An Introduction to Thermal Physics

1 ,withattribution, ,includingre-postingonanypublicWebsite, ,exceptforfiguresthatareattributedtoothe rsources, 2000, ,mechanically,anddi usivelywithitsenvironment exchangingenergy,volume, , 2000, ,whichmeasuretheexpansionofmercury(forhi ghertemperatures)andalcohol(forlowertemp eratures).Thedialthermometertotherightme asurestheturningofacoilofmetal, ajunctionoftwometals scones, 2000, ( C)Pressure (atmospheres) 200 ( ).Thethreedatasetsareforthreedi erentamountsofgas(air) ,thepressureisalinearfunctionoftemperatu rethatextrapolatestozeroatapproximately 280 C.(Moreprecisemeasurementsshowthatthezer o-pointdoesdependslightlyontheamountofga s,buthasawell-definedlimitof Casthedensityofthegasgoestozero.)

2 Copyrightc 2000, =LPiston area =AVolume =V=LA! , 2000, , ,downthelengthofthemolecule, 2000, bed-spring , , 2000, 2000,Addison-Wesley. U=Q+ ,thevol-umeofthegaschangesby V(anegativeamount)andtheworkdoneonthegas (assumingquasistaticcom-pression)is P 2000, area =AForce =F x V= A xVolumePressurePViVfArea=P (Vf Vi)Area= , 2000,Addison-Wesley.(a)(b) 2000, ,thePVgraphisaconcave-uphyperbola, , 2000, (calledanadiabat) 2000, (K) (H2) , (1948).Copyrightc 2000, (K)200300400 LeadAluminumDiamond3 RHeat capacity (J/K) (datapoints)foronemoleeachofthreedi , cientlyhightemperatures, , ,ed.

3 ,ThermophysicalPropertiesofMatter(Plenum ,NewYork,1970).Copyrightc 2000, ,themagicianmustsummonupnotonlytheenergy Uoftherabbit,butalsosomeadditionalenergy ,equaltoPV, ,H=U+ 2000, xArea = 2000, ! ,itsweepsoutacylinderwhosevolumeis4 r2 .Copyrightc 2000,Addison-Wesley.!Box 1 Box 2xArea = , 2000, , , (1994).Copyrightc 2000, T( K)kt(W/m K) zFluidArea = :twoparallelsurfacesslidingpasteachother , ,thefluidflowislaminar:Atthemacroscopics calethefluidmovesonlyhorizontally, 2000, ,therewillbedi usion,anetflowofmolecules, 2000, ! mi-crostates ofasetofthreecoins(whereHisforheadsandTi sfortails).

4 Copyrightc 2000,Addison-Wesley.! , 2000, ,anysystemwithaquadraticpotentialenergyf unctionhasevenlyspacedenergylevelssepara tedinenergybyhf, , 2000, :#1#2#3 Energy:000100010001200020002110101011 Oscillator:#1#2#3 ,containingatotalofzero,one,two, 2000, ,qASolidBNB, , 2000, AqB B total= A B0 16 28281 35 21632 64 15903 103 101004 1526905 2113636 280128462 =6+6 160qA ,eachcontainingthreeoscillators, 2000, AqB B total01100 1081130099 1083245150 98 10853 4545100 97 10896 106841 1011460 106940 1011461 106939 101151100qA total( 10114) ,with300and200oscillatorsrespectively, 2000, ,q few hundredN,q few ,con-tainingafewhundredoscillatorsandene rgyunits(left)andafewthousand(right)

5 Asthesizeofthesystemincreases, q 1020, 2000, !NNe N 2 NErrorlnN!NlnN 1 101579 sapproximation( )toexactvaluesforN=1,10, 2000,Addison-Wesley. maxq/2 Width =q/ NFull scale (high-temperaturelimit). 2000, , 2000, = 2mU x pxLLpPosition spaceMomentum independent ,theybecomewiderinmomentumspace, 2000, , 2000, ,VA,NUB,VB, ,eachconfinedtoafixedvolume, 2000, ,asafunctionoftheenergyandvolumeofgasA(w iththetotalenergyandtotalvolumeheldfixed ).Ifthenumberofmoleculesineachgasislarge , 2000, 2000, , , 2000, erentgases, ,eachgasexpandstofillthewholecontainer, 2000, ASA/kqB BSB/k ,multiplicities,andentropiesofasystemoft woEinsteinsolids,onewith300oscillatorsan dtheotherwith200, 2000, (units ofk) (qA=60),thetotalentropyisamaximumsoitsgr aphhasahorizontaltangent; (forinstance,atqA=12),thesolidwhosegraph hasthesteepertangentlinetendstogainenerg yspontaneously.

6 2000, Normal Miserly Enlightened ( )fora normal systemthatbecomeshotter(moregenerous)asi tgainsenergy;a miserly systemthatbecomescolder(lessgenerous)asi tgainsenergy;andan enlightened systemthatdoesn 2000, ,initialUB, 2000, K300 K1500 J SA= 3 J/K SB= +5 ,itsentropydecreasesby3 ,itsentropyincreasesby5 2000, (Q)thatleavesahotobjectisrequiredtocarry someentropy(Q/T) , 2000,Addison-Wesley.! ,consistingofNmicroscopicmagneticdipoles ,eachofwhichiseither up or down ;theydonotinteractwiththeirneighbors(exc epttoexchangeenergy).Copyrightc 2000, B(forthe up state)and+ B(forthe down state).

7 Copyrightc 2000,Addison-Wesley. Up Down + B B0 EnergyN U/ BM/N S/kkT/ BC/Nk100 99 492 . 484 .. ,N .Themultiplicity ,whiletheentropySiskln .Thelasttwocolumnsshowthetemperatureandt heheatcapacity, 2000,Addison-Wesley. 100 0 50 100S/kU/ B 2000, (Thisgraphwasplot-tedfromtheanalyticform ulasde-rivedlaterinthetext; )Copyrightc 2000, BkT/ B 11 20 101020kT/ B 11 10M/N 5105kT/ (com-putedfromtheanalyticformulasderived laterinthetext).Copyrightc 2000,Addison-Wesley. 11xtanhx 1 2 ,theargumentxofthehyperbolictangentis 2000, 1/T(K 1) ( B/kT)Curie s DPPH (ina1:1complexwithbenzene),takenatB= (with = B),whilethedashedlineisthepredictionofCu rie slawforthehigh-temperaturelimit.

8 (Becausethee ectivenumberofelementarydipolesinthisexp erimentwasuncertainbyafewpercent,thevert icalscaleofthetheoreticalgraphshasbeenad justedtoobtainthebestfit.) , , ,JournalofChemicalPhysics68,5225(1978).C opyrightc 2000, ,VA,SAUB,VB, 2000, 2000, ,considertheprocessintwosteps:chang-ingU whileholdingVfixed, 2000,Addison-Wesley. U VStep 1 Step :veryfastcompressionthatcreatesinternald isequilibrium, 2000,Addison-Wesley.! 2000, ,NA,SAUB,NB, 2000,Addison-Wesley. A , 2000, 3,q= 3, = 10N= 4,q= 2, = (representedbyabox)tothisverysmallEinste insolidwhileholdingtheentropy(ormultipli city)fixed,wemustremoveoneunitofenergy(r epresentedbyadot).

9 Copyrightc 2000, S U V,NmechanicalvolumepressurePT= S V U,Ndi usiveparticleschemicalpotential T= S N U, , 2000, , 2000, reservoir,ThCold reservoir,TcEngineQhQcWQhQc(a)(b)(c)(d) :(a)isothermalexpansionatThwhileabsorbin gheat;(b)adiabaticexpansiontoTc;(c)isoth ermalcompressionatTcwhileexpellingheat;a nd(d) (a)andwiththecoldreservoirduringstep(c). Copyrightc 2000, 2000, , 2000, reservoir,ThCold reservoir, , , 2000, 2000, ,shownduringthepowerstrokewhenthehotpist onismovingoutwardandthecoldpistonisatres t.(Forsimplicity,thelinkagesbetweenthetw opistonsarenotshown.)Copyrightc 2000, reservoirCold reservoirQhQcW1234 PumpBoilerTurbineCondenser(Water)(Steam) (Water + steam) (nottoscale), ,whereitissteam, 2000, ( C)(bar)(kJ)(kJ)(kJ/K)(kJ/K) ,where1bar=105Pa ,andaremeasuredrelativetoliquidwateratth etriplepoint( ).

10 ExcerptedfromKeenanetal.(1978).Copyright c 2000, ( C)P(bar) (kJ)28753074327834883705S(kJ/K) (kJ)28663069327534863703S(kJ/K) (kJ)28283051326434793698S(kJ/K) (kJ)2994323134573682S(kJ/K) (kJ)309733743625S(kJ/K) (kJ)215130813444S(kJ/K) , (1978).Copyrightc 2000, reservoirCold reservoirWPressureVolumeQhQc1234 Condenser(Liquid)(Gas)(Liquid + gas) (nottoscale) ,gas, 2000, , 2000, (bar)( C)(kJ)(kJ)(kJ/K)(kJ/K) (atitsboilingpointforeachpressure).Allva luesarefor1kgoffluid,andaremeasuredrelat ivetoanarbitrarilychosenreferencestate,t hesaturatedliquidat 40 (1995).Copyrightc 2000, ( C)P(bar) (kJ)274284295S(kJ/K) (kJ)269280291S(kJ/K) (kJ)276287S(kJ/K) (gaseous) , (1995).