Third Law and Absolute Zero

The third law of thermodynamics describes how entropy behaves as temperature approaches absolute zero, implying that absolute zero cannot be reached in a finite number of steps.

Definition

The third law of thermodynamics states that as the temperature of a system approaches absolute zero, its entropy approaches a constant minimum value, which is zero for a perfect crystalline substance, and that absolute zero cannot be attained in a finite sequence of processes.

Scope

This topic covers the Nernst heat theorem and the Planck statement of the third law, the vanishing of entropy differences and of entropy itself for perfect crystals at absolute zero, the unattainability of absolute zero, and consequences such as the vanishing of heat capacities and thermal expansion coefficients as temperature drops. Residual entropy and the role of quantum ground-state degeneracy are noted.

Core questions

• What does the Nernst heat theorem assert about entropy changes near absolute zero?
• Why does the entropy of a perfect crystal tend to zero at absolute zero?
• Why is absolute zero unattainable in finitely many steps?
• How do heat capacities and other response functions behave as temperature approaches zero?

Key concepts

• Nernst heat theorem
• Planck statement and zero entropy of perfect crystals
• Unattainability of absolute zero
• Residual entropy and ground-state degeneracy
• Vanishing of heat capacities at low temperature

Key theories

Nernst heat theorem

As temperature approaches absolute zero the entropy change of any isothermal reversible process tends to zero, so entropy differences between states vanish in the low-temperature limit.

Clinical relevance

The third law governs cryogenics and low-temperature physics, constrains cooling techniques such as adiabatic demagnetization, and connects macroscopic entropy to the quantum mechanical ground state of matter.

History

Walther Nernst introduced his heat theorem in 1906 to compute chemical equilibria from thermal data; Planck and Einstein later sharpened it, and the development of quantum statistics gave the vanishing of entropy at absolute zero its microscopic explanation.

Key figures

• Walther Nernst
• Max Planck

Seminal works

• nernst1906
• callen1985

Frequently asked questions

Why can't absolute zero ever be reached?

Each cooling step removes a smaller fraction of the remaining entropy as the temperature falls, so reaching exactly zero entropy and zero temperature would require infinitely many steps, which the third law renders impossible in finite time.