Heat capacity

From the first law of thermodynamics we have

$\left.\delta Q\right.=dU+pdV$

the heat capacity is given by

$C={\frac {\delta Q}{\partial T}}$

At constant volume

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle C_{v}=\left.{\frac {\delta Q}{\partial T}}\right\vert _{V}=\left.{\frac {\partial U}{\partial T}}\right\vert _{V}}

where U is the internal energy, T is the temperature, and V is the volume.

At constant pressure

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle C_{p}=\left.{\frac {\delta Q}{\partial T}}\right\vert _{p}=\left.{\frac {\partial U}{\partial T}}\right\vert _{p}+p\left.{\frac {\partial V}{\partial T}}\right\vert _{p}}

where p is the pressure.