Definitions

# Isochoric process

An isochoric process, also called an isovolumetric process, is a process during which volume remains constant. The name is derived from the Greek isos, "equal", and khora, "place."

If an ideal gas is used in an isochoric process, and the quantity of gas stays constant, then the increase in energy is proportional to an increase in temperature and pressure. Take for example a gas heated in a rigid container: the pressure and temperature of the gas will increase, but the volume will remain the same.

In the ideal Otto cycle we found an example of an isochoric process when we assume an instantaneous burning of the gasoline-air mixture in an internal combustion engine car. There is an increase in the temperature and the pressure of the gas inside the cylinder while the volume remains the same.

## Equations

If the volume stays constant ($Delta V = 0$), this implies that the process does no pressure-volume work, since such work is defined by

$Delta W = P Delta V$,
where P is pressure (no minus sign; this is work done by the system).

By applying the first law of thermodynamics, we can deduce that $Delta U$ the change in the system's internal energy, is

$Delta U = Q$
for an isochoric process: all the heat being transferred to the system is added to the system's internal energy, U. If the quantity of gas stays constant, then this increase in energy is proportional to an increase in temperature,
$Q = m C_V Delta T$
where CV is molar specific heat for constant volume.

On a pressure volume diagram, an isochoric process appears as a straight vertical line. Its thermodynamic conjugate, an isobaric process would appear as a straight horizontal line.