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

$\left.dH\right.=TdS+Vdp$

For Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H(S,p)} we have the following total differential

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle dH=\left(\frac{\partial H}{\partial S}\right)_p dS + \left(\frac{\partial H}{\partial p}\right)_S dp}