Classical thermodynamics, heat transfer Definition

State function

Builds on Thermodynamic system Thermodynamic state Thermodynamic equilibrium

Definition

Let $\Sigma$ be a thermodynamic system and let $\mathcal{S}$ be the set of its equilibrium states. A state function of $\Sigma$ is a function $F \colon \mathcal{S} \to \R$ . For a process from a state $A$ to a state $B$ , the change of $F$ is $\Delta F = F(B) - F(A)$ . So $\Delta F$ depends only on $A$ and $B$ , not on the path between them.

Remarks

For a fixed amount of ideal gas with states $(p, V)$ , the temperature $T = pV/(nR)$ is a state function. Here $n$ is the amount of gas and $R$ is the gas constant. The work done on the gas is not a state function: it is not determined by the end states, since two paths between the same states can give different work. When $\mathcal{S}$ is a smooth manifold and $F$ is differentiable, the differential $dF$ is exact, and $\oint dF = 0$ around every closed path.

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Tag	`VKYKGC4P8B`
URI	`m2://VKYKGC4P8B`
Kind	definition
Writing	W0 stub
MSC	80A05, 80A10
Defines	State function
Uses	Thermodynamic system, Thermodynamic state, Thermodynamic equilibrium
Changed	3 November 2026

State function

Definition

Remarks

Reading path

Further reading

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