Isochoric Process - Formalism

Formalism

An isochoric thermodynamic process is characterized by constant volume, i.e., . 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.

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, the previous equation now gives

Using the definition of specific heat capacity at constant volume,

,

Integrating both sides yields

Where is the specific heat capacity at constant volume, is initial temperature and is 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.