Second law of thermodynamics

For a reversible change

$\left.dQ\right.=TdS$

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

$\left.dU\right.=TdS-PdV$

where $U$ is the internal energy. For an open system:

$\left.dU\right.=TdS-PdV+\mu dN$

where $\mu$ is the chemical potential.

For $U(S,V)$ one has 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 dU=\left(\frac{\partial U}{\partial S}\right)_V dS + \left(\frac{\partial U}{\partial V}\right)_S dV}