Enthalpy

Definition of the enthalpy, H

$\left.H\right.=U+pV$

where $U$ is the internal energy, $p$ is the pressure, $V$ is the volume and (-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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle dH=\left({\frac {\partial H}{\partial S}}\right)_{p}dS+\left({\frac {\partial H}{\partial p}}\right)_{S}dp}