A key feature of thermodynamics is the fact that the internal energy, Eint of a system and its entropy, S, are state variables; that is, they depend only on the thermodynamic state of the system and not on the processes by which it reached that state (unlike, for example, the heat content, Q). This means that the differentials dEint = TdS − pdV and dS = T−1dEint + pT−1dV, where T is temperature (in kelvins), p is pressure, and V is volume, are exact differentials as defined in calculus. What relationships follow from this fact?
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