Table of thermodynamic equations

Common thermodynamic equations and quantities in thermodynamics, using mathematical notation, are as follows:

Definitions
Many of the definitions below are also used in the thermodynamics of chemical reactions.

Equations
The equations in this article are classified by subject.

Entropy

 * $$ S = k_\mathrm{B} \ln \Omega $$, where kB is the Boltzmann constant, and Ω denotes the volume of macrostate in the phase space or otherwise called thermodynamic probability.
 * $$ dS = \frac{\delta Q}{T} $$, for reversible processes only

Statistical physics
Below are useful results from the Maxwell–Boltzmann distribution for an ideal gas, and the implications of the Entropy quantity. The distribution is valid for atoms or molecules constituting ideal gases.

Corollaries of the non-relativistic Maxwell–Boltzmann distribution are below.

Quasi-static and reversible processes
For quasi-static and reversible processes, the first law of thermodynamics is:
 * $$dU=\delta Q - \delta W$$

where δQ is the heat supplied to the system and δW is the work done by the system.

Thermodynamic potentials
The following energies are called the thermodynamic potentials,

and the corresponding fundamental thermodynamic relations or "master equations" are:

Maxwell's relations
The four most common Maxwell's relations are:

More relations include the following.

Other differential equations are:

Quantum properties
where N is number of particles, h is that Planck constant, I is moment of inertia, and Z is the partition function, in various forms:
 * $$ U = N k_\text{B} T^2 \left(\frac{\partial \ln Z}{\partial T}\right)_V $$
 * $$ S = \frac{U}{T} + N k_\text{B} \ln Z - N k \ln N + Nk $$  Indistinguishable Particles