The Bertholet’s equation of state for 1 mole real gas is given as under:
$\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{TV}}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$
Where a and b are van der Waal’s constants. van der Waal’s constant “a” signifies, the force of attraction among the gas molecules. van der Waal’s constant “b” signifies incompressible volume i.e. volume having no effect of compression and expansion. It is also known as co-volume. Thereby the volume having effect of compression and expansion i.e. compressible volume = V – b (for 1 mole real gas).One of the form of van der Waal’s equation of state is virial equation. The virial equation for 1 mole real gas is as under:
$\mathrm{PV}=\mathrm{RT}\left[1+\frac{\mathrm{A}}{\mathrm{V}}+\frac{\mathrm{B}}{{\mathrm{V}}^2}+\frac{\mathrm{C}}{{\mathrm{V}}^3}+\dots \text{ to higher power of }\mathrm{n}\right]$
where A, B, C are known as 2^nd, 3^rd and 4^th virial coefficients respectively. The temperature at which real gases obey ideal gas equation (PV = RT), is known as Boyles temperature i.e. T_B.