# gas laws

## Gas Laws Relating Three Variables

The three gas laws relating two variables can be combined into a single law relating pressure, temperature, and volume, which states that the product of pressure and volume is directly proportional to the absolute temperature, or *PV* = *kT.* This law describes the behavior of real gases only with a certain range of values for the variables. At temperatures or pressures near those at which the gas condenses to a liquid, the behavior departs from this equation. Nevertheless, it is useful to consider an ideal gas, or perfect gas, an imaginary substance that conforms to this equation for all values of the variables.

The behavior of an ideal gas can be described in terms of the kinetic-molecular theory of gases and leads directly to the relationship *PV* = *kT,* which is therefore called the ideal gas law, or general gas law. The constant of proportionality *k* is usually expressed as the product of the number of moles, *n,* of the gas and a constant *R,* known as the universal gas constant. In MKS units, *R* has the value 8.3149 × 10^{3} joules/kilogram-mole-degree. The ideal gas law can be further simplified by replacing the ordinary volume *V* by the specific volume *v,* which is equal to *V* / *n.* The law then has the form *Pv* = *RT.* This form has the advantage that all of the variables are intensive; that is, none of the variables depends on the mass of the gas.

The van der Waals equation (for the Dutch physicist Johannes van der Waals) is another gas law involving pressure, temperature, and volume. It takes into account the variations in behavior of different real gases from that of an ideal gas. The van der Waals equation is usually given as ( *P* + *a* / *v* ^{2})( *v* - *b* ) = *RT,* where *a* and *b* are constants that have different particular values for different real gases. Other, more complicated equations exist that describe the behavior of real gases over an even wider range of values for pressure, temperature, and volume.

See also thermodynamics.

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*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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