# Doubts about the characteristics of a real gas

I was studying about ideal gases and the changes made in the ideal gas equations to transform it into the real gas equation. So firstly in the book they considered the effect of finite volume of the gas molecules in the equation which was completely neglected in the case of ideal gas. My question is - Suppose we consider a gas which follows all the properties of an ideal gas except that the volume of the gas molecules is not negligible , that is the molecules have some finite volume. Now can we compare the collision frequency of the gas which we have considered now with an ideal gas which is totally same with this gas except that the volume of the molecules is negligible ? By comparison i want to know whose collision frequency will be more. Here collision frequency refers to the number of collision of the gas molecules with the walls of a closed container in which it is placed per unit time per unit area.

## 1 Answer

I think the difficulty you may be having is assuming the reason an ideal gas molecule has to have negligible volume is related to the collision frequency of the molecules with each other and the walls of the container. Generally that's not the reason. Collision frequency doesn't matter because the collisions are considered to be perfectly elastic.

In actuality, there are several reasons to consider the molecules at solid point masses. Here are two (there may be others).

One is the size of the particles needs to be small compared to the distance between the particles so that the otherwise attractive electrostatic intermolecular forces (van der Waals forces) can be considered negligible. It is for this reason a gas behaves more like an ideal gas at higher temperatures and lower pressures since this results in greater separation of the molecules making the potential energy due to intermolecular forces much less than the particles kinetic energy

The other is the collision of point particles with each other and the container walls can be considered as perfectly elastic. In other words the particles do not lose kinetic energy as a result of collisions so that the kinetic energy of the system is unchanged. Therefore any change in the internal energy of the system is due only to temperature change. The temperature of the gas is a measure of the average kinetic energy of the particles.

Hope this helps.