 Isothermal compression

ID: isothermal-compression

Codex  0 Created 2026-10-05 Updated 2026-10-14

An isothermal compression reduces the volume of a thermodynamic system at fixed temperature. For a fixed-composition ideal gas compressed reversibly from

V_{i}

V_{f} < V_{i}

W_{by, rev} = n RT ln (V_{f} / V_{i}) < 0, Q = W_{by, rev} < 0, Δ U = 0.

The surroundings supply positive work

W_{on}

, and the gas rejects the same amount of heat to the heat bath. Compressing

1 mol

300 K

from

20

10 L

requires approximately

1.729 kJ

of work input and rejects

1.729 kJ

of heat. If that heat transfer cannot keep up, the temperature rises: the process departs from isothermal compression toward adiabatic compression. The finite-rate isothermal piston model explains the required small temperature excess.

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