Isothermal Process
A process carried out at constant temperature, with heat exchanged as needed to maintain it.
Formula / equation
ΔU = 0 (ideal gas), w = −nRT ln(V₂/V₁)
Unit
J
In depth
For an ideal gas internal energy depends only on temperature, so an isothermal change involves no change in U and all the work done is exactly balanced by heat flow. Achieving isothermal conditions requires the process to be slow enough for thermal equilibrium to be maintained throughout.
Examples in the real world
A gas expanding slowly in a cylinder immersed in a large constant-temperature water bath.