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612_Physics ProblemsTechnical Physics

612_Physics ProblemsTechnical Physics - 614 The Kinetic...

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614 The Kinetic Theory of Gases Section 21.4 The Equipartition of Energy P21.33 The heat capacity at constant volume is nC V . An ideal gas of diatomic molecules has three degrees of freedom for translation in the x , y , and z directions. If we take the y axis along the axis of a molecule, then outside forces cannot excite rotation about this axis, since they have no lever arms. Collisions will set the molecule spinning only about the x and z axes. (a) If the molecules do not vibrate, they have five degrees of freedom. Random collisions put equal amounts of energy 1 2 k T B into all five kinds of motion. The average energy of one molecule is 5 2 k T B . The internal energy of the two-mole sample is N k T nN k T n R T nC T B A B V 5 2 5 2 5 2 F H G I K J = F H G I K J = F H G I K J = . The molar heat capacity is C R V = 5 2 and the sample’s heat capacity is nC n R nC V V = F H G I K J = F H G I K J = 5 2
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