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# 2.2: The Zeroth Law of Thermodynamics

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Equilibrium is established by the exchange of energy, volume, or particle number between different systems or subsystems: \begin{aligned} \hbox{ energy exchange} &\qquad\Longrightarrow\qquad& T = \ { constant} & \qquad\Longrightarrow\qquad& \hbox{ thermal equilibrium}\\ \hbox{ volume exchange} &\qquad\Longrightarrow\qquad& {p\over T} = \ { constant} & \qquad\Longrightarrow\qquad& \hbox{ mechanical equilibrium}\bvph\\ \hbox{ particle exchange} &\qquad\Longrightarrow\qquad& {\mu\over T} = \ { constant} & \qquad\Longrightarrow\qquad& \hbox{ chemical equilibrium}\end{aligned} Equilibrium is transitive, so

If A is in equilibrium with B, and B is in equilibrium with C, then A is in equilibrium with C.

This known as the Zeroth Law of Thermodynamics5.