Classical thermodynamics, heat transfer Definition

Temperature

Builds on Thermodynamic equilibrium Thermodynamic state Equivalence relation

Definition

Let $\mathcal{S}$ be the set of equilibrium states of all thermodynamic systems. Write $a \sim b$ when systems in states $a$ and $b$ are in thermal equilibrium with each other. By the zeroth law of thermodynamics, $\sim$ is an equivalence relation on $\mathcal{S}$ . An empirical temperature is a function $\theta \colon \mathcal{S} \to \R$ such that $\theta(a) = \theta(b)$ if and only if $a \sim b$ .

Remarks

The height of a column of mercury in a thermometer, put in thermal contact with a system, defines an empirical temperature over its working range. A constant function on $\mathcal{S}$ is not an empirical temperature. It fails the "only if" part, since it does not separate states that are not in thermal equilibrium. The usual convention orders the values so that heat flows from higher to lower $\theta$ . Two empirical temperatures that both follow this convention are related by a strictly increasing map. The thermodynamic temperature is the one fixed by the second law.

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Tag	`K5CGPTZF79`
URI	`m2://K5CGPTZF79`
Kind	definition
Writing	W0 stub
MSC	80A05, 80A10
Defines	Temperature
Uses	Thermodynamic equilibrium, Thermodynamic state, Equivalence relation
Changed	3 November 2026

Temperature

Definition

Remarks

Reading path

Further reading

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