Fundamental thermodynamic relation

In thermodynamics, the fundamental thermodynamic relation is generally expressed as an microscopic change in internal energy in terms of microscopic changes in entropy, and volume for a closed system in thermal equilibrium in the following way.

Here, U is internal energy, T is absolute temperature, S is entropy, P is pressure, and V is volume. This relation applies to a reversible change, or to a change in a closed system of uniform temperature and pressure at constant composition.

This is only one expression of the fundamental thermodynamic relation. It may be expressed in other ways, using different variables (e.g. using thermodynamic potentials). For example, the fundamental relation may be expressed in terms of the enthalpy as

in terms of the Helmholtz free energy (F) as

and in terms of the Gibbs free energy (G) as

The first law of thermodynamics states that:

where ${\displaystyle \delta Q}$ and ${\displaystyle \delta W}$ are infinitesimal amounts of heat supplied to the system by its surroundings and work done by the system on its surroundings, respectively.

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