What form of energy is represented in the Helmholtz free energy equation?

The Helmholtz free energy, represented by the equation F = U - TS, where F is the Helmholtz free energy, U is the internal energy, T is the temperature, and S is the entropy, specifically involves internal energy. Internal energy refers to the total energy contained within a system, encompassing kinetic energy (from the motion of molecules) and potential energy (from interactions between molecules). However, the focus of the Helmholtz free energy is on the energy available to do work at constant temperature and volume, and internal energy is critical in this context.

In thermodynamic terms, the Helmholtz free energy essentially accounts for the internal energy of the system minus the energy that is "lost" to the entropy contribution at a given temperature. Thus, the Helmholtz free energy is a measure of the useful work that can be extracted from a system under isothermal and isochoric (constant volume) conditions, which directly ties back to internal energy.