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# Temperature dependence of heat capacity of diatomic gas

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Describe the temperature dependence of the heat capacity of a diatomic gas.

https://brainmass.com/physics/atoms-molecules/temperature-dependence-heat-capacity-diatomic-gas-186041

#### Solution Preview

You should just draw the sketches qualitatively, don't do any complicated computations here.

At zero temperature the heat capacity is zero. All the degrees of freedom are "frozen", i.e. k T is smaller than the spacing of the energy levels. Then, if we raise the temperature, the heat capacity of the translational degrees of freedom rises to it's asymptotic value of 3/2 k. Depending on the volume this transition from zero to 3/2 k happens over the course of
10^(-10) K. So, this would be the first part of the sketch.

Next the rotational degrees of freedom start to kick in. This happens at a few tens of K, you can take e.g. 40 K. So, what you see is that the value of the heat capacity slowly starts to rise from 3/2 k to 5/2 k around 40 K ...

#### Solution Summary

A detailed explanation is given. The expert examines temperature dependence of heat capacity of diatomic gas.

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