Isochoric process

An isochoric process (also called isovolumetric or isometric) holds the volume of the system fixed while pressure and temperature change. On a pressure–volume diagram it is a vertical line. Because the boundary does not move, no work is done — W = ∫P dV = 0 — and the first law reduces to ΔU = Q: every joule of heat goes directly into internal energy.

This is why the constant-volume heat capacity C_v is the more fundamental of the two heat capacities: it measures the heat needed to raise temperature when none of it is siphoned off as expansion work. Heating a gas in a sealed rigid vessel, or the explosive pressure rise in a constant-volume combustion, are isochoric to good approximation.

The isochoric leg is a canonical building block of cycles such as the Otto cycle of the petrol engine, where constant-volume heat addition (the spark-ignited burn) drives the pressure up before the power stroke expands the gas.

Distinguished as a canonical process alongside the others once the PV diagram made the four shapes explicit; its role in idealising the petrol engine was formalised in the Otto cycle of the 1870s.