one model of ideal gas is that 1 they are composed of particles so tiny compared to volume of the gas that they can be considered zero-volume point in space, and 2 they are no interactions,attractive or repulsive, between the individual gas particles. However,real gas ultimately have behaviors due to the facts that 1 gas atoms and molecules do have a size, and 2 there is some interaction between the gas particles, which can range from minimal to very large. In considering the state variables of a gas, the volume of the gas particles should have an effect on the volume V of the gas. the interaction between gas particles would have an effect on the pressure P of the gas. Perhaps a better equation of state for a gas should take these effect into account.
In 1873, suggested a somewhat corrected version of the ideal gas law.It is one of the simpler equations of state for real gas, and it referred to as the van der walls equation
where n is the number of moles of gas, and a and b are the van der waals constants for a particular gas. the van der waals constants a represents the pressure