Enthalpy

Definition:

$H=U+pV$

(-pV) is a conjugate pair. The differential of this function is

$dH=dU+pdV+Vdp$

but from equation \ref{secondlaw} we obtain

$dH=TdS-pdV+pdV+Vdp$

thus we arrive at

$dH=TdS+Vdp$

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

$dH={(\frac{\partial H}{\partial S})}_{p}dS+{(\frac{\partial H}{\partial p})}_{S}dp$