State functions

In thermodynamics, a state function or function of state is a function defined for a system relating several state variables or state quantities that depends only on the current equilibrium state of the system. State functions do not depend on the path by which the system arrived at its present state. A state function describes the equilibrium state of a system.

For example, internal energy, enthalpy, and entropy are state quantities because they describe quantitatively an equilibrium state of a thermodynamic system, irrespective of how the system arrived in that state. In contrast, mechanical work and heat are process quantities or path functions, because their values depend on the specific transition (or path) between two equilibrium states. The mode of description breaks down for quantities exhibiting hysteresis effects.

It is likely that the term “functions of state” was used in a loose sense during the 1850s and 60s by those such as Rudolf Clausius, William Rankine, Peter Tait, William Thomson, and it is clear that by the 1870s the term had acquired a use of its own. In 1873, for example, Willard Gibbs, in his paper “Graphical Methods in the Thermodynamics of Fluids”, states: “The quantities V, B, T, U, and S are determined when the state of the body is given, and it may be permitted to call them functions of the state of the body.

A thermodynamic system is described by a number of thermodynamic parameters (e.g. temperature, volume, pressure) which are not necessarily independent. The number of parameters needed to describe the system is the dimension of the state space of the system (D). For example, a monatomic gas having a fixed number of particles is a simple case of a two-dimensional system (D = 2). In this example, any system is uniquely specified by two parameters, such as pressure and volume, or perhaps pressure and temperature. These choices are equivalent. They are simply different coordinate systems in the two-dimensional thermodynamic state space. Given pressure and temperature, the volume is calculable from them. Likewise, given pressure and volume, the temperature is calculable from them. An analogous statement holds for higher-dimensional spaces, as described by the state postulate.

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