Equations of State

In physics and thermodynamics, an equation of state is a thermodynamic equation relating state variables which describes the state of matter under a given set of physical conditions. It is a constitutive equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature, pressure, volume, or internal energy. Equations of state are useful in describing the properties of fluids, mixtures of fluids, solids, and the interior of stars.

The most prominent use of an equation of state is to correlate densities of gases and liquids to temperatures and pressures. One of the simplest equations of state for this purpose is the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures. However, this equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensation from a gas to a liquid. Therefore, a number of more accurate equations of state have been developed for gases and liquids. At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions.

Measurements of equation-of-state parameters, especially at high pressures, can be made using lasers.

In addition, there are also equations of state describing solids, including the transition of solids from one crystalline state to another. There are equations that model the interior of stars, including neutron stars, dense matter (quark–gluon plasmas) and radiation fields. A related concept is the perfect fluid equation of state used in cosmology.

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