An ideal gas is only ideal within certain limits of temperature, pressure and volume. Within these limits the behaviour of the gas will be described by

Boyle's Law:if the temperature is kept constant.

Charles's Law:if the pressure is kept constant.

The Pressure Law:if the volume is kept constant.

These can be combined into the Ideal Gas Equation, or The Equation of State:(1) where

p = Pressure in Pa or N/m²

V = Volume in m³

n = number of moles in the gas mixture.

R = 8.314 J/mol K. - The Universal Gas Constant or Universal Molar Gas Constant.

T = Temperature.

No reference is made in the above equation to the type of gas or the mass or type of molecules – whether large or small.. In fact these factors are irrelevant – the equations apply to all type of gas withou modification. In fact it is part of the theory that all gases at s.t.p. - standard temperature (0 degrees Celsius, 273.15 degrees Kelvin) and pressure (1.013*10⁵ Pa) occupy the same volume of 22400 cm^3.

The equation(1) is not the only possible form of the equation of state. We may express it in terms of the average kinetic energy of the gas molecules:

(2)

The kinetic energy of a particle massisTogether with the equation above we have where N is the total number of gas molecules.

By putting the right hand side of (1) equal to the right hand side of (2) we obtain

so

n is the number of moles and N is the number of atoms soAvagadro's Number (=6.023*10²³).

Hencewhere k=Boltsmann's constant =1.38*10^-23 J/molecule K