**The Nernst Heat Theorem**

Let us consider the Gibbs-Helmholtz equation which includes chemical reaction i.e.:

∆G – ∆H = T (∂ (∆G)/∂T) _{P} ………………………………….. (1)

Where ∆G ——-> change in free energy

∆H ——-> change in enthalpy

At absolute zero i.e. T = 0,

Equation (1) will become:

∆G = ∆H

A scientist Richard measures the E.M.F. of the cells at different temperatures. He found that the value of ∂ (∆G)/∂T decreases with decrease in temperature.

Hence from this it is concluded that ∆G and ∆H tends to approach each other more and more closely as the temperature is lowered. Nernst discovered that ∂ (∆G)/∂T tends to approach to zero as the temperature is lowered to absolute zero. This is known as Nernst Heat Theorem.

Mathematically, The Nernst Heat Theorem can be expressed as:

Lt (T –> 0) [∂ (∆G) / ∂T] _{P} = Lt (T –> 0) [∂ (∆H) / ∂T] _{P} = 0 ………………………….. (2)

Where Lt means limiting value.

From the second law of thermodynamics,

[∂ (∆G) / ∂T] _{P} = – ∆S ……………………. (3)

And [∂ (∆H) / ∂T] _{P} = ∆C_{P} …………………… (4)

Where ∆S ———-> Entropy change of the reaction

∆C_{P} ——-> difference in the heat capacities of the products and the reactants.

From equation (2), (3) and (4), we will get:

Lt (T –> 0) ∆S = 0

Lt (T –> 0) ∆C_{P} = 0

This means that entropy change of a reaction tends to approach to zero and the difference in the heat capacities of the products and the reactants also tends to approach to zero as the temperature is lowered to absolute zero.