Second law of thermodynamics

The second law of thermodynamics for a reversible change (that is to say that the system evolves through a succession of equilibrium states) can be written as

$\left.dQ\right.=TdS$

Thus for a closed system, having a fixed number of atoms/molecules, one has

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

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

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

See also

• Entropy
• Fluctuation theorem
• H-theorem

References

1. Nicolas Léonard Sadi Carnot "Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance" (1824), printed in Annales scientifiques de l'École Normale Supérieure Sér. 2, 1 pp. 393-457 (1872)