Third law of thermodynamics
Encyclopedia
The third law of thermodynamics is a statistical law of nature regarding entropy
:
For other materials, the residual entropy
is not necessarily zero, although it is always zero for a perfect crystal in which there is only one possible ground state.
during the years 1906-1912, and is therefore often referred to as Nernst's theorem or Nernst's postulate. The third law of thermodynamics states that the entropy of a system at absolute zero
is a well-defined constant. This is because a system at zero temperature exists in its ground state
, so that its entropy is determined only by the degeneracy
of the ground state. It means that "it is impossible by any procedure, no matter how idealised, to reduce any system to the absolute zero of temperature in a finite number of operations".
An alternative version of the third law of thermodynamics as stated by Gilbert N. Lewis
and Merle Randall
in 1923:
This version states not only ΔS will reach zero at 0 K, but S itself will also reach zero as long as the crystal has a ground state with only one configuration. Some crystals form defects which causes a residual entropy. This residual entropy disappears when the kinetic barriers to transitioning to one ground state are overcome.
With the development of statistical mechanics
, the third law of thermodynamics (like the other laws) changed from a fundamental law (justified by experiments) to a derived law (derived from even more basic laws). The basic law from which it is primarily derived is the statistical-mechanics definition of entropy for a large system:
where S is entropy, kB is the Boltzmann constant, and
is the number of microstate
s consistent with the macroscopic configuration.
The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero (provided that its ground state is unique, whereby ln(1)k = 0).
An example of a system which does not have a unique ground state is one containing half-integer spins
, for which time-reversal symmetry gives two degenerate ground states (an entropy of ln(2) kB, 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. Ground-state helium (unless under pressure) remains liquid.
In addition, glasses
and solid solutions retain large entropy at 0K, because they are large collections of nearly degenerate states, in which they become trapped out of equilibrium. Another example of a solid with many nearly-degenerate ground states, trapped out of equilibrium, is ice Ih
, which has "proton disorder".
For the third law to apply strictly, the magnetic moments of a perfectly ordered crystal must themselves be perfectly ordered; indeed, from an entropic perspective, this can be considered to be part of the definition of "perfect crystal". Only ferromagnetic, antiferromagnetic, and diamagnetic materials can satisfy this condition. Materials that remain paramagnetic at 0K, by contrast, may have many nearly-degenerate ground states (for example, in a spin glass
), or may retain dynamic disorder (a spin liquid
).
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
:
- The entropy of a perfect crystal approaches zero as temperature approaches absolute zero.
For other materials, the residual entropy
Residual entropy
Residual entropy is small amount of entropy which is present even after a substance is cooled arbitrarily close to absolute zero. It occurs if a material can exist in many different microscopic states when cooled to absolute zero...
is not necessarily zero, although it is always zero for a perfect crystal in which there is only one possible ground state.
History
The third law was developed by the chemist Walther NernstWalther Nernst
Walther Hermann Nernst FRS was a German physical chemist and physicist who is known for his theories behind the calculation of chemical affinity as embodied in the third law of thermodynamics, for which he won the 1920 Nobel Prize in chemistry...
during the years 1906-1912, and is therefore often referred to as Nernst's theorem or Nernst's postulate. The third law of thermodynamics states that the entropy of a system at absolute zero
Absolute zero
Absolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....
is a well-defined constant. This is because a system at zero temperature exists in its ground state
Ground state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
, so that its entropy is determined only by the degeneracy
Degenerate energy level
In physics, two or more different quantum states are said to be degenerate if they are all at the same energy level. Statistically this means that they are all equally probable of being filled, and in Quantum Mechanics it is represented mathematically by the Hamiltonian for the system having more...
of the ground state. It means that "it is impossible by any procedure, no matter how idealised, to reduce any system to the absolute zero of temperature in a finite number of operations".
An alternative version of the third law of thermodynamics as stated by Gilbert N. Lewis
Gilbert N. Lewis
Gilbert Newton Lewis was an American physical chemist known for the discovery of the covalent bond , his purification of heavy water, his reformulation of chemical thermodynamics in a mathematically rigorous manner accessible to ordinary chemists, his theory of Lewis acids and...
and Merle Randall
Merle Randall
Merle Randall was an American physical chemist famous for his work, over the period of 25 years, in measuring free energy calculations of compounds with Gilbert N. Lewis...
in 1923:
- If the entropy of each element in some (perfect) crystalline state be taken as zero at the absolute zero of temperature, every substance has a finite positive entropy; but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances.
This version states not only ΔS will reach zero at 0 K, but S itself will also reach zero as long as the crystal has a ground state with only one configuration. Some crystals form defects which causes a residual entropy. This residual entropy disappears when the kinetic barriers to transitioning to one ground state are overcome.
With the development of statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, the third law of thermodynamics (like the other laws) changed from a fundamental law (justified by experiments) to a derived law (derived from even more basic laws). The basic law from which it is primarily derived is the statistical-mechanics definition of entropy for a large system:
where S is entropy, kB is the Boltzmann constant, and
is the number of microstateMicrostate (statistical mechanics)
In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations...
s consistent with the macroscopic configuration.
Overview
In simple terms, the third law states that the entropy of a perfect crystal approaches zero as the absolute temperature approaches zero. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy.The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero (provided that its ground state is unique, whereby ln(1)k = 0).
An example of a system which does not have a unique ground state is one containing half-integer spins
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
, for which time-reversal symmetry gives two degenerate ground states (an entropy of ln(2) kB, which is negligible on a macroscopic scale). Some crystalline systems exhibit geometrical frustration
Geometrical frustration
In condensed matter physics, the term geometrical frustration means a phenomenon in which the geometrical properties of the crystal lattice or the presence of conflicting atomic forces forbid simultaneous minimization of the interaction energies acting at a given site.This may lead to highly...
, where the structure of the crystal lattice prevents the emergence of a unique ground state. Ground-state helium (unless under pressure) remains liquid.
In addition, glasses
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
and solid solutions retain large entropy at 0K, because they are large collections of nearly degenerate states, in which they become trapped out of equilibrium. Another example of a solid with many nearly-degenerate ground states, trapped out of equilibrium, is ice Ih
Ice Ih
thumb|Photograph showing details of an ice cube under magnification. Ice Ih is the form of ice commonly seen on earth.Ice Ih is the hexagonal crystal form of ordinary ice, or frozen water. Virtually all ice in the biosphere is ice Ih, with the exception only of a small amount of ice Ic which is...
, which has "proton disorder".
For the third law to apply strictly, the magnetic moments of a perfectly ordered crystal must themselves be perfectly ordered; indeed, from an entropic perspective, this can be considered to be part of the definition of "perfect crystal". Only ferromagnetic, antiferromagnetic, and diamagnetic materials can satisfy this condition. Materials that remain paramagnetic at 0K, by contrast, may have many nearly-degenerate ground states (for example, in a spin glass
Spin glass
A spin glass is a magnet with frustrated interactions, augmented by stochastic disorder, where usually ferromagnetic and antiferromagnetic bonds are randomly distributed...
), or may retain dynamic disorder (a spin liquid
Spin liquid
In solid-state physics, spin liquid denotes a state of matter, where local permanent magnetic moments are present in the material, but do not show any sign of ordering down to the lowest temperatures despite comparable strong antiferromagnetic interactions.Even though many theories study spin...
).
See also
- Adiabatic processAdiabatic processIn thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...
- Ground stateGround stateThe ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
- Laws of thermodynamicsLaws of thermodynamicsThe four laws of thermodynamics summarize its most important facts. They define fundamental physical quantities, such as temperature, energy, and entropy, in order to describe thermodynamic systems. They also describe the transfer of energy as heat and work in thermodynamic processes...
- Residual entropyResidual entropyResidual entropy is small amount of entropy which is present even after a substance is cooled arbitrarily close to absolute zero. It occurs if a material can exist in many different microscopic states when cooled to absolute zero...
- Thermodynamic entropy
- Timeline of thermodynamics, statistical mechanics, and random processesTimeline of thermodynamics, statistical mechanics, and random processesA timeline of events related to thermodynamics.- Before 1800 :* 1650 – Otto von Guericke builds the first vacuum pump* 1660 – Robert Boyle experimentally discovers Boyle's Law, relating the pressure and volume of a gas...
Further reading
- Goldstein, Martin & Inge F. (1993) The Refrigerator and the Universe. Cambridge MA: Harvard University Press. ISBN 0674753240. Chpt. 14 is a nontechnical discussion of the Third Law, one including the requisite elementary quantum mechanicsIntroduction to quantum mechanicsQuantum mechanics is the body of scientific principles that explains the behavior of matter and its interactions with energy on the scale of atoms and atomic particles....
.