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Some books say when heat flows into a monatomic gas at constant volume, all of the added energy goes into an increase in random translational molecular kinetic energy. But when the temperature is increased by the same amount in a diatomic or polyatomic gas, additional heat is needed to supply the increased rotational and vibrational energies. Thus polyatomic gases have larger molar heat capacities than monatomic gases.

Does the absolute temperature reflect translation kinetic energy of gases only? If all types of kinetic energy of gas particles are related to temperature, why polyatomic gases have larger molar heat capacities than monatomic gases?

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Absolute temperature relates only to translational degrees of freedom (connection to pressure via momentum exchange with a supposed exterior membrane).

Since energy is constantly being randomly reshuffled between translational and non-translational degrees of freedom, the molar heat capacity is greater.

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  • $\begingroup$ What confuses me, however, is that the principle of equipartition of energy says every degree of freedom contributes to 1/2 kT so total kinetic energy of diatomic molecule including rotational kinetic energy is 5/2 kT. How can we say absolute temperature relates only to translational degrees of freedom? $\endgroup$ – Kelvin S Dec 11 '14 at 1:28
  • $\begingroup$ I see the point you're making, and I'll say upfront that I can't get to the very bottom of it with my answer. $\endgroup$ – Daniel Dec 15 '14 at 14:05
  • $\begingroup$ I see the point you're making, and I'll say upfront that I can't get to the very bottom of it with my answer. I unsusccessfully tried typing up a satisfactory answer about three times (mostly focusing on how the energy exchange with an imagined membrane measuring pressure is apparently different from the "reshuffling" energy exchange between molecules inside the membrane). I should now probably get back to work, so I'll just say that measurement seems to confirm it ;-) $\endgroup$ – Daniel Dec 15 '14 at 14:13

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