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Approximate the rotational partition function in the low temperature limit and explain whether the results you obtain are consistent with the third law of thermodynamics.

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(c) Determine the average (internal) energy of the system, ⟨?⟩.
According to the energy according to the equipartition theorem of degrees of freedom, what is the internal energy of 5 moles of rigid diatomic ideal gas molecules at equilibrium at temperature T?
When developing the partition functions for each degree of freedom in a diatomic ideal gas, we made some approximations. Match the degree of freedom with the approximation(s) we made. Classical (energy levels are continuous) and the addition of one extra state. Classical (energy levels are continuous) no approximations excited states do not contribute significantly [Choose ] [Choose ] [Choose ] [Choose ] ♦
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Consider a classical ideal gas of N diatomic heterogeneous molecules at temperature T. The charac- teristic rotational energy parameter is € = 1 and the natural frequency of vibrations is wo. Consider the temperature region where T≫er/kB, but T is of the order of ħwo/kB. Ignore contributions from all other internal modes. Calculate the canonical partition function, the average energy, and the heat capacity at constant volume, Cv.
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