Helmholtz free energy
/ HELM-holts /
The Helmholtz free energy is the close cousin of Gibbs energy for situations where the volume is held fixed rather than the pressure — picture a reaction sealed inside a rigid steel bomb that can't expand. Like its cousin, it tells you in one number how much of a system's energy is genuinely free to do useful work once the surroundings have taken their unavoidable cut as heat, and it tells you which way a change at constant temperature will spontaneously go.
It is defined as A = U − TS, where U is the internal energy (the total energy stored in the system), T is the absolute temperature, and S is the entropy. At constant temperature and volume, a change happens on its own exactly when A decreases, and the drop in A equals the most work the system could possibly deliver in that change. That second meaning is why it carries the old nickname 'work function.'
Why it matters: Helmholtz energy is the natural quantity in physics and engineering — gases in fixed tanks, the statistical mechanics of partition functions, and computer simulations all live most comfortably at constant volume. Chemists more often reach for Gibbs energy because lab reactions sit at constant pressure; the two are simple siblings related by the pressure-volume term, and either one will correctly call which way a process turns.
Burn a fuel inside a sealed, rigid calorimeter bomb at constant temperature: the fall in Helmholtz energy sets the absolute ceiling on the useful work that reaction could deliver — no real engine can squeeze out more.
At constant T and V, the drop in A is the maximum work obtainable.
Named for Hermann von Helmholtz. The symbol is A (from the German Arbeit, 'work') in chemistry, but physicists frequently write F for it — a common source of confusion when switching textbooks.