Heat Capacity at Constant Volume

Heat capacity at constant volume, abbreviated as \(C_v\), is a measure of the amount of heat energy required to raise the temperature of a substance by one degree Celsius (or one Kelvin) while keeping the volume constant.

The heat capacity at constant volume is particularly relevant for gases.  For an ideal gas, the molar heat capacity at constant volume is related to the gas constant.  This means that for an ideal gas, the heat capacity at constant volume is independent of temperature and depends only on the gas constant.

In general, for solids and liquids, the heat capacity at constant volume can depend on the specific properties of the substance and may not follow a simple formula like that for ideal gases.

 

Heat Capacity at Constant Volume Formula
\( C_v =   Q \;/\; n \; \Delta T \)     (Heat Capacity at Constant Volume) \( Q = n \; C_v \; \Delta T\) \( n =   Q \;/\; C_v \; \Delta T \) \( \Delta T =   Q \;/\; n \; C_v \)
Symbol	English	Metric
\( C_v \) = Heat Capacity at Constant Volume	\(Btu\;/\;F\)	\(kJ\;/\;K\)
\( Q \) = Heat Transfer	\(Btu\;/\;hr\)	\(W\)
\( n \) = Substance Amount	\(lbm\)	\(kg\)
\( \Delta T \) = Temperature Differential	\(F\)	\(K\)