(Solved): Using the equation for the entropy of an ideal gas calculated in the microcan ...

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Using the equation for the entropy of an ideal gas calculated in the microcanonical ensemble $$S=Nk\log \left(\frac{V}{N}{u}^{3/2}\right)+\frac{3}{2}Nk\left(\frac{5}{3}+\log \frac{4?m}{3h^2}\right),$$ where $$u=\frac{3}{2}kT$$, work out the entropy of mixing for the case of different gases and for the case of identical gases, thus showing explicitly that here is no Gibbs paradox. Problem: Calculate the thermodynamic properties - $$S$$ entropy - Equations of state - $$?$$ chemical potential - Heat capacities of a system of $$N$$ classical distinguishable harmonic oscillators with frequency $$?$$ in the microcanonical ensemble.