Third Law of Thermodynamics

The beginnings of thermodynamics

The article is part of the Thermodynamics series.
Initial provisions of thermodynamics
Zero start of thermodynamics
The first law of thermodynamics
The second law of thermodynamics
Third Law of Thermodynamics
Sections of thermodynamics
The beginnings of thermodynamics
Equation of state
Thermodynamic quantities
Thermodynamic potentials
Thermodynamic cycles
Phase transitions

See also “Physical Portal”

The third law of thermodynamics ( Nernst’s theorem, Nernst’s thermal theorem ) is a physical principle that determines the behavior of entropy as the temperature approaches absolute zero . It is one of the tenets of thermodynamics , adopted on the basis of a generalization of a significant amount of experimental data on the thermodynamics of galvanic cells. The theorem was formulated by Walter Nernst in 1906. The modern statement of the theorem belongs to Max Planck .

Walter Nernst

Content

1 Nernst wording
2 Planck wording
3 Consequences
- 3.1 Unattainability of absolute zero temperature
- 3.2 The behavior of thermodynamic coefficients
4 Violations of the third law of thermodynamics in models
5 See also
6 Literature

Nernst Wording

Nernst’s theorem states that any thermodynamic process occurring at a fixed temperature $T$ ${\ displaystyle T}$ arbitrarily close to zero $T_{0}<T\to 0$ ${\ displaystyle T_ {0} <T \ to 0}$ should not be accompanied by a change in entropy $S$ ${\ displaystyle S}$ , i.e. isotherm $T=0$ ${\ displaystyle T = 0}$ coincides with the limiting adiabat $S_{0}$ ${\ displaystyle S_ {0}}$ .

There are several statements of the theorem that are equivalent to each other:

Entropy $S$ ${\ displaystyle S}$ any system at absolute zero temperature , $T=0$ ${\ displaystyle T = 0}$ is a universal constant $S_{0}$ ${\ displaystyle S_ {0}}$ , independent of any variable parameters (pressure, volume, etc.).
When approaching absolute zero , $T\to 0$ ${\ displaystyle T \ to 0}$ entropy $S$ ${\ displaystyle S}$ tends to a certain limit $S_{0}$ ${\ displaystyle S_ {0}}$ independent of the final state of the system.
When approaching absolute zero, $T\to 0$ ${\ displaystyle T \ to 0}$ , increment of entropy $\Delta S$ ${\ displaystyle \ Delta S}$ independent of the specific values of the thermodynamic parameters of the state of the system and tends to a well-defined finite limit.
All processes at absolute zero, $T=0$ ${\ displaystyle T = 0}$ , in which the system passes from one equilibrium state to another, occur without a change in entropy.

Mathematically, you can write:

\lim \limits _{T\to \,0\,K}\left[S(T,x_{2})-S(T,x_{1})\right]=0

{\ displaystyle \ lim \ limits _ {T \ to \, 0 \, K} \ left [S (T, x_ {2}) - S (T, x_ {1}) \ right] = 0}

or

\lim \limits _{T\to \,0\,K}\left({\frac {\partial S}{\partial x}}\right)_{T}=0,

{\ displaystyle \ lim \ limits _ {T \ to \, 0 \, K} \ left ({\ frac {\ partial S} {\ partial x}} \ right) _ {T} = 0,}

Where $x$ ${\ displaystyle x}$ - any thermodynamic parameter.

The third law of thermodynamics refers only to equilibrium states. The validity of the Nernst theorem can only be proved by an experimental verification of the consequences of this theorem.

Since, based on the second law of thermodynamics, entropy can be determined only up to an arbitrary additive constant (that is, it is not the entropy itself that is determined, but only its change):

dS={\frac {\delta Q}{T}},

{\ displaystyle dS = {\ frac {\ delta Q} {T}},}

the third law of thermodynamics can be used to accurately determine entropy. In this case, the entropy of the equilibrium system at an absolute zero temperature is considered equal to zero.

The third law of thermodynamics allows us to find the absolute value of entropy, which cannot be done in the framework of classical thermodynamics (based on the first and second principles of thermodynamics). In classical thermodynamics, entropy can be determined only up to an arbitrary additive constant $S_{0}$ ${\ displaystyle S_ {0}}$ , which does not interfere with thermodynamic studies, since the difference in entropies in different states is actually measured. According to the third law of thermodynamics, when $T\to 0$ ${\ displaystyle T \ to 0}$ value $\Delta S\to 0$ ${\ displaystyle \ Delta S \ to 0}$ .

Planck wording

In 1911, Max Planck formulated the third law of thermodynamics as a condition for the vanishing of the entropy of all bodies as the temperature tends to absolute zero: $S{\xrightarrow {T\to 0}}0$ ${\ displaystyle S {\ xrightarrow {T \ to 0}} 0}$ . From here $S_{0}=0$ ${\ displaystyle S_ {0} = 0}$ , which makes it possible to determine the absolute value of entropy and other thermodynamic potentials . Planck's formulation corresponds to the definition of entropy in statistical physics through the thermodynamic probability $(W)$ ${\ displaystyle (W)}$ system status $S=k\ln W$ ${\ displaystyle S = k \ ln W}$ . At absolute zero temperature, the system is in the ground quantum-mechanical state. If it is not degenerate, then $W=1$ ${\ displaystyle W = 1}$ (the state is realized by a single microdistribution), and entropy $S$ ${\ displaystyle S}$ at $T\to 0$ ${\ displaystyle T \ to 0}$ equal to zero. In fact, in all measurements, the tendency of entropy to zero begins to manifest much earlier than the discreteness of the quantum levels of the macroscopic system and the influence of quantum degeneracy can become significant.

Consequences

Unattainability of absolute zero temperature

From the third law of thermodynamics it follows that an absolute zero of temperature cannot be achieved in any final process associated with a change in entropy, it can only be approached asymptotically, therefore the third law of thermodynamics is sometimes formulated as the principle of the unattainability of an absolute zero of temperature.

Thermodynamic coefficient behavior

A number of thermodynamic consequences follow from the third law of thermodynamics: when $T\to 0$ ${\ displaystyle T \ to 0}$ should tend to zero heat capacity at constant pressure and at a constant volume, thermal expansion coefficients and some similar values. The validity of the third law of thermodynamics was at one time questioned, but it was later found out that all the apparent contradictions (the non-zero value of entropy in a number of substances at $T=0$ ${\ displaystyle T = 0}$ ) are associated with metastable states of matter that cannot be considered thermodynamically equilibrium.

Violations of the Third Law of Thermodynamics in Models

The third law of thermodynamics is often disrupted in model systems. So, with $T\to 0$ ${\ displaystyle T \ to 0}$ the entropy of a classical ideal gas tends to minus infinity. This suggests that at low temperatures the Mendeleev-Clapeyron equation inadequately describes the behavior of real gases.

Thus, the third law of thermodynamics indicates the insufficiency of classical mechanics and statistics and is a macroscopic manifestation of the quantum properties of real systems.

In quantum mechanics , however, in model systems, the third principle may also be violated. These are all cases when the Gibbs distribution is applied, and the ground state is degenerate.

Failure to comply with the third law in the model, however, does not exclude the possibility that in a certain range of changes in physical quantities this model can be quite adequate.

Literature

Bazarov I.P. Thermodynamics. M.: Higher School, 1991 .-- 376 p.
Bazarov I.P. Errors and errors in thermodynamics. Ed. 2nd fix M .: URSS editorial, 2003.— 120 p.
Kvasnikov I. A. Thermodynamics and statistical physics. T.1: Theory of equilibrium systems: Thermodynamics. Ed. 2, rev. and add. M .: URSS, 2002 .-- 240 s.
Sivukhin D.V. General course of physics. - M .: Nauka , 1975 .-- T. II. Thermodynamics and molecular physics. - 519 p.
Nernst's theorem - an article from the Great Soviet Encyclopedia .