Virial expansion
Encyclopedia
The classical virial expansion expresses the pressure
of a many-particle system in equilibrium
as a power series in the density
.
The virial expansion was introduced in 1901 by Heike Kamerlingh Onnes
as a generalization of the ideal gas
law. He wrote for a gas containing
atoms
or molecules,
where
is the pressure, 
is the Boltzmann constant, 
the absolute temperature, and
is the number density of the
gas.
Note that for a gas containing a fraction
of 
(Avogadro's number) molecules, truncation of the virial expansion after the
first term leads to
, which is the ideal gas
law.
Writing
, the virial expansion can be written in closed form as
.
The virial coefficient
s
are characteristic of the interactions between the particles in the system and in general depend on the temperature 
.
Pressure
Pressure 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 :...
of a many-particle system in equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...
as a power series in the density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
.
The virial expansion was introduced in 1901 by Heike Kamerlingh Onnes
Heike Kamerlingh Onnes
Heike Kamerlingh Onnes was a Dutch physicist and Nobel laureate. He pioneered refrigeration techniques, and he explored how materials behaved when cooled to nearly absolute zero. He was the first to liquify helium...
as a generalization of the ideal gas
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...
law. He wrote for a gas containing
atomsor molecules,
where
is the pressure, is the Boltzmann constant, the absolute temperature, and is the number density of thegas.
Note that for a gas containing a fraction
of (Avogadro's number) molecules, truncation of the virial expansion after thefirst term leads to
, which is the ideal gasIdeal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...
law.
Writing
, the virial expansion can be written in closed form as.The virial coefficient
Virial coefficient
Virial coefficients B_i appear as coefficients in the virial expansion of the pressure of a many-particle system in powers of the density, providing systematic corrections to the ideal gas law...
s
are characteristic of the interactions between the particles in the system and in general depend on the temperature .