apter 22 Heat Engnes, Entropy, and te Seond Law o erodynas 1. e Zerot Law o erodynas: equlbru -> te sae 2. e Frst Law o erodynas: de d + d > adabat, sobar, sovoluetr, soteral 22.1 Heat Engnes and te Seond Law o erodynas as denton o e: eng e 1 (or derent engnes you ay derve te dependene o e by oter paraeters, e.g. or ) e seond law o terodynas (eat-engne stateent): It s possble to onstrut a eat engne tat, operatng n a yle, produes no eet oter tan te adsorpton o energy ro a reservor and te perorane o an equal aount o work. (Kelvn Stateent) You an not nd te eeny e 1 ( 0) o an engne. de d + d or one dreton o terodyna proess, te energy s onserved, or a yle o terodyna proess, you dentely lose soe energy or work, onvertng to eat -> rreversble Exaple: e Eent o an Engne n engne transers 2.00 x 10 3 J o energy ro a ot reservor durng a yle and transers 1.50 x 10 3 J to a old reservor. (a) Fnd te eeny o te engne. (b) How u work does te engne do n one yle? 1.5 3 e 1 25%, ( 2 1.5) 10 J 2 1
22.2 Heat Pups and Rergerators Hot reservor Heat pup old reservor e eat and work transerred to te syste are and, respetvely. energy transerred out o te pup s. e eat e OP o a rergerator or o a eat pup used n oog yle s OP( oog _ ode), OP te greater te OP, te better te rergerator. arnot, e seond law o terodynas (rergerator stateent): It s possble or a rergerator n a yle to produe only te eet o extratng eat ro a old objet and rejet te sae aount o eat to a ot objet. (lausus Stateent) lausus stateent o te seond law: Energy does not low spontaneously ro a old objet to a ot objet. 22.3 Reversble and Irreversble Proesses ere are any rreversble proesses tat annot be desrbed by te eat-engne or rergerator stateents o te seond law, su as a glass alg to te loor and breakng or a balloon poppng. However, all rreversble proesses ave one tng n oon te syste plus ts surroundngs oves toward a less ordered state. Irreversble proess: tey our naturally n only one dreton -> energy nu? lted eeny o a eat engne -> a ane apable o ontnuously onvertng nternal energy n a yl proess opletely to oter ors o energy annot be onstruted. reversble proess: one or w te syste an be returned to ts ntal ondton 2
along te sae pat and or w every pont along te pat s an equlbru state. general araterst o a reversble proess s tat no dsspatve eets (su as turbulene or rton) tat onvert eanal energy to nternal energy an be present. rreversble proess: a proess tat does not satsy tese requreents, ost natural proesses are known to be rreversble. Real proesses proeed n a preerred dreton rreversble. 22.4 e arnot Engne 1824, a Fren engneer Sad arnot desrbed a teoretal engne e net work done by a workng substane taken troug te arnot yle s te greatest aount o work possble or a gven aount o energy suppled to te substane at te upper teperature. 1. ssue an deal gas 2. yder walls and te pston are terally nonondutve. e proess: -> soteral adsorbs energy and does work at, -> adabat, teperature ro to and does work, ->D soteral expels energy and te work done on te gas s D at, D-> adabat, teperature ro to and te work done on te gas s D, 3
ds, ds e 1 e eeny s zero. e eeny s 1 0. ll real engnes are less eent tan te arnot engne beause tey all operate rreversbly n order to oplete a yle n a bre te perod. Exaple: In te proess o te arnot yle (1 ole o deal gas wt γ 1.4), te ntal pressure s 1 X 10 5 Pa, te volue s expanded ro 0.02 3 to 0.04 3, (a) How u energy o eat ( ) does te gas absorb? (b) In te proess, te volue s expanded to 0.06 3, wat s? P 240. 55K nr 2000 04 0., Pd d 2000[ ] 0.02 1386 γ 1 0.4 0.04 240.55 204. 5 0.06 0.04 0.02 K y? nr d nr D D nr d nr D ( / ) ( / ) D γ 1 γ 1, ( γ 1) 1/ ( γ 1) 1/ D ( / ) ( / ) D 4
at an we obtaned ro te P dagra or te arnot yle? proess (soteral at a teperature o ): P nr P, S Pd nr d proess (adabat, teperature varaton ro to ) P P, we know, we an alulate γ γ D proess (soteral at ) D nr d D proess (adabat, ro to ) ork done n te D yle? 5
22.5 Gasoe and Desel Engnes Gasoe and Desel Engne P dagra or te Otto yle P dagra or an deal desel engne Let: n, n Rgt: n, n P 6
22.6 Entropy a state varable: entropy S te arnot engne:, + 0, 0 ts equaton s true or any reversble yles dr onsder any nntesal proess, ds te eat s to be deterned along a reversble proess en eat s absorbed by te syste, d r s postve and ene te entropy nrease. en teral energy s expelled by te syste, d r s negatve and te entropy derease. work eatng eatng Entropy and te seond law o terodynas e entropy o te Unverse nreases n all natural proesses. oal tat we onsue n our le. onsder te ol or S ds d r reversble and adabat proess -> sentrop proess S 0 d r 0 Exaple: ange n Entropy Meltng sold substane as a latent eat o uson L elts at a teperature. alulate 7
te ange n entropy wen a ass o ts substane s elted. L S 22.7 Entropy ange n rreversble proess: Isoteral expanson gves S > 0. e total entropy o an solated syste tat undergoes a ange annot derease. 1. Entropy o an deal gas: drev ds, dent drev + d drev Pd 3 E nr de n d 2 de + Pd ds n d + Pd nr n d + d d S ds n + nr d n 2 + nr 1 2 1 2. Entropy ange n an soteral expanson: S ds n S nr 2 1 2 + 2 nr nr 1 1 2 1 3. Entropy ange n a ree expanson: Denton o ree expanson: 0 at walls, 0 at walls, E E > de 0 or te wole syste, no net energy s delvered to te syste troug te wall, d + d 0 or te syste S 1 1 d Pd nr 8
Exaple: Suppose tat 1 ol o an deal gas undergoes a ree expanson to our tes ts ntal volue. (a) alulate te entropy anges. (b) alulate te entropy ro tat o rostates. S R ( ) R 4 S S S k k R 4 Entropy ange n a onstant-pressure proess: d n d, P ds d n P d Entropy ange n an nelast ollson: rev S g Entropy ange n eat onduton ro one reservor to anoter: S H Entropy ange n a arnot yle: H S H S H 22.8 Entropy on a Mrosop Sale at s entropy n rosop vewponts? at s nternal energy? e portane o entropy grew treendously as te eld o pyss alled statstal eans. Entropy solated systes tend toward dsorder, an entropy s a easure o tat dsorder. e two des syste: te arostate orresponds to te su o nubers o te two des. e low probablty arostate o 2 as only one possble rostate o 1 1. e g probablty rostate o 7 as sze possble rostates. Hg probablty arostates are dsordered arostates, and low probablty arostates are ordered arostates; 9
10 ll pysal proesses tend toward ore probable states or te syste and ts surroundngs. e ore probable state s always one o ger dsorder. e entropy s a easure o te dsorder o a state. Entropy an be dened usng te arosop onepts o eat and teperature. Suppose te gas oupes volue ntally and ten expands to ll. ssue ea oleule oupes a rosop volue. e nuber o possble rostates or oleules s P P nr k k k k S S S Entropy s a easure o rosop dsorder.