1PHYS1001Physics 1REGULARModule 2 Thermal PhysicsHEAT ENGINEap06/p1/thermal/ptG_engines.ppt2HEAT ENGINES AN RE!RIGERAT"RSHeat engines: Entropy (#20$1%&'(#20$2%&') #20$) %&*2+ Heat engines: Carnot cycle (#20$&%&*, #20$'%&-0+Internal Combstion Engines: !tto " #iesel Cycles(#20$(%&'*+ $e%rigerators (#20$,%&*0+ $e%erences:&ni'ersity (hysics 12th e) *ong " +ree)man,Heat engine: )e'ice that trans%orms heat partly into -or. (mechanical energy/ by a -or.ing sbstance n)ergoing a cyclic process. 0HEAT ENGINEHot reservoir (heat source) THCold reservoir (heat sink) TCQHQCWuseful mechanical work outputDissipative losses friction, turbulenceCyclic process: W = |QH| - |QC|Engine working substancepetrol engine 1 hot e2hast gases 3 cooling system petrol engine: %el 3 air W > 0|QH| = |W|+|QC|45ll heat engines absorb heat QH %rom a sorce at a relati'ely high temperatre (hot reser'oir H/6 per%orm some -or. W an) re7ect some heat QC at a lo-er temperatre (col) reser'oir C/.+irst 8a- %or a cyclic process: ! = 0 = Qnet W Qnet = |QH| - |QC| = W9hermal e%%iciency6 e represents the %raction o% QH that is con'erte) to se%l -or..HCHQQQWe = = 16Pro.lem /Y 0 !E1am%le 20$1+5 large trc. is tra'elling at :: .m.h11. 9he engine ta.es in 10 000 ; o% heat an) )eli'ers 2 000 ; o% mechanical energy per cycle. 9he heat is obtaine) by brning petrol (heat o% combstion "co#b < 4.010= ;..g11/. 9he engine n)ergoes 24 cycles per secon). #ensity o% petrol< =00 .g.m1,(a/ >hat is the thermal e%%iciency o% the heat engine?(b/ Ho- mch heat is )iscar)e) each cycle?(c/ Ho- mch petrol is brnt per hor (.g.h11/?()/ >hat is the petrol consmption o% the trc. in 8/100 .m?=@oltionI S E Ev = 88km.h-1 QH = 1.0104!c"cle W = #10$!c"cle"co#b = %.010&.k'-1 f = #%c"cles.s-1(a)e = $e = W % QH = (#10$) ! (1.0104) = 0.#0 = #0*sensi+le(+)QC = ,|QH| - |QC| = W|QC| = 8.010$!c"cle:(c)QH = 1104!c"cle-H !t = (#%)(1104).s-1 = #.%10%.s-1 "C = %.010&.k'-1QH!t = %t' "co#b#%t = (QH!t )! "co#b = (#.%10% ) ! (%.010&) = %10-$k'.s-1#%t= (%10-$)(.0)(.0) = 18 k'.h-1(/)fuel consumption = ,0!100 kmv = 88 km.h-1v = (!t t = ,h( = 100km t = ( ! v = 100 ! 88h = 1.1$.4hmass use/ tra1elin' 100 km # = (#%t't = (18)(1.1$.4) = #0.4%%k' = # )10$0 = 1m$1olume use/ in tra1elin' 100 km )= # ! = (#0.4%% ! &00)m$ = 0.0#2# m$ = #2.# 0petrol consumption = #2.# 0!100 kmAHot $eser'oirQHEngine@rron)ingsWCan a heat engine be 100B e%%icient in con'erting heat into mechanical -or. ?>hy )oes this engine 'iolate the @econ) 8a- ?QC= 010ENTROPY consi/erations3*(en'ine) = 0 c"clic process*(surroun/in') = 0no heat transfer to surroun/in's*(hot reser1oir) 4 0heat remo1e/*(total) 4 01iolates 5econ/ 0aw5ll heat engines (heat to -or./: e%%iciency6 e C 111Hot reser'oirCol) reser'oirEngine srron)ingsQHQCW12*(hot reser1oir) = - |QH|! H*(col/ reser1oir) = + |QC|! C5(en'ine) = 0(c"clic process)*(surroun/in's) = 0(no heat transfer to surroun/in's)*(total) = - |QH|! H + |QC|! C 6seful work can onl" +e /one if *(total) 0 | QH| / TH | QC | / TC1,5n i)eal engine e.g. Carnot Cycle* = 0 | QH ! H | = | QC ! C |e = W ! QHW = |QH| - |QC|e = (|QH| - |QC| ! QH)= 1 - |QC| ! |QH|e = 1 C ! H4 19his is the absolte ma2 e%%iciency o% a heat engine@a)i Carnot (1:20/+renchmanD!9E: 5ll heat (QH " QC/ e2changes occrre) isothermally in calclating the e%%iciency e = + C% H 102ARN"T 2Y2LEHeat engine -ith the ma2imm possible e%%iciency consistent -ith 2n) la-.5ll thermal processes in the cycle mst be re'ersible1 all heat trans%er mst occr isothermally becase con'ersion o% -or. to heat is irre'ersible.>hen the temperatre o% the -or.ing sbstances changes6 there mst be Eero heat e2change F a)iabatic process.Carnot cycle F consists o% t-o re'ersible isotherms an) t-o re'ersible a)iabats 144312QHQCrelease/ tosurroun/in's),Carnot Cyclea/ia+atic isothermalsDiagra# not to scale, a(iabats are #uc- steeper t-an s-ownWD!9E: 5ll heat (QH " QC/ e2changes occrre) isothermally in calclating the e%%iciency e = + C % H 162 ,5)iabaticcompression1 2IsothermalcompressionQCQH, 0Isothermale2pansion0 15)iabatice2pansion5ll energy e2changes are re'ersible F there are no non1reco'erable energy losses)p43121 an) 2: Gcol)H, an) 0: GhotH1=(roo%: e = 1 - |QC| ! |QH| = 1 - C ! HIso3hermal cha45eQ = n .ln()f !)i)1 2: Isothermal compression heat QC re7ecte/ to sink at constant temperature C. |QC | = n . C ln()# ! )1)$ 0: Isothermal e2pansion heat QH supplie/ from source at constant temperature|QH | = n . H ln()4 ! )$) e = 1 - |QC| ! |QH| = 1 C ln()# ! )1) ! H ln()4 ! )$) (EI. 1/)p43121 an) 2: Gcol)H, an) 0: GhotH5)iabatic change Q = 0i)i-1 = f)f-1 1:2 ,:5)iabatic e2pansione = 1 - C ln()1 ! )#) ! H ln()4 ! )$)In practice6 the Carnot cycle cannot be se) %or a heat engine becase the slopes o% the a)iabatic an) isothermal lines are 'ery similar an) the net -or. otpt (area enclose) by p) )iagram/ is too small to o'ercome %riction " other losses in a real engine.E%%iciency o% 2ar4o3 e45i4e1 ma2 possible e%%iciency %or a heat engine operating bet-een TC an) TH1 1# # $ $ ) ) =1 11 1 4 4)) =0 1:5)iabatic e2pansion1 # $ 4= =1 11 4# $1 4# $) )) )) )) ) = = 1CH

e

= (EI. 1/1A2ar4o3 E45i4e00.10.20.,0.00.40.60.=0.:0.A10 200 000 600 :00 1000 1200 1000 1600 1:00 2000Tem%era3ure TH/o2+e66icie4cy9he strength " har)ness o% metals)ecreases rapi)ly abo'e =40 oC

C = #% oCCCarnotH1

e

= G$e1athorH *"+ E2ample 20.,20#iathermal -all: 5 highly thermally con)cting -all.212AR ENGINE9he 6our7s3ro8e "TT" cycle o% a con'entional petrol engine 229he 6our7s3ro8e "TT" cycle o% a con'entional petrol engine inta.e compressionignition po-er e2haststro.estro.estro.estro.einta.e stro.e: isobaric e2pansioncompression stro.e: adia.a3ic compressionignition: isochoric heating o% gas po-er stro.e: adia.a3ic e2pansion o% gas e2hast stro.e: isochoric cooling o% gas / isobaric compression2,Inta.e1Compression 2(o-er ,E2hast 02054312,oQHQCrelease/ tosurroun/in's),Otto Cyclea/ia+atic isothermalsWcooling o% e2hast gasesIGDI9I!D%el combstionpo-er stro.ecompression stro.einta.e stro.e e2hast stro.e)1 = r )# r = compression ratio)2111 er = 24) 1: i4le3 s3ro8e 'olme increases as piston mo'es )o-n creating a partial 'acm to ai) air/%el entering cylin)er 'ia the open inlet 'al'e.54312,o)#)1QHQCrelease/ tosurroun/in's), Otto Cyclea/ia+atic isothermals261 2: com%ressio4 s3ro8e inlet 'al'e closes piston mo'es p compressing the air/%el mi2tre adia.a3ically.54312,o)#)1QHQCrelease/ tosurroun/in's), Otto Cyclea/ia+atic isothermals2=2 (: i54i3io4 F spar. plg %ires igniting mi2tre 1 constant 'olme combstion.54312,o)#)1QHQCrelease/ tosurroun/in's), Otto Cyclea/ia+atic isothermals2:( ,: e1%a4sio4 or %o9er s3ro8e F heate) gas e2pan)s a)iabatically as the piston is pshe) )o-n )oing -or. ()ma8 = r )min/.Compression ratio6 r54312,o)#)1QHQCrelease/ tosurroun/in's), Otto Cyclea/ia+atic isothermals2A, 1 start o% E1haus3 s3ro8e F otlet 'al'e opens an) mi2tre e2pelle) at constant 'olme then1 )54312,o)#)1QHQCrelease/ tosurroun/in's), Otto Cyclea/ia+atic isothermals,01 ): E1haus3 s3ro8e F piston mo'es p pro)cing a compression at constant pressre6 Po (atmospheric pressre/.54312,o)#)1QHQCrelease/ tosurroun/in's), Otto Cyclea/ia+atic isothermals,1"33o cycle 7 s3a4dard %e3rol e45i4e /, s3ro8e+I)ealiEe) mo)el o% the thermo)ynamic processes in a typical car engine.+or compression ratio6 r J : an) < 1.0 (air/

H (pea./ J 1:00 KCC (base/ J 40 KC e J 46B (i)eal engine/ e J ,4B (real engine/.E%%iciency increases -ith larger r engine operates at higher temperatres preFignition .noc.ing son) an) engine can be )amage).!ctane rating F measre o% anti1.noc.ing F premim petrol r J 12.In practice6 the same air )oes not enter the engine again6 bt since an eIi'alent amont o% air )oes enter6 -e may consi)er the process as cyclic. 111 er = ,2Comparison o% theoretical an) actal pL )iagrams %or the %or1stro.e !tto Cycle engine. p),,iesel 2ycle4 to 1:inta.e stro.eisobaric e2pansion1 to 2:compression stro.e abiabatic compression2 to ,:ignitionisobaric heating, to 0:po-er stro.e a)iabatic e2pansion0 to 1:e2hast stro.e (start/ isochoric cooling1 to 4: e2hast stro.e (%inish/ isobaric compression54312,o)#)1QHQCrelease/ tosurroun/in's),a/ia+atic isothermals$)ol% #iesel,054312,o)#)1QHQCrelease/ tosurroun/in's), Diesel Cyclea/ia+atic isothermalspower strokecoolin' of e8haust 'asescompression stro.e%el ignition,4,6IESEL 2Y2LEDo %el in the cylin)er at beginning o% compression stro.e. 5t the en) o% the a)iabatic compression high temperatres are reache) an) then %el is in7ecte) %ast enogh to .eep the pressre constant. 9he in7ecte) %el becase o% the high temperatres ignites spontaneosly -ithot the nee) %or spar. plgs. #iesel engines operate at higher temperatres than petrol engines6 hence more e%%icient.+or r J 1: an) < 1.0 (air/ H (pea./ J 2000 KCC (base/ J 40 KC e J 6:B (i)eal engine/real e%%iciency J 00 B(etrol engineJ 46B (i)eal engine/real e%%iciency J ,4 B,=iesel e45i4esMHea'ier (higher compression ratios/6 lo-er po-er to -eight ratio.MHar)er to start.MNore e%%icient than petrol engines (higher compression ratios/.MDo pre1ignition o% %el since no %el in cylin)er )ring most o% the compressionM9hey nee) no carbrettor or ignition system6 bt the %el1in7ection systemreIires e2pensi'e high1precision machining.M&se cheaper %els less re%ine) hea'y oils F %el )oes nee) to be 'aporiEe) in carbrettor6 %el less 'olatile hence sa%er %rom %ire or e2plosion.M #iesel cycle F can control amont o% in7ecte) %el per cycle F less %el se) atlo- spee)s.,: http://people.bath.ac../ccsshb/12cyl/9hese engines -ere )esigne) primarily %or 'ery large container ships. ,A(roblem+or the theoretical !tto cycle6 calclate:(a/ ma2 cycle temperatre(b/ -or. per .ilogram o% %el(c/ E%%iciency()/ Na2 e%%iciency Carnot engine -or.ing bet-een same temperatresEngine characteristics:cp < 1.004 .;..g11.O11 c9 < 0.=1: .;..g11.O11compression ratio < ::1Inlet con)itions p < A=.4 .(a an)< 40 oCHeat spplie) < A40 .;..g1100@oltionIdentify / Setupcp < 1.004 .;..g11.O11

c9 < 0.=1: .;..g11.O11)1! )# < :p1 < A=.410, (a

1 < 40 oC < ,2, OQH < A40 .;..g11

H < $ < ? OW < ? .;..g11e < ? eCarnot < ?5)iabatic change Q = 0 ) -1 = constant = cp ! c9 = 1.00% ! 0.&18 = 1.4Qp = # cp Q9 = # c9 W = |QH| - |QC|e = W ! |QH|eCarnot = 1 C ! H54312,o)#)1QHQCrelease/ tosurroun/in's), Otto Cyclea/ia+aticisothermals015)iabatic compressionExecute

# ! 1 = ()1!)#)-1

# = 1()1 ! )#)-1 = ($#$)(8)0.4 : = &4# :Constant 'olme heatingQH = # c9 ($ #)

$ = (QH!#)!c9 +# = (2%0!0.&18 + &4#) : = 205 ! " 1#$2 oC5)iabatic e2pansion

4 ! $ = ()$ !)4)-1

4 = $(1!8)0.4 = 822 :Constant 'olme heat re7ectionQC = # c9 (4 $) QC!# = (0.&18)(822 - $#$) k.k'-1 = 414 k.k'-1W = |QH| - |QC| = (2%0 414) k.k'-1 =53 %&'%()1 e = W ! |QH| = %$. ! 2%0 = 0.%. (real en'ine 4 0.4)eCarnot = 1 C ! H = 1 $#$ ! #0.& = 0'*40254312,o)# )1QHQCrelease/ tosurroun/in's),Diesel Cyclea/ia+atic isothermalsCalclate the abo'e Iantities %or the )iesel cycle -ith a compression ratio < 200,5)iabatic compression)1 ! )# = #0

# ! 1 = ()1!)#)-1 # = 1()1 ! )#)-1 = ($#$)(#0)0.4 : = 10&1 :Isobaric heatingQH = # cp ($-#) QH!# = cp ($ #)

$ = # + (1!cp)(QH%#) = 10&1 +(1!1.00%)(2%0) : = #01. :Isobaric heating / 5)iabatic e2pansion)# ! # = )$ ! $ )$ ! )# = $ ! # )4 ! )# = #0)# = )4 ! #0)$ ! )4 = (1!#0)($!#) = (1!#0)(#01.!10&1) = 0.0241

$)$-1 = 4)4-1

4 = $ ()$!)4)-1 = (#01.)(0.0241)0.4 = &8$ : Isochoric coolingQC = # cv (4 1)QC%# = cv (4 1) = (0.&18)(&8$ $#$) : = $$0.$ k.k'-1W = QH QC = (2%0 $$0) k = .#0 k.k'-1e = W ! QH = .#0 ! 2%0 = 0..%e = 1- QC!QH = 1 $$0!2%0 = 0..% 9he -or. otpt an) e%%iciency are consi)erably higher than %or !tto Cycle00E1am%le Consi)er t-o engines6 the )etails o% -hich are gi'en in the %ollo-ing )iagrams. +or both engines6 calclate the heat %lo- to the col) reser'oir an) the changes in entropy o% the hot reser'oir6 col) reser'oir an) engine. >hich engine 'iolates the @econ) 8a-? >hat is the e%%iciency o% the -or.ing engine?04@oltion+irst 8a-: ! = Qnet W Engine: cyclic process ! < 0 Qnet = W |QH| - |QC| |QC | = |QH| - WEngine 1: PQC| < 1000 1 200 < :00 ;Engine 2: PQC| < 1000 1 ,00 < =00 ;06*(total) = - |QH|! H + |QC|! CEngine 1: * = (- #.% + #.&) .:-1 = + 0.#.:-1 > 0 @econ) 8a- 'ali)ate)Engine 2: * = (- #.% + #.$) .:-1= - 0.# .:-1 4 0 @econ) 8a- 4o3 'ali)ate) Engine 1 is the -or.ing enginee%%iciency6 e < (-or. ot / energy inpt/ 100< (200 / 1000/(100/ < 20 B0=@emester 16 200= E2amination Iestion (4 mar.s/5 hybri) petrol1engine car has a higher e%%iciency than a petrol1only car becase it reco'ers some o% the energy that -ol) normally be lost as heat to the srron)ing en'ironment )ring brea.ing.(a/I% the e%%iciency o% a typical petrol1only car engine is 20B6 -hat e%%iciency col) be achie'e) i% the amont o% heat loss )ring brea.ing is hal'e)?(b/Is it possible to reco'er all the energy lost as heat )ring bra.ing an) con'ert it into mechanical energy? E2plain yor ans-er.0:@oltionIdentify / Setupe%%iciency 1H C CH H HW Q Q QeQ Q Q= = = @econ) 8a- o% 9hermo)ynamics 100B o% heat can not be trans%orme) into mechanical energy e C 1Execute(a/1 0.# 0.80C CH HQ QeQ Q= = =$e)ce heat loss by hal%0.40 0..CHQeQ= =(b/ >ol) reIire PQCP < 06 this -ol) be a 'iolation o% the @econ) 8a-1 1 0 0C CCH HQ Qe QQ Q= < > >0A>hat is a heat pmp ?Qetter by this Iic.: 400 B e%%iciency40WQCQHe:a%ora3orgas absorbs heat %rom interior o% %rig.coldhotcom%ressorheats gas by compressionco4de4sergas to liIi) (high pressre/e1%a4sio4 :aluerapi) e2pansion: liIi) to gas6 s))en large )rop in temp (J,4 oC/|-H| = |-c| + |;|419he com%ressor compresses the gas (e.g. ammonia/. 9he compresse) gas heats p as it is pressriEe) (orange/. 9he gas represents the -or.ing sbstance eg ammonia an) the compressor )ri'en by an electric motor )oes -or. W.9he co4de4ser coils at the bac. o% the re%rigerator let the hot ammonia gas )issipate its heat QH. 9he ammonia gas con)enses into ammonia liIi) ()ar. ble/ at high pressre gas (gas liIi)/. 9he high1pressre ammonia liIi) %lo-s throgh the e1%a4sio4 :al:e 9he liIi) ammonia imme)iately boils an) 'aporiEes (light ble/6 its temperatre )ropping to abot F,4 KC by the e2pansion. 9his ma.es the insi)e o% the re%rigerator col)by absorption o% heat QC .9he col) ammonia gas enters the com%ressor an) the cycle repeats. 42Re6ri5era3io4 2ycleHeat engine operating in re'erse F it ta.es heat %rom a col) place an) gi'es it o%% at a -armer place6 this reIires a net inpt o% -or.. |QH| = |QC| + |W|Qest re%rigerator F one that remo'es the greatest amont o% heat PQCP %rom insi)e the re%rigerator %or the least e2pen)itre o% -or. PWP coe++icient o+ ,er+or-ance< / (hi'her / 1alue< +etter the refri'erator)CH CCQ Q/W Q Q= =/ < -hat -e -ant / -hat -e pay %or/ < e2traction o% ma2 heat %rom col) reser'oir / least amont o% -or.4, p)QHQC;40Re+ri(erator;alls of room

CW 0 1QCQHQC= QH - ;refri'erator=nsi/e refri'erator|-H| = |-c| + |;|44.ir Con/itioner;alls of room

CW 0 1QCQHQH= W 2 QC>utsi/e|-H| = |-c| + |;|46Heat P0-,;alls of room

CW 0 1QCQHQH= W 2 QC >utsi/e|-H| = |-c| + |;|4=(H*@1001 200A E2am Restion 10In the %igre abo'e6 cylin)er 5 is separate) %rom cylin)er Q by an a)iabatic piston -hich is %reely mo'able. In cylin)er 5 there is 0.010 mole o% an i)eal monatomic gas -ith an initial temperatre ,00 O an) a 'olme o% 1.021010 m,. In cylin)er Q6 there is 0.010 mole o% the same i)eal monatomic gas -ith the same initial temperatre an) the same 'olme as the gas in cylin)er 5. @ppose that heat is allo-e) to %lo- slo-ly to the gas in cylin)er 56 an) that the gas in cylin)er Q n)ergoes the thermo)ynamic process o% a)iabatic compression. Heat %lo-s into cylin)er 5 ntil %inally the gas in cylin)er Q is compresse) to a 'olme o% 0.421014 m,. 5ssme that CV < 12.0= ;.mol11.O11 an) the ratio o% heat capacities is < 1.6=. (a/ Calclate the %inal temperatre an) pressre o% the i)eal monatomic gas in cylin)er Q a%ter the a)iabatic compression. (b/ Ho- mch -or. )oes the gas in cylin)er Q )o )ring the compression? E2plain the meaning o% the sign o% the -or.. (c/ >hat is the %inal temperatre o% the gas in the cylin)er 5? (Hint: the pressre e2erte) by the gas in cylin)er 5 on the piston is eIal to that e2erte) by the gas in cylin)er Q on the piston./ ()/ Ho- mch heat %lo-s to the gas in the cylin)er 5 )ring the process? 4:4A606162