(9.2.2)--5.2-2ExamplesofCarnottheorem.pdf
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(9.2.2)--5.2-2ExamplesofCarnottheorem.pdf
Examples of Carnot theoremCarnot theorem(1)All reversible engines operating at the same hot reservoir and the same cold reservoir have the same efficiency,regardless of the working substance.(2)In all engines working between the same hot reservoir and the same cold reservoir,the efficiency of an irreversible engine cannot be greater than that of a reversible engine.221111QTQT 卡热Example:Prove that the internal energy density u(the energy of photonic gas per unit volume)of equilibrium thermal radiation is proportional to the quadrature of the absolute temperature.The photonic gas pressure is p=(1/3)u,and u is only a function of T.Answer:Photonic gases that balance heat radiation are very similar to ideal gasesdpppVdTTT1Q2QpV126IncpAt 动量13IPnpcAt 动量hchpc动量photon111()333Pnuu T4)(aTTudpppVdTTT1Q2QpV(d)dWV pppV p (d)()Uu TTVu TV The change of internal energy can only come from the increase in volumeUse the first law of thermodynamics1(d)QUppV 4()()()3u TVu Tp TVThe efficiency of heat engine13dd4()4()Wp VuQu TVu TThen the cyclic work is(d)ddTTTTTTTThe efficiency of Carnot cycledd4TuTu4)(aTTuLaw of thermal radiation1()3pu T Thanks
