This post is part of a series,
Nonsense and the Second Law of Thermodynamics. The previous post is entitled
Entropy as Religious, Spiritual or Self-Help Metaphor.
You cannot get something for nothing, and the term "free energy" does not mean energy that has no cost. Rather it refers to energy that is available to do something useful. The use of the word "free" is in the sense of "liberated." Free energy is energy that can be liberated to do something useful.
We know that the second law places limitations on how much energy can be used to do useful work. In most situations, some of the energy must be dissipated as heat that cannot be used to do something useful. The portion of the energy that can do something useful is the free energy.
At constant volume, the free energy is the Helmholtz Free Energy, given the variable A.