Second law of thermodynamics

For a reversible change

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

Thus for a closed system ($n$ fixed):

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

For an open system:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle dU=TdS-PdV+\mu dN}

For $U(S,V)$ one has the following total differential

$dU=\left({\frac {\partial U}{\partial S}}\right)_{V}dS+\left({\frac {\partial U}{\partial V}}\right)_{S}dV$