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Is the average kinetic energy per molecule of all ideal (mono, di and poly atomic) gases 3/2kT or is this just the translational kinetic energy per molecule?

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$\frac{3}{2}kT$ is only translational kinetic energy. If it is diatomic or polyatomic molecule, there is also rotational kinetic energy and the formula is $$<K>=\dfrac{f}{2}kT$$
where $f$ is degree of freedom

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