Thermodynamic Potentials

Helmholtz free energy, enthalpy, Gibbs free energy, and Maxwell thermodynamic relations.

General idea of the topic

Each thermodynamic potential is the useful energy of a system under a different set of controlled conditions (constant pressure, constant temperature, variable composition...). This topic shows why several potentials are needed and when to use each one.

What you will truly understand

• Why enthalpy is the natural quantity for constant-pressure processes, where it replaces internal energy.
• Why Helmholtz free energy predicts the spontaneity of a process at constant volume and temperature.
• Why Gibbs free energy does the same but at constant pressure and temperature, the most common case in chemistry and laboratory processes.
• How chemical potential generalizes these potentials to systems where composition (number of particles) can also vary.

Recommended learning route

1. Enthalpy: the natural potential at constant pressure.
2. Helmholtz Free Energy: spontaneity at constant volume and temperature.
3. Gibbs Free Energy: spontaneity at constant pressure and temperature.
4. Chemical Potential: the energy associated with changing the number of particles.

Physical criterion you must acquire

Choose the thermodynamic potential according to which variables remain fixed in the real process: using the wrong potential does not produce an obvious numerical error, but it invalidates the interpretation of spontaneity or equilibrium.

Connection with real problems

Spontaneous chemical reactions, phase equilibria, constant-pressure industrial process design, and combustion thermochemistry are systematically analyzed with these potentials.

Final goal of the topic

Choose the appropriate thermodynamic potential according to the process conditions and use it to predict spontaneity, equilibrium, and the available energy of the system.