Zeroth law of thermodynamics

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The zeroth law of thermodynamics states that "if two systems are in thermal equilibrium with a reservoir, then they are in thermal equilibrium with each other." It means that thermal equilibrium is a transitive relation. It's not possible to have three systems, A, B and C, where A is in equilibrium with B and B in equilibrium with C, but A is not in equilibrium with C. If this was possible, periodically connecting the systems A and C through a heat engine would create a perpetual motion machine.

The zeroth law is kind of a no-brainer, and was obviously known before the first, second, and third laws of thermodynamics were described. The need to formulate it as a formal law arose after the other laws had been established, so it was named the zeroth law in a backronym-ish manner. In fact, it's arguably not really a "law" at all, but more just a definition of what is meant by "temperature".

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