Thermodynamic potential in the context of "Internal energy"

In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ${\displaystyle G}$) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure–volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as$${\displaystyle G(p,T)=U+pV-TS=H-TS}$$where:

• ${\textstyle U}$ is the internal energy of the system
• ${\textstyle H}$ is the enthalpy of the system
• ${\textstyle S}$ is the entropy of the system
• ${\textstyle T}$ is the temperature of the system
• ${\textstyle V}$ is the volume of the system
• ${\textstyle p}$ is the pressure of the system (which must be equal to that of the surroundings for mechanical equilibrium).

The Gibbs free energy change (⁠${\displaystyle \Delta G=\Delta H-T\Delta S}$⁠, measured in joules in SI) is the maximum amount of non-volume expansion work that can be extracted from a closed system (one that can exchange heat and work with its surroundings, but not matter) at fixed temperature and pressure. This maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state under these conditions, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces.

In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium.

In contrast, the Gibbs free energy or free enthalpy is most commonly used as a measure of thermodynamic potential (especially in chemistry) when it is convenient for applications that occur at constant pressure. For example, in explosives research Helmholtz free energy is often used, since explosive reactions by their nature induce pressure changes. It is also frequently used to define fundamental equations of state of pure substances.