Nernst's heat theorem

Nernst's heat theorem states that the entropy change accompanying any isothermal process tends to zero as the temperature approaches absolute zero: lim(T→0) ΔS = 0. Equivalently, all substances converge on the same entropy at the bottom, whatever that common value may be. Nernst deliberately did not say what the value was; his measurements — of galvanic cell voltages and reaction heats — could not have told him, and the theorem does not need it.

The motivation was industrial rather than philosophical. The Gibbs free energy change ΔG = ΔH − TΔS decides whether a reaction proceeds, and ΔH is straightforward to measure with a calorimeter. But classical thermodynamics defines only entropy differences, via dS = δQ_rev/T, so integrating from a reference state always leaves an unknown constant, and no calorimetry could pin it down. Nernst's theorem eliminates it: if every substance shares the same entropy at T = 0, the constant is common and cancels from every ΔS. Chemical equilibrium becomes computable from thermal data alone — which is what Nernst, then consulting for the German chemical industry, actually wanted.

Planck's 1911 sharpening — that the common value is exactly zero for a perfect crystal — is the form usually quoted, but it is the weaker claim in one important sense: it carries a qualifier that Nernst's does not. Ice and carbon monoxide have degenerate ground states and retain a residual entropy at T → 0, denting Planck's zero. Nernst's statement survives untouched, because a constant entropy offset cancels out of every difference. The theorem that looks vaguer is the one that is exactly true.

Nernst presented the theorem to the Göttingen Academy on 23 December 1906, based on measurements of galvanic cells and reaction heats at low temperature. It was contested for years — Nernst's evidence was indirect and his extrapolation bold — and its verification drove much of the low-temperature research programme of the following decades, notably William Giauque's at Berkeley. Nernst was awarded the 1920 Nobel Prize in Chemistry for it. He never much liked quantum theory, despite having measured one of its most direct consequences nineteen years before matrix mechanics existed.