A state function could also describe the number of a certain type of atoms or molecules in a gaseous, liquid, or solid form in a heterogeneous or homogeneous mixture, or the amount of energy required to create such a system or change the system into a different equilibrium state.
In contrast, mechanical work and heat are process quantities or path functions because their values depend on a specific "transition" (or "path") between two equilibrium states that a system has taken to reach the final equilibrium state.
Exchanged heat (in certain discrete amounts) can be associated with changes of state function such as enthalpy.
[2] It is likely that the term "functions of state" was used in a loose sense during the 1850s and 1860s by those such as Rudolf Clausius, William Rankine, Peter Tait, and William Thomson.
For example, a monatomic gas with a fixed number of particles is a simple case of a two-dimensional system (D = 2).
Choosing a different pair of parameters, such as pressure and volume instead of pressure and temperature, creates a different coordinate system in two-dimensional thermodynamic state space but is otherwise equivalent.
An analogous statement holds for higher-dimensional spaces, as described by the state postulate.
Generally, a state space is defined by an equation of the form
The path can be specified by noting the values of the state parameters as the system traces out the path, whether as a function of time or a function of some other external variable.
In order to calculate the work W in the above integral, the functions P(t) and V(t) must be known at each time t over the entire path.
In contrast, a state function only depends upon the system parameters' values at the endpoints of the path.
The product PV is therefore a state function of the system.
The symbol δ will be reserved for an inexact differential, which cannot be integrated without full knowledge of the path.
For example, δW = PdV will be used to denote an infinitesimal increment of work.
For example, the state function PV is proportional to the internal energy of an ideal gas, but the work W is the amount of energy transferred as the system performs work.
Work is the amount of energy that has changed its form or location.