热力学和统计力学

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1、第四节热力学和统计力学Questions1-2TheMaxwelldistributionofmolecularspeedsinagasisgivenbywhereAisconstant.1.Themostprobablespeedis(A)(B)(C)(D)(E)解：所谓最可几速度，指出现几率最大的速度，即n(v)最大。由，得。解得。选(A)。2.Theroot-mean-squarespeedis(A)(B)(C)(D)(E)解：由能均分定理，均方根速度为。选(B)。3.Foranidealgas,thespecificheatatc

2、onstantpressureCpisgreaterthanthespecificheatatconstantvolumeCvbecausethe(A)gasdoesworkonitsenvironmentwhenitspressureremainsconstantwhileitstemperatureisincreased(B)heatinputperdegreeincreaseintemperatureisthesameinprocessesforwhicheitherthepressureorthevolumeiskeptconst

3、ant(C)pressureofthegasremainsconstantwhenitstemperatureremainsconstant(D)increaseinthegas’sinternalenergyisgreaterwhenthepressureremainsconstantthanwhenthevolumeremainsconstant(E)heatneededisgreaterwhenthevolumeremainsconstantthanwhenthepressureremainsconstant解：理想气体在定压过程中

4、如果温度升高，体积会膨胀，对外做功。为了做这部分功气体要吸额外的热，因此定压比热大于定容比热。选（A）。4.ThenumberofwaysofdistributingNdistinguishablemoleculesinKstates,withN1instate1,N2instate2,etc.,is(A)(B)(C)(D)(E)解：可能状态数为，计算方法为。答案显然为。选(D)。5.Anengineabsorbsheatatatemperatureof727°Candexhaustsheatatatemperatureof527°C,i

5、ftheengineoperatesatmaximumpossibleefficiency,for2000joulesofheatinputtheamountofworktheengineperformsismostnearly(A)400J(B)1450J(C)1600J(D)2000J(E)2760J解：可以证明，Carnot热机具有最高的效率，且不由工作介质决定。工作在温度为T1和T2（T1>T2）的热源间的Carnot热机效率为。所以最大做功为。选(A)。6.InacertaingroupofNparticles,thenumbe

6、rofparticleswithspeedsintherangedvisgivenbydN=kvdv,wherekisaconstant.Thespeedsareintherangebetweenzeroandamaximumvaluevmax.Theaveragespeedoftheparticleis(A)(B)(C)(D)(E)解：关键是别忘了归一化，或者说除以总粒子数。选（D）。7.IntermsoftheBoltzmannconstantk,theclassicalconstant-volumespecificheatpermo

7、leculeofheliumgasis(A)(B)k(C)(D)2k(E)3k解：由能均分定理，温度为T的经典系统，每个自由度的能量为。氦气为单元子分子，只有3个自由度，所以每个分子能量为，比热为。选(C)。Question8-9refertothefollowingprocessesinvolvingsystemslabeledbynumbers1through8.Abarofiron(1)at300Kisbroughtintothermalcontactwithabody(2)at400K,thetwobeingthermallyis

8、olatedfromallothersystems.Anidealgas(3)iscompressedreversiblywhileincontactwithareservoir(4),the