Work (Thermodynamics)

Thermodynamic potentials
Internal energy	U(S,V)
Helmholtz free energy	A(T,V) = U − TS
Enthalpy	H(S,P) = U + PV
Gibbs free energy	G(T,P) = U + PV − TS

In thermodynamics, thermodynamic work is a generalisation of the concept of mechanical work in mechanics.

As discussed in the article First Law of Thermodynamics it is useful to separate changes to the internal energy of a thermodynamic system into two sorts of energy transfers. Work refers to forms of energy transfer, which can be accounted for in terms of changes in the macroscopic physical variables of the system, for example energy which goes into expanding the volume of a system against an external pressure, by say driving a piston-head out of a cylinder against an external force. This is in distinction to heat energy carried into or out of the system in the form of transfers in the microscopic thermal motions of particles.

The concept of thermodynamic work is a little more general than that of mechanical work, because it also includes other energy transfers - for example electrical work, the movement of charge against an external electrical field to charge up a battery say, which may or may not necessarily be thought of as strictly mechanical in nature.

According to the First Law of Thermodynamics, any net increase in the internal energy U of a thermodynamic system must be fully accounted for, in terms of heat δQ entering the system less work δW done by the system:

The Roman letter d indicates that internal energy U is a property of the state of the system, so changes in the internal energy are exact differentials - they depend only on the original state and the final state, not the path taken. In contrast the Greek δs in this equation reflect the fact that the heat transfer and the work transfer are not properties of the final state of the system. Given only the initial state and the final state of the system, all one can say is what the total change in internal energy was, not how much of the energy went out as heat, and how much as work. This can be summarised by saying that heat and work are not state functions of the system.

The amount of useful work which can be extracted from a thermodynamic system is discussed in the article Second Law of Thermodynamics. Under many practical situations this can be represented by the thermodynamic Availability or Exergy function. Two important cases are thermodynamic systems where the temperature and volume are held constant, and the measure of "useful" work attainable reduces to the Helmholtz free energy function; and systems where the temperature and pressure are held constant, and the measure of "useful" work attainable reduces to the Gibbs free energy determines