -. he rae is given as a pwer (00 W = 00 J/s) C P ka l ka 0.J s C l P 00 W 7. his is a hea ransfer by cnducin, and s Eq. - is applicable. 0 C 0 C P ka 0.8J s C 6. 0 W l 0. If we assue ha all f he energy fr he ligh bulbs ges in his cnducin, hen: bulb. 0 W. bulbs and s bulbs are needed. 00 W 8. Eq. -7 gives he hea absrpin rae fr an bjec facing he Sun. he hea required el he ice is he ass f he ice ies he laen hea f fusin fr he ice. he ass is fund by uliplying he vlue f ice ies is densiy. L VL A x L 000 W f f f eacs A x L x L f f 000 W eacs 000 W e cs kg J kg 000 W cs s 0 h 9. Fr he eperaure a he jin reain cnsan, he hea flw in bh rds us be he sae. Ne ha he crss-secinal areas and lenghs are he sae. Use Eq. - fr hea cnducin. h iddle iddle cl k A k A Cu Al l l Cu Al k k 80 J s C 50 C 00 J s C 0.0 C Cu h Al cl iddle k Cu k Al 80 J s C 00 J s C.6 0 C 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 9

11 Chaper Hea 0. (a) he crss-secinal area f he Earh, perpendicular he Sun, is a circle f radius R, and Earh s has an area f R. Muliply his area ies he slar cnsan ge he rae a which he Earh Earh is receiving slar energy. 6 7 R slar cnsan W.7 0 W Earh (b) Use Eq. -5 calculae he rae f hea upu by radiain. e A / A 78 K 5 C J s W K /. his is an exaple f hea cnducin, and he eperaure difference can be calculaed by Eq. -. Pl 95 W.0 0 P ka 0C l ka 0.8 J s C.0 0. he cnducin raes hrugh he w aerials us be equal. If hey were n, he eperaures in he aerials wuld be changing. Call he eperaure a he bundary beween he aerials x. l l x x k A k A ; x x l l k A k A Add hese w equains geher, and slve fr he hea cnducin rae. l l l l k A k A k k A x x A A l l R R k k his is abu Was. F 0 f Bu h. 0 Bu h 9 f h F Bu. (a) We assue ha. he cnducin raes hrugh he hree aerials us be equal. If hey were n, he eperaures in he aerials wuld be changing. Call he eperaure a he bundary beween he air and he lef-s piece f glass,, and he eperaure a he x bundary beween he air and he righ-s piece f glass,. Wrie he cnducin rae fr y each aerial separaely, and slve fr he eperaure differences. x y x y k A k A k A l l l l l l ; ; x y x y k A k A k A Add hese hree equains geher, and slve fr he hea cnducin rae. 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 50

12 Giancli Physics: Principles wih Applicains, 6 h Ediin l l l l l l k A k A k A k k k A x y x y A l k l k l k (b) Fr n aerials placed nex ne anher, he expressin wuld be A A l k R n n i i i i i. his is an exaple f hea cnducin. he hea cnduced is he hea released by he eling ice, L. he area hrugh which he hea is cnduced is he al area f he six surfaces f ice fusin he bx, and he lengh f he cnducing aerial is he hickness f he Syrfa. We assue ha all f he hea cnduced in he bx ges in eling he ice, and nne in raising he eperaure inside he bx. he ie can hen be calculaed by Eq. -. L l ka ice fusin l ka 5.0 kg. 0 J kg J s C C.5 0 s h 5. he hea needed war he liquid can be calculaed by Eq. -. c 0.0 kg.00 kcal kg C 7 C 5 C 6. kcal 6. C 6. Since 0% f he hea generaed is ls up he chiney, he hea required hea he huse is 70% f he hea prvided by he cal MJ.0 0 MJ MJ kg kg kg MJ kg 7. he hea released can be calculaed by Eq. -. find he ass f he waer, use he densiy (f pure waer). c Vc kg J kg C C 0 J 8. We assue ha he iniial kineic energy f he bulle all ges in heaing he wd and he bulle. v c c v i bulle i bulle lead lead wd wd wd c c bulle lead wd wd bulle 0.05 kg 0J kg C.05 kg 700J kg C 0.00C 0.05 kg 69 s 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 5

13 Chaper Hea 9. (a) Use Eq. -5 fr al pwer radiaed. e A e 8 8 R W K K Sun W. 0 W (b) Assue ha he energy fr he Sun is disribued syerically ver a spherical surface wih he Sun a he cener. P A W.0 0 W. 0 W RSun-Earh he eperaure rise can be calculaed fr Eq kcal h.00 h c c 70 kg 0.8kcal kg C.8C 5. We assue ha he saring speed f he bulder is zer, and ha 50% f he riginal penial energy f he bulder ges heaing he bulder. gh s 0 PE gh c arble c 860 J kg C arble 0.80C 5. he hea ls by he lead us be equal he hea gained by he waer. Ne ha L f waer has a ass f kg. c c Pb Pb i Pb eq HO HO eq i HO. kg 0 J kg C 8.0 C.5 kg 86 J kg C 8.0C i Pb i Pb 08 C 0 C 5. Use he hea cnducin rae equain, Eq. -. (a) (b) ka l ka l C 0 C 0.05J s C. 6 W.5 0 C 0 C J s C W 5. We assue ha all f he hea prvided by eablis ges in evapraing he waer. Fr he energy required fr he evaprain f waer, we use he hea f vaprizain a r eperaure (585 kcal/kg), since he runner s eperaure is clser r eperaure han 00 C. 950 kcal kg H O.5 h. kg h 585 kcal 55. Fr an esiae f he hea cnducin rae, use Eq. -. ka 7 C C 0.J s C.5.5W 0 W l.0 0 his is nly abu 0% f he cling capaciy ha is needed fr he bdy. hus cnvecin cling is clearly necessary. 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 5

14 Giancli Physics: Principles wih Applicains, 6 h Ediin 56. (a) calculae hea ransfer by cnducin, use Eq. - fr all hree areas walls, rf, and windws. Each area has he sae eperaure difference. ka ka ka cnducin l l l walls rf windws 0.0J s C 0 0.J s C c 0.8 J s C W.6 0 W (b) he energy being added us bh hea he air and replace he energy ls by cnducin, as cnsidered abve. he hea required raise he eperaure is given by Eq. -, c. he ass f he air can be fund fr he densiy f he air ies is raise air air waring ep vlue. he cnducin hea lss is prprinal he eperaure difference beween he inside and uside, which varies fr 0C C. We will esiae he average eperaure difference as 6.5 C and scale he answer fr par (a) accrdingly. Vc added raise cnducin air air waring ep (c) We assue a nh is 0 days. 0.9 gas nh gas kg kcal 86 J cnducin C kg C kcal J 6.5 C s. 0 J cnducin cnducin 5 8 s C.6 0 J $ s C h 600 s nh d h kg $ J kg J s 0 d J 57. (a) he bulle will gain an aun f hea equal 50% f is lss f kineic energy. Iniially assue ha he phase f he bulle des n change, s ha all f he hea causes a eperaure increase. i f 0 s 60 s v v c C i f Pb cpb 0 J kg C (b) he final eperaure f he bulle wuld be abu 6 C, which is n abve he eling eperaure f lead, which is 7 C. hus nne f he bulle will el. 58. (a) he rae f absrbing hea fr an bjec facing he Sun is given by Eq. -7. he rise in eperaure is relaed he absrbed hea by Eq. -. We assue ha all absrbed hea raises he eperaure f he leaf. v v 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 5

15 Chaper Hea c ea 000 W cs 000 W c 000 W eacs 0 c.c s c 86 J.5 0 kg 0.80 kcal kg C kcal (b) We assue ha he rae f hea lss by radiain us equal he rae f hea absrpin f slar energy. Ne ha he area f he leaf ha radiaes is wice he area ha absrbs hea energy. 000 W ea cs e A absrb radiae Slar heaing radiain / / 000 W cs 000 W 9 K 8 57 K 8 C W K his is very h, which indicaes ha he leaf us lse energy by her eans han jus radiain. (c) he leaf can als lse hea by cnducin he cler air arund i; by cnvecin, as he wind cninually ves cler air ver he surface f he leaf; and evaprain f waer. 59. he rae f energy absrpin fr he Sun us be equal he rae f lsing energy by radiain plus he rae f lsing energy by evaprain if he leaf is ainain a seady eperaure. he laen hea f evaprain is aken be he value a 0 C, which is 50 kj/kg. Als ne ha he area f he leaf ha radiaes is wice he area ha absrbs hea energy. Slar heaing radiain evaprain 000 W ea cs e A HO ea absrb radiae absrb 000 W cs L evaprain L HO evaprain W W K 08 K 9 K J kg 6. 0 kg s.g h 60. Assue ha he final speed f he eerie, as i cpleely els, is 0, and ha all f is iniial kineic energy was used in heaing he irn he eling pin and hen eling he irn. v c L i Fe el i fusin v c L i 5 50 J kg C 808 C 5 C.89 0 J kg Fe el i fusin.5 0 s 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 5

16 Giancli Physics: Principles wih Applicains, 6 h Ediin 6. (a) We cnsider jus he 0 f crus iediaely belw he surface f he Earh, assuing ha all he hea fr he inerir ges ransferred he surface, and s i all passes hrugh his 0 layer. his is a hea cnducin prble, and s Eq. - is apprpriae. he radius f he 6 Earh is abu ka l.0c 86, 00 s ka 0.80 J s C R day inerir Earh l J. 0 J 0 day (b) he crss-secinal area f he Earh, perpendicular he Sun, is a circle f radius s has an area f Earh R, and Earh R. Muliply his area ies he slar cnsan f 50 W ge he aun f energy inciden n he Earh fr he Sun per secnd, and hen cnver energy per day. hus Sun inerir Sun R 86, 00 s 50 W day.9 0 J day Earh J.9 0 J , r. 0 Sun inerir. 6. Assue ha he lss f kineic energy is all urned in hea which changes he eperaure f he squash ball. i f s s 0.C ls i f KE v v c v v c 00 J kg C 6. he hea gained by he ice ( el i and war i) us be equal he hea ls by he sea (in cndensing and cling). L c 0 L c 00 C eq F HO eq V HO eq L V L HO F 60kJ kg kj kg 50 C 50 C 80 C c.86kj kg C his answer is n pssible. Because his answer is high, he sea us n all cndense, and nne f i us cl belw 00 C. Calculae he energy need el a kilgra f ice and war i 00 C. L c 0 kg kj kg.86 kj kg C 00C 75.6 kj F HO eq Calculae he ass f sea ha needs cndense in rder prvide his uch energy kj L 0.kg V L 60 kj kg V hus ne-hird f he riginal sea ass us cndense liquid a 00 C in rder el he ice and war he eled ice 00 C. he final ixure will be a 00 C, wih / f he al ass as sea, and / f he al ass as waer. 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 55

17 Chaper Hea 6. he bdy s eablis (bld circulain in paricular) prvides cling by cnvecin. If he eablis has spped, hen hea lss will be by cnducin and radiain, a a rae f 00 W, as given. he change in eperaure is relaed he bdy s hea lss by Eq. -, c. P c P c 70 kg 70 J kg C 6.6 C 5.6 C 00 W 00 s 0 in 65. (a) he aun f hea energy required is given by Eq. -. L f waer has a ass f kg. c kg 86 J kg C 50 C 0 C J. 0 J (b) he hea energy is he pwer inpu ies he ie. P P J W 60s. 0 s 5 in 66. We assue ha he ligh bulb eis energy by radiain, and s Eq. -6 applies. Use he daa fr he 60-W bulb calculae he prduc e A fr he bulb, and hen calculae he eperaure f he 50-W bulb. e A e A 60 W 60 W 60 W r 60 W r W 7 65 K 7 8 K W K 9 e A 50 W 50 W r 50 W 50 W r 9 e A / W W K 9 K / 85 K C 0 C 005 Pearsn Educain, Inc., Upper Saddle River, NJ. All righs reserved. his aerial is preced under all cpyrigh laws as hey currenly exis. N prin f his aerial ay be reprduced, in any fr r by any eans, wihu perissin in wriing fr he 56