n is the number density, i.e. number of molecules per unit volume. k B is the Boltzmann constant introduced above. Its value in SI units is .
× – J K – . Another useful form of Eq. ( . ) is P ρ ( .
) where ρ is the mass density of the gas. A gas that satisfies Eq. ( . ) exactly at all pressures and temperatures is defined to be an ideal gas .
An ideal gas is a simple theoretical model of a gas. No real gas is truly ideal. Fig. .
shows departures from ideal gas behaviour for a real gas at three different temperatures. Notice that all curves approach the ideal gas behaviour for low pressures and high temperatures. At low pressures or high temperatures the molecules are far apart and molecular interactions are negligible. Without interactions the gas behaves like an ideal one.
If we fix µ and T in Eq. ( . ), we get PV = constant ( . ) i.e., keeping temperature constant, pressure of a given mass of gas varies inversely with volume.
This is the famous Boyle’s law . Fig. . shows comparison between experimental P-V curves and the theoretical curves predicted by Boyle’s law.
Once again you see that the agreement is good at high temperatures and low pressures. Next, if you fix P , Eq. ( . ) shows that V ∝ T i.e., for a fixed pressure, the volume of a gas is proportional to its absolute temperature T (Charles’ law) .
. Experimental P-V curves (solid lines) for steam at three temperatures compared with Boyle’s law (dotted lines). P is in units of atm and V in units of . litres.
Finally, consider a mixture of non-interacting ideal gases: µ moles of gas , µ moles of gas , etc. in a vessel of volume V at temperature T and pressure P . It is then found that the equation of state of the mixture is : PV = ( µ + µ +… ) RT ( . ) i.e.