Table of thermodynamic equations


This article is a summary of common equations and quantities in thermodynamics. SI units are used for absolute temperature, not Celsius or Fahrenheit.

Definitions

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

General basic quantities

Q, qJ2−2Latent HeatQLJ2−2

General derived quantities

,J K−12−2 −1PressurePPaM L−1T−2Internal EnergyUJ2−2EnthalpyHJ2−2Partition FunctionZdimensionlessdimensionlessGibbs free energyGJ2−2Chemical potential μi
, where F is not proportional to N because μi depends on pressure.
, where G is proportional to N because μi depends only on temperature and pressure and composition.J2−2Helmholtz free energyA, FJ2−2Landau potential, Landau Free Energy, Grand potentialΩ, ΦGJ2−2Massieu Potential, Helmholtz free entropyΦJ K−12−2 −1Planck potential, Gibbs free entropyΞJ K−12−2 −1

Thermal properties of matter

Thermal transfer

Equations

The equations in this article are classified by subject.

Thermodynamic processes

For an ideal gas




Isothermal process
For an ideal gas
Isobaric processp1 = p2, p = constant
Isochoric processV1 = V2, V = constant
Free expansionWork done by an expanding gasProcess

Net Work Done in Cyclic Processes

Kinetic theory


Pressure of an ideal gas

Ideal gas



Internal Energy
ΔU



Enthalpy
ΔHEntropy
Δs

Constant

Entropy

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.Non-relativistic speeds

Relativistic speeds
Entropy Logarithm of the density of states


where:
Entropy change
Entropic forceEquipartition theorem

Average kinetic energy per degree of freedom
Internal energy
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:
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 Planck's constant, I is moment of inertia, and Z is the partition function, in various forms:

Thermal properties of matter

Since
Since
,

Thermal transfer

Internal energy of a substance

Meyer's equation

Effective thermal conductivities

Series
Parallel

Thermal efficiencies

Thermodynamic engine:

Carnot engine efficiency:
Refrigeration

Refrigeration performance
Carnot refrigeration performance