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As it was taught to me, that at least from the phenomenological point of view, the entropy is more fundamental than temperature. The first law of thermodynamics postulates the existance a state function $U$ that we call internal energy. Then the second law of thermodynamics postulates the existance a state function $S$ that we call entropy. They satisfy ...


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For an irreversible process path, the change in entropy is not the integral of dQ/T. It is only dQ/T for an alternate reversible path that you have devised separately between the same two thermodynamic end states. So, for an irreversible process, the first thing you need to do is totally forget about the actual irreversible path; this is no longer relevant....


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