Classical thermodynamics, heat transfer Definition

Internal energy

Builds on Thermodynamic system Thermodynamic state State function Thermodynamic work

Definition

Let $\Sigma$ be a closed thermodynamic system enclosed by adiabatic walls, which let no heat through. Assume the following postulate. For any two equilibrium states $A$ and $B$ , one of them can be reached from the other by a process in these walls. The work done on $\Sigma$ is the same for every such process. Write $W_{\mathrm{ad}}(A \to B)$ for this work. The internal energy is the state function $U$ with $U(B) - U(A) = W_{\mathrm{ad}}(A \to B)$ .

Remarks

If only $A$ can be reached from $B$ , set $W_{\mathrm{ad}}(A \to B) = -W_{\mathrm{ad}}(B \to A)$ . The postulate determines $U$ up to an additive constant, fixed by choosing $U$ at one reference state. For $n$ moles of a monatomic ideal gas at thermodynamic temperature $T$ , $U = \tfrac{3}{2} nRT + U_0$ , where $R$ is the gas constant. A ball of gas thrown through the air has extra kinetic energy as a whole. That bulk kinetic energy is not part of $U$ , since it does not depend on the thermodynamic state.

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Tag	`R20RQ9ZH37`
URI	`m2://R20RQ9ZH37`
Kind	definition
Writing	W0 stub
MSC	80A05, 80A10
Defines	Internal energy
Uses	Thermodynamic system, Thermodynamic state, State function, Thermodynamic work
Changed	3 November 2026

Internal energy

Definition

Remarks

Reading path

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