Real gases are nonideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the
ideal gas law
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...
.
To understand the behaviour of real gases, the following must be taken into account:
*
compressibility
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a fl ...
effects;
*variable
specific heat capacity
In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
;
*
van der Waals force
In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and th ...
s;
*non-equilibrium thermodynamic effects;
*issues with molecular dissociation and elementary reactions with variable composition
For most applications, such a detailed analysis is unnecessary, and the
ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
approximation can be used with reasonable accuracy. On the other hand, real-gas models have to be used near the
condensation
Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor to ...
point of gases, near
critical points, at very high pressures, to explain the
Joule–Thomson effect
In thermodynamics, the Joule–Thomson effect (also known as the Joule–Kelvin effect or Kelvin–Joule effect) describes the temperature change of a ''real'' gas or liquid (as differentiated from an ideal gas) when it is forced through a valv ...
, and in other less usual cases. The deviation from ideality can be described by the
compressibility factor
In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. It is simply defined as the ratio of the molar volume of a gas to ...
Z.
Models
Van der Waals model
Real gases are often modeled by taking into account their molar weight and molar volume
:
or alternatively:
:
Where ''p'' is the pressure, ''T'' is the temperature, ''R'' the ideal gas constant, and ''V''
m the
molar volume
In chemistry and related fields, the molar volume, symbol ''V''m, or \tilde V of a substance is the ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar ...
. ''a'' and ''b'' are parameters that are determined empirically for each gas, but are sometimes estimated from their
critical temperature
Critical or Critically may refer to:
*Critical, or critical but stable, medical states
**Critical, or intensive care medicine
*Critical juncture, a discontinuous change studied in the social sciences.
*Critical Software, a company specializing in ...
(''T''
c) and
critical pressure
In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions ...
(''p''
c) using these relations:
:
The constants at critical point can be expressed as functions of the parameters a, b:
:
With the
reduced properties
In thermodynamics, the reduced properties of a fluid are a set of state variables scaled by the fluid's state properties at its critical point. These dimensionless thermodynamic coordinates, taken together with a substance's compressibility facto ...
the equation can be written in the ''reduced form'':
:
Redlich–Kwong model
The
Redlich–Kwong equation is another two-parameter equation that is used to model real gases. It is almost always more accurate than the
van der Waals equation
In chemistry and thermodynamics, the Van der Waals equation (or Van der Waals equation of state) is an equation of state which extends the ideal gas law to include the effects of interaction between molecules of a gas, as well as accounting for ...
, and often more accurate than some equations with more than two parameters. The equation is
:
or alternatively:
:
where ''a'' and ''b'' are two empirical parameters that are not the same parameters as in the van der Waals equation. These parameters can be determined:
:
The constants at critical point can be expressed as functions of the parameters a, b:
:
Using
the equation of state can be written in the ''reduced form'':
:
with
Berthelot and modified Berthelot model
The Berthelot equation (named after D. Berthelot) is very rarely used,
:
but the modified version is somewhat more accurate
: