## Ideal Gases, the Equation of State, Boyle's Law, Charles's Law, the Pressure Law

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/m ^{2 }

V = Volume in m ^{3 }

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*10 ^{5 } 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 havewhere 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*10 ^{23 }).

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