Third law of thermodynamics

Third law of thermodynamics. The third law of thermodynamics is a fundamental principle concerning the behavior of systems as they approach the lowest possible temperature, absolute zero. It establishes that the entropy of a perfect crystalline substance becomes zero at absolute zero, providing an absolute reference point for entropy. This law implies that reaching absolute zero through a finite number of thermodynamic processes is impossible, a statement known as the unattainability principle.

Statement of the law

The most common formulation, attributed to Walther Nernst, states that the entropy change for any isothermal process approaches zero as the temperature approaches absolute zero. A more specific statement, associated with Max Planck, asserts that the entropy of a perfect crystal of any pure substance approaches zero at absolute zero. This provides a well-defined zero point for the absolute entropy scale, unlike energy or enthalpy. The Nernst heat theorem formalizes this, distinguishing it from the earlier laws formulated by Rudolf Clausius and Lord Kelvin.

Historical development

The law emerged from early 20th-century studies of chemical reactions at low temperatures. Walther Nernst formulated his heat theorem in 1906 based on work with Hermann von Helmholtz on electrochemical cells. Max Planck later extended and strengthened the postulate in 1911. Significant experimental support came from the low-temperature research of Heike Kamerlingh Onnes, who achieved the liquefaction of helium. Theoretical consolidation followed through the statistical mechanics work of Gilbert N. Lewis and Merle Randall, linking entropy to quantum mechanics and the ground state.

Implications and consequences

A primary consequence is the unattainability of absolute zero; it cannot be reached in a finite number of steps, as formalized by Ralph H. Fowler. This law allows the calculation of absolute entropies from calorimetric data via the Debye model and the Einstein solid model. It underpins the Nernst–Simon statement regarding phase changes and justifies the use of entropy as a criterion for chemical equilibrium in processes like the Haber process. It also implies that heat capacity must vanish at absolute zero.

Relation to other laws

It complements the first law of thermodynamics (conservation of energy) and the second law of thermodynamics (defining entropy increase). While the first and second laws define changes in state functions, this law provides an absolute scale. It is consistent with the zeroth law of thermodynamics (defining temperature) by fixing the lower limit of the Kelvin scale. In statistical mechanics, as developed by Ludwig Boltzmann and Josiah Willard Gibbs, it corresponds to a single microstate for a perfect crystal at zero temperature.

Experimental verification

Verification involves measuring entropy changes and heat capacities near absolute zero. Landmark experiments include those by William F. Giauque and Peter Debye on the magnetic cooling of gadolinium sulfate. The adiabatic demagnetization technique, pioneered by Giauque and Dirk Coster, provided strong evidence. Studies on superconductivity by John Bardeen and glassy states also test its limits, showing residual entropy in non-crystalline materials. Cryogenic research at institutions like the National Institute of Standards and Technology continues to test predictions.

Limitations and exceptions

The law strictly applies only to systems in internal thermodynamic equilibrium. Exceptions arise for substances that do not form perfect crystals, such as glasses or disordered magnets, which retain residual entropy. Supercooled liquids and certain copolymer configurations also violate the perfect crystal condition. In quantum mechanics, systems may have degenerate ground states, leading to non-zero entropy, a consideration addressed in the work of John von Neumann. The law does not govern individual atoms or small systems described by quantum thermodynamics.

Category:Thermodynamics Category:Physics laws