Equation of state

An equation of state relates thermodynamic properties of a system, such as pressure, volume, temperature, and composition. It describes how those properties constrain one another in a specified state.

Thermodynamic state: A system’s condition, specified by values of its macroscopic thermodynamic properties. An equation of state constrains which combinations of state properties are possible.
Ideal gas law: The relation PV = nRT connecting pressure, volume, temperature, and amount for an ideal gas. It is the simplest widely used equation of state for gases.
Real gas: A gas whose behavior departs from the ideal-gas model because its molecules interact and occupy finite volume. Real-gas calculations require equations that account for nonideal behavior.
Ideal gas: A simplified gas model whose particles have negligible volume and no intermolecular forces except during collisions. The ideal-gas model defines the assumptions behind the simplest gas equation of state.
Pressure: Force exerted per unit area by a fluid or other material. Pressure is one of the principal variables related by many equations of state.
Van der Waals equation: A cubic equation of state that corrects the ideal gas law for molecular attraction and finite molecular size. Its corrections model real-gas behavior absent from the ideal gas law.
Phase diagram: A map showing which phases of a substance are stable under different conditions, such as pressure and temperature. An equation of state can help calculate phase boundaries and coexistence conditions.
Cubic equation of state: A family of fluid equations of state that are cubic in molar volume or compressibility factor. Several practical real-fluid models belong to this broad equation-of-state family.
Volume: The amount of three-dimensional space occupied by a substance or system. Volume often appears alongside pressure and temperature in equations of state.
Virial equation of state: A series expansion expressing a gas’s compressibility factor in powers of inverse volume or density. Its coefficients encode departures from ideality through molecular interactions.

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