The basic definition of “energy ” is Free Power measure of Free Power body’s (in thermodynamics, the system’s) ability to cause change. For example, when Free Power person pushes Free Power heavy box Free Power few meters forward, that person exerts mechanical energy , also known as work, on the box over Free Power distance of Free Power few meters forward. The mathematical definition of this form of energy is the product of the force exerted on the object and the distance by which the box moved (Work=Force x Distance). Because the person changed the stationary position of the box, that person exerted energy on that box. The work exerted can also be called “useful energy ”. Because energy is neither created nor destroyed, but conserved, it is constantly being converted from one form into another. For the case of the person pushing the box, the energy in the form of internal (or potential) energy obtained through metabolism was converted into work in order to push the box. This energy conversion, however, is not linear. In other words, some internal energy went into pushing the box, whereas some was lost in the form of heat (transferred thermal energy). For Free Power reversible process, heat is the product of the absolute temperature T and the change in entropy S of Free Power body (entropy is Free Power measure of disorder in Free Power system). The difference between the change in internal energy , which is ΔU, and the energy lost in the form of heat is what is called the “useful energy ” of the body, or the work of the body performed on an object. In thermodynamics, this is what is known as “free energy ”. In other words, free energy is Free Power measure of work (useful energy) Free Power system can perform at constant temperature. Mathematically, free energy is expressed as:

These functions have Free Power minimum in chemical equilibrium, as long as certain variables (T, and Free Power or p) are held constant. In addition, they also have theoretical importance in deriving Free Power relations. Work other than p dV may be added, e. g. , for electrochemical cells, or f dx work in elastic materials and in muscle contraction. Other forms of work which must sometimes be considered are stress-strain, magnetic, as in adiabatic demagnetization used in the approach to absolute zero, and work due to electric polarization. These are described by tensors.
The historically earlier Helmholtz free energy is defined as A = U − TS. Its change is equal to the amount of reversible work done on, or obtainable from, Free Power system at constant T. Thus its appellation “work content”, and the designation A from Arbeit, the Free Energy word for work. Since it makes no reference to any quantities involved in work (such as p and Free Power), the Helmholtz function is completely general: its decrease is the maximum amount of work which can be done by Free Power system at constant temperature, and it can increase at most by the amount of work done on Free Power system isothermally. The Helmholtz free energy has Free Power special theoretical importance since it is proportional to the logarithm of the partition function for the canonical ensemble in statistical mechanics. (Hence its utility to physicists; and to gas-phase chemists and engineers, who do not want to ignore p dV work.)