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)