# Nernst Heat Theorem

In 1906, Walther Nernst, studied the variation of enthalpy change and free energy change as a function of temperature. His results known as *Nernst heat theorem*.

Gibbs Helmholtz equation-

It is obvious from the above equation that the free energy change will become equal to the enthalpy change when the temperature is reduced to absolute zero i.e.

ΔF = ΔH at T = 0.

Nernst also noted that the magnitude of δ(ΔF)/δT decreases gradually and approaches the zero with the decrease of temperature.

In other words, Nernst observed that as the temperature is decreased continuously, the Gibbs free energy change was decreasing while the enthalpy change was increasing gradually with the same magnitude. Therefore, the change in slope in both curves must become zero near absolute zero. Mathematically represented as-

and graph may be plotted as-

We know that variation of free energy change with the temperature at constant pressure is equal to the negative of entropy change and Also, from the definition of change in the heat capacity, we have-

After putting the values of equation-2 and equation-3 in equation-1, we get-

(Limit T → 0), ΔS = 0 and

(Limit T → 0), ΔC_{P} = 0

Hence, all processes should occur without entropy and heat capacity changes in the vicinity of absolute zero.

This is Nernst Heat Theorem. Nernst heat theorem is also called third law of thermodynamics. Since gases and liquid does not exist at absolute zero, Hence, this theorem is applicable only to solid.

## Limitations of the Nernst Heat Theorem

Limitations of Nernst Heat Theorem are given below-

1. This theorem strictly applies to pure and perfect crystalline substances. Real substances often contain defects and impurities that can prevent the entropy from reaching zero at absolute zero.

2. The Nernst Heat Theorem is based on classical thermodynamic principles, does not account for these quantum mechanical effects that can dominate at very low temperatures which can lead to deviations from the expected behavior.

3. Reaching absolute zero or near absolute zero temperatures is theoretically impossible.

4. This theorem does not provide clear guidance for non-crystalline substances (e.g., glasses, amorphous materials) where the entropy may not approach zero at absolute zero. Amorphous and non-Crystalline substances can have residual entropy at absolute zero due to their disordered nature.

5. Near absolute zero, materials can undergo phase transitions (e.g., superconductivity, superfluidity) that complicate the application of the theorem.

6. In very small systems (nanoscale materials), finite size effects can lead to deviations from the behaviour predicted by the Nernst Heat Theorem.

**Share**