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# Gas laws

This articles outlines the historical development of the laws describing ideal gases. For a detailed description of the ideal gas laws and their further development, see Ideal gas and Ideal gas law

The gas laws are a set of laws that describe the relationship between thermodynamic temperature (T), pressure (P) and volume (V) of gases. They are a loose collection of rules developed between the late Renaissance and early 19th century.

Three earlier gas laws:

were combined to form the combined gas law

$\frac {P_1V_1} {T_1} = \frac {P_2V_2} {T_2}.$

$PV = nRT \,$,

where

P is the pressure (SI unit: pascal)
V is the volume (SI unit: cubic metre)
n is the amount of substance (loosely number of moles of gas)
R is the ideal gas constant (SI: 8.3145 J/(mol K))
T is the thermodynamic temperature (SI unit: kelvin).

(The law works with any consistent set of units, provided that the temperature scale starts at absolute zero, and the appropriate gas constant is used.)

An equivalent formulation of this law is:

$PV = NkT \,$

where

N is the number of molecules
k is the Boltzmann constant.

These equations are exact only for an ideal gas, which is a mathematical model. However, they are good approximations for many gases under many circumstances.

This law has the following important consequences:

1. If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas.
2. If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present.
3. If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume.
4. If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature.

Other gas laws of historical importance include:

Graham's law is an empirical relationship between the rate at which gas molecules effuse through porous barriers and molecular weight. These early molecule-based laws developed into the full kinetic theory of gases.
Dalton's law relates the pressure of a mixture of gases and the partial pressures of individual components. This empirical relationship was later readily explained in terms of the ideal gas laws.