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If the pressure and volume of a system are given, is he temperature always uniquely determined?
No, the temperature is always not uniquely determined, if the pressure and volume of a system are given. In the case of free expansion, the initial state is an equilibrium state, as in the final state; but at intermediate times, as the gas rushes from one side to the other, the temperature and the pressure do not have unique values. That is why, if the pressure and volume of a system are given, the temperature is not uniquely determined.
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