Common thermodynamic equations and quantities in thermodynamics, using mathematical notation, are as follows: Many of the definitions below are also used in the thermodynamics of chemical reactions.
μ
depends on pressure.
μ
is proportional to
(as long as the molar ratio composition of the system remains the same) because
μ
depends only on temperature and pressure and composition.
μ
τ = − 1
The equations in this article are classified by subject.
For an ideal gas
γ
For an ideal gas
Net work done in cyclic processes
(for diatomic ideal gas)
(for diatomic ideal gas) 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.
K2 is the modified Bessel function of the second kind.
Relativistic speeds (Maxwell–Jüttner distribution)
Internal energy
Corollaries of the non-relativistic Maxwell–Boltzmann distribution are below.
For quasi-static and reversible processes, the first law of thermodynamics is: where δQ is the heat supplied to the system and δW is the work done by the system.
The following energies are called the thermodynamic potentials, and the corresponding fundamental thermodynamic relations or "master equations"[2] are: The four most common Maxwell's relations are:
More relations include the following.
Other differential equations are: 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: Since Since (where δWrev is the work done by the system),
η =
Carnot engine efficiency:
η
Carnot refrigeration performance