# Specific Heat Capacity at Constant Volume

on . Posted in Thermodynamics

Specific heat capacity at constant volume, abbreviated as $$C_v$$, is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius while keeping the volume constant.  It measures the ability of a substance to absorb heat energy at a constant volume without undergoing a phase change (melting or boiling).

In this equation, $$C_p$$ is greater than $$C_v$$ for ideal gases because at constant pressure, some of the heat energy added is used to do work on the gas as it expands, in addition to raising its temperature.  For ideal gases, $$C_v$$ and $$C_p$$ are related by the gas constant, and their values depend on the specific gas.

Specific heat capacity values are essential in thermodynamics and heat transfer calculations, helping to determine how substances respond to changes in temperature and volume.  These values can be experimentally determined for different materials and are important in various scientific and engineering applications.

## Specific Heat Capacity at Constant Volume Formula

$$\large{ C_v = \left(\frac{ \partial U }{ \partial T }\right)_v }$$
Symbol English Metric
$$\large{ C_v }$$ = heat constant volume $$\large{ ft^3 }$$  $$\large{ m^3 }$$
$$\large{ \partial }$$  (symbol partial) = designates heat as a path function $$\large{ F }$$ $$\large{K }$$
$$\large{ \partial U }$$ = internal energy rate of change $$\large{ Btu }$$ $$\large{ J }$$
$$\large{ \partial T }$$ = temperature rate of change $$\large{ F }$$ $$\large{K }$$
$$\large{ v }$$ = volume $$\large{ ft^3 }$$ $$\large{ m^3 }$$