Enthalpy

Definition of the enthalpy, H

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

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

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 \left.dH\right.=dU+pdV+Vdp}

From the Second law of thermodynamics one obtains

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 \left.dH\right.=TdS -pdV +pdV+Vdp}

thus we arrive at

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

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

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