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Who is right depends on what your model for the gas is. In short, you are right for models that incorporate inter-particle interactions. The internal energy of an ideal gas, which is a model that neglects interactions between particles, can be written only in terms of the number of particles $N$ in the gas sample and the absolute temperature $T$ of the ...


Thank you joshphysics for this wonderful answer. I myself was confused like Sanyia. I just wanted to add in a point on what caused this confusion. In the left-hand side of the equation, when we see the term $cv$, we automatically assume that the all terms should have this same condition. But this is wrong because joshphysics pointed out that $$(dE/dT)v dT + ...

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