Enthalpy

Enthalpy (\(H\)) is defined as:

\[\left.H\right.=U+pV\]

where \(U\) is the internal energy, \(p\) is the pressure, \(V\) is the volume. \(pV\) is a conjugate pair. The differential of this function is

\[\left.dH\right.=dU+pdV+Vdp\]

From the Second law of thermodynamics one obtains

\[\left.dH\right.=TdS -pdV +pdV+Vdp\]

thus we arrive at

\[\left.dH\right.=TdS +Vdp\]

For \(H(S,p)\) we have the following total differential

\[dH=\left(\frac{\partial H}{\partial S}\right)_p dS + \left(\frac{\partial H}{\partial p}\right)_S dp\]