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### 5 Common Thermodynamic Potentials

**Internal energy**, the capacity to do work and the capacity to release heat- Natural variables:
- = entropy of the system
- = volume of the system
- = number of particles of type $i$ in the system

- Formula: where the chemical potential of

- Natural variables:
**Helmholz free energy**, the capacity to do mechanical and non-mechanical work- Natural variables:
- temperature of the system

- Formula:

- Natural variables:
**Enthalpy,**the capacity to do non-mechanical work and the capacity to release heat- Natural variables:
- Formula:

- Natural variables:
**Gibbs free energy,**the capacity to do non-mechanical work- Natural variables:
- Formula:

**Landau (or grand) potential,**the characteristic state function for the grand canonical ensemble (i.e., the statistical ensemble used to represent the possible states of a mechanical system of particles maintained in thermodynamic equilibrium with a reservoir)- Natural varaiables:
- Formula:

### Four Most Common Relations

Note: pressure (), volume (), entropy (), temperature ()