# What is free energy

1. Jul 24, 2014

### Greg Bernhardt

Definition/Summary

Free energy is energy available for doing work. Free energy as an independent concept does not really make any sense unless conditions are specified under which the work is to be done, for example:

Helmholtz free energy (or Helmholtz energy) $A\ =\ U\ - TS$ is the energy available for doing work, at constant volume and temperature.

Gibbs free energy (or Gibbs energy) $G\ =\ H\ -\ TS\ =\ A\ +\ PV\ =\ U\ +\ PV\ -\ TS$ is the energy available for doing work, at constant pressure and temperature.

The melting point of a material is the temperature at which the Gibbs free energies of the solid and liquid forms are equal.

Equations

Helmholtz free energy (internal energy minus absolute temperature times entropy):

$$A\ =\ U\ - T\,S$$

Gibbs free energy (enthalpy minus absolute temperature times entropy):

$$G\ =\ H\ - T\,S\ =\ U\ +\ P\,V\ -\ T\,S$$

Extended explanation

Spontaneity of physical and chemical processes

For a physical or chemical process at constant temperature and pressure, the change in Gibbs free energy determines whether the process is spontaneous or not.

Consider the chemical reaction

AB

The reaction is spontaneous, i.e. the reaction will occur in the direction of the products, if the change in G is negative:

ΔGGB - GA < 0​

For a more intuitive sense of why this is so, consider that

G = U + PV - TS

Since a lower value of G is favored, it means that a chemical reaction favors the direction that:

• Minimizes the internal energy U,
• Minimizes the volume, in the presence of nonzero pressure, and
• Maximizes the entropy
Moreover:
• Increasing the pressure increases the tendency to minimize the volume
• Increasing the temperature increases the tendency to maximize the entropy
It can be shown that a negative ΔG always results in an entropy increase for the "universe", i.e. the entropy of the system plus the surrounding environment.

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