614 The Kinetic Theory of GasesSection 21.4The Equipartition of EnergyP21.33The heat capacity at constant volume is nCV. An ideal gas of diatomic molecules has three degrees offreedom for translation in the x, y, and z directions. If we take the yaxis along the axis of a molecule,then outside forces cannot excite rotation about this axis, since they have no lever arms. Collisionswill set the molecule spinning only about the xand zaxes.(a)If the molecules do not vibrate, they have five degrees of freedom. Random collisions putequal amounts of energy 12k TBinto all five kinds of motion. The average energy of onemolecule is 52k TB. The internal energy of the two-mole sample isNk TnNk TnR TnC TBABV525252FHGIKJ=FHGIKJ=FHGIKJ=.The molar heat capacity is CRV=52and the sample’s heat capacity isnCnRnCVV=FHGIKJ=⋅FHGIKJ=52
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