Write down the total differential using the equalities
$T=\left.\frac{\partial E}{\partial S}\right|_V$ and
$-p=\left.\frac{\partial E}{\partial V}\right|_S$.
- Use Legendre transformation to get the potentials
+ Apply Legendre transformation to the following potentials
\begin{itemize}
\item $H=E+pV$ (Enthalpy)
\item $F=E-TS$ (Helmholtz free energy)
volume $V$, the coefficient of thermal expansion $\alpha_V$ and
the inverse bulk modulus (isothermal compressibility)
$\frac{1}{B}=-\frac{1}{V}\left.\frac{\partial V}{\partial p}\right|_T$.\\
- $C_p=\left.\frac{\partial E}{\partial T}\right|_p$ is the heat capacity
+ $C_p=\left.\frac{\partial H}{\partial T}\right|_p$ is the heat capacity
for constant pressure and
$C_V=\left.\frac{\partial E}{\partial T}\right|_V$ is the heat capacity
for constant volume.