Third law of thermodynamics

This constant value cannot depend on any other parameters characterizing the system, such as pressure or applied magnetic field.

is a universal constant that applies for all possible crystals, of all possible sizes, in all possible external constraints.

The Nernst statement concerns thermodynamic processes at a fixed, low temperature, for condensed systems, which are liquids and solids: The entropy change associated with any condensed system undergoing a reversible isothermal process approaches zero as the temperature at which it is performed approaches 0 K. That is,

Or equivalently, At absolute zero, the entropy change becomes independent of the process path.

The unattainability principle of Nernst:[4] It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations.

The third law of thermodynamics states that the entropy of a system at absolute zero is a well-defined constant.

In 1912 Nernst stated the law thus: "It is impossible for any procedure to lead to the isotherm T = 0 in a finite number of steps.

This residual entropy disappears when the kinetic barriers to transitioning to one ground state are overcome.

The basic law from which it is primarily derived is the statistical-mechanics definition of entropy for a large system: where

The third law provides an absolute reference point for the determination of entropy at any other temperature.

Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant kB = 1.38×10−23 J K−1.

The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because ln(1) = 0.

Suppose a system consisting of a crystal lattice with volume V of N identical atoms at T = 0 K, and an incoming photon of wavelength λ and energy ε.

The entropy, energy, and temperature of the closed system rises and can be calculated.

[9] A single atom is assumed to absorb the photon, but the temperature and entropy change characterizes the entire system.

For such systems, the entropy at zero temperature is at least kB ln(2) (which is negligible on a macroscopic scale).

Some crystalline systems exhibit geometrical frustration, where the structure of the crystal lattice prevents the emergence of a unique ground state.

Glasses and solid solutions retain significant entropy at 0 K, because they are large collections of nearly degenerate states, in which they become trapped out of equilibrium.

[citation needed] Another example of a solid with many nearly-degenerate ground states, trapped out of equilibrium, is ice Ih, which has "proton disorder".

[citation needed] The third law is equivalent to the statement that The reason that T = 0 cannot be reached according to the third law is explained as follows: Suppose that the temperature of a substance can be reduced in an isentropic process by changing the parameter X from X2 to X1.

One can think of a multistage nuclear demagnetization setup where a magnetic field is switched on and off in a controlled way.

[11] If there were an entropy difference at absolute zero, T = 0 could be reached in a finite number of steps.

Suppose we have a large bulk of paramagnetic salt and an adjustable external magnetic field in the vertical direction.

A non-quantitative description of his third law that Nernst gave at the very beginning was simply that the specific heat of a material can always be made zero by cooling it down far enough.

The same argument shows that it cannot be bounded below by a positive constant, even if we drop the power-law assumption.

[citation needed] On the other hand, the molar specific heat at constant volume of a monatomic classical ideal gas, such as helium at room temperature, is given by CV = (3/2)R with R the molar ideal gas constant.

That is, a gas with a constant heat capacity all the way to absolute zero violates the third law of thermodynamics.

(14), which yields In the limit T0 → 0 this expression diverges, again contradicting the third law of thermodynamics.

The conflict is resolved as follows: At a certain temperature the quantum nature of matter starts to dominate the behavior.

Nature solves this paradox as follows: at temperatures below about 100 mK, the vapor pressure

(a) Single possible configuration for a system at absolute zero, i.e., only one microstate is accessible. Thus S = k ln W = 0. (b) At temperatures greater than absolute zero, multiple microstates are accessible due to atomic vibration (exaggerated in the figure). Since the number of accessible microstates is greater than 1, S = k ln W > 0.
Fig. 1 Left side: Absolute zero can be reached in a finite number of steps if S (0, X 1 ) ≠ S (0, X 2 ) . Right: An infinite number of steps is needed since S (0, X 1 ) = S (0, X 2 ) .
Gadolinium alloy heats up inside the magnetic field and loses thermal energy to the environment, so it exits the field and becomes cooler than when it entered.