= Heat capacity at constant volume
{title2=$C_V$}
= Constant-volume heat capacity
{synonym}
For a fixed-composition <closed system>, the <heat capacity> at fixed <volume (thermodynamics)> is $C_V=(\partial U/\partial T)_V$, with <internal energy> $U$. Under the <quasistatic process> assumptions in <heat capacity>, only <pressure>-<volume (thermodynamics)> <work> is permitted, so $dV=0$ gives $\delta Q=dU=C_V\,dT$. A rigid vessel therefore needs $Q=\Delta U$, or $Q=C_V\Delta T$ when $C_V$ is constant. Its per-unit-<mass> counterpart is <specific heat capacity at constant volume>.
Back to article page
