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In a previous lecture we learned that the canonical partition function for a monatomic ideal gas is (2tmkg -, where (V.T) = V N! 12 Q(N,V, T) – 9(V,7) and q is the translational partition function. This model is not appropriate for ideal diatomic ideal gas since it neglects rotational and vibrational energy. The rigid rotator-harmonic oscillator model incorporates additional energy terms to account for these additional degrees of freedom The molecular partition function for the rigid rotator harmonic oscillator model is 2.mk, 18 T 9(0.7) = h PL where is the moment of inertia, is the vibrational frequency of the diatomic gas (Note the exponential in the numerator has a 2 where the exponential in the denominator does not) a) Derive an expression for the molt internal energy, (u) using rigid rotator-harmonic oscillator model The following mathematical relationship may be helpful