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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 $$(dE/dT)v dT + ... 0 Actually, that is not the correct formula for gases. In the usual model of ideal gases, the volume is given as a function of both temperature and pressure by the equation:$$V=\frac{n\bar RT}{p} Both formulas you wrote are valid for solids and liquids (but not for gases). In those phases, volume is much more affected by temperature than by pressure, so ...