The
grand potential is a quantity used in
statistical mechanicsStatistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force...
, especially for
irreversibleIrreversible may refer to:*Irreversibility, in thermodynamics, a process that is not reversible*Irréversible, a 2002 film*Irréversible , soundtrack to the film Irréversible...
processes in
open system-----Headline text--68.60.171.151 22:28, 19 October 2009 jenise:Open system may refer to:*Open system , one of a class of computers and associated software that provides some combination of interoperability, portability and open software standards, particularly Unix and Unix-like systems*Open...
s.
Grand potential is defined by
Where E is the
energyIn physics, energy is a scalar physical quantity that describes the amount of work that can be performed by a force, an attribute of objects and systems that is subject to a conservation law...
, T is the
temperatureIn physics, temperature is a physical property of a system that underlies the common notions of hot and cold; something that feels hotter generally has the higher temperature. Temperature is one of the principal parameters of thermodynamics...
of the system, S is the
entropyEntropy is a concept of information maintaining great importance in physics, chemistry, and information theory...
, μ is the
chemical potentialChemical potential, symbolized by μ, is a quantity first described by the American engineer, chemist and mathematical physicist Josiah Williard Gibbs...
, and N is the number of particles in the system.
The change in the grand potential is given by
Where P is
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
and V is
volumeThe volume of any solid, liquid, gas, plasma, theoretical object, or vacuum is how much three-dimensional space it occupies, often quantified numerically. One-dimensional figures and two-dimensional shapes are assigned zero volume in the three-dimensional space...
.
When the system is in
thermodynamic equilibriumIn thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. Classical thermodynamics deals with dynamic equilibrium states...
, Φ
G is a minimum.
The
grand potential is a quantity used in
statistical mechanicsStatistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force...
, especially for
irreversibleIrreversible may refer to:*Irreversibility, in thermodynamics, a process that is not reversible*Irréversible, a 2002 film*Irréversible , soundtrack to the film Irréversible...
processes in
open system-----Headline text--68.60.171.151 22:28, 19 October 2009 jenise:Open system may refer to:*Open system , one of a class of computers and associated software that provides some combination of interoperability, portability and open software standards, particularly Unix and Unix-like systems*Open...
s.
Grand potential is defined by
Where E is the
energyIn physics, energy is a scalar physical quantity that describes the amount of work that can be performed by a force, an attribute of objects and systems that is subject to a conservation law...
, T is the
temperatureIn physics, temperature is a physical property of a system that underlies the common notions of hot and cold; something that feels hotter generally has the higher temperature. Temperature is one of the principal parameters of thermodynamics...
of the system, S is the
entropyEntropy is a concept of information maintaining great importance in physics, chemistry, and information theory...
, μ is the
chemical potentialChemical potential, symbolized by μ, is a quantity first described by the American engineer, chemist and mathematical physicist Josiah Williard Gibbs...
, and N is the number of particles in the system.
The change in the grand potential is given by
Where P is
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
and V is
volumeThe volume of any solid, liquid, gas, plasma, theoretical object, or vacuum is how much three-dimensional space it occupies, often quantified numerically. One-dimensional figures and two-dimensional shapes are assigned zero volume in the three-dimensional space...
.
When the system is in
thermodynamic equilibriumIn thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. Classical thermodynamics deals with dynamic equilibrium states...
, Φ
G is a minimum. This can be seen by considering that dΦ
G is zero if the volume is fixed and the temperature and chemical potential have stopped evolving.
For an ideal gas,
where Ξ is the grand partition function, k
B is
Boltzmann constantThe Boltzmann constant is the physical constant relating energy at the particle level with temperature observed at the bulk level. It is the gas constant R divided by the Avogadro constant N
A:...
, Z
1 is the
partition functionPartition function may refer to:*Partition function *Partition function , which generalizes its use in statistical mechanics and quantum field theory:**Partition function...
for 1 particle and β is equal to 1 / k
BT.
Landau free energy
Some authors refer to the
Landau free energy or
Landau potential as:
named after Russian physicist
Lev LandauLev Davidovich Landau was a prominent Soviet physicist who made fundamental contributions to many areas of theoretical physics...
, which may be a synonym for the grand potential, depending on system stipulations.
External links