Constant volume process
An isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant. An isochoric process is exemplified by the heating or the cooling of the contents of a sealed, inelastic container: The thermodynamic process is the addition or removal of heat; the isolation of the contents of the container establishes the closed system; and the inability of the container to deform imposes the constant-volume condition. The isochoric process here should be a quasi-static process.
An isochoric thermodynamic process is characterized by constant volume, i.e., ΔV = 0. The process does no pressure-volume work, since such work is defined by
where P is pressure. The sign convention is such that positive work is performed by the system on the environment.
If the process is not quasi-static, the work can perhaps be done in a volume constant thermodynamic process.
For a reversible process, the first law of thermodynamics gives the change in the system's internal energy:
Replacing work with a change in volume gives
Since the process is isochoric, dV = 0, the previous equation now gives
Using the definition of specific heat capacity at constant volume,
Integrating both sides yields
Where cv is the specific heat capacity at constant volume, T1 is the initial temperature and T2 is the final temperature. We conclude with:
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.
...
Wikipedia