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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle U(S,V)} one has the following total differential

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

See also

• Entropy
• H-theorem

References

1. Nicolas Léonard Sadi Carnot "Reflexions sur la Puissance Motrice de Feu et sur les Machines Propres a Développer cette Puissance" (1824), printed in Annales scientifiques de l'École Normale Supérieure Sér. 2, 1 pp. 393-457 (1872)