# Specific Heat Capacity at Constant Volume

Specific heat ratio, abbreviated as \(C_v\), is the ratio of two specific heats. If we specify any two properties of the system, then the state of the system is fully specific.

### Specific Heat Capacity at Constant Volume Formula

\(\large{ C_v = \left(\frac{ \partial U }{ \partial T }\right)_v }\)

Where:

\(\large{ C_v }\) = heat constant volume

\(\large{ \partial }\) (symbol partial) = designates heat as a path function

\(\large{ \partial U }\) = internal energy rate of change

\(\large{ \partial T }\) = temperature rate of change

\(\large{ v }\) = volume

Solve for:

\(\large{ \partial U = C_v \; \partial T }\)