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. Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.dH\right.=TdS+Vdp}

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

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