# Under what conditions does Real Gases show Ideal Behaviour? [closed]

MY textbook says : Real gases show Ideal Behavior under low pressure ,high temperature.

So I wanted to know what happens to real gases at high pressure ,low pressure Do they also show ideal behavior under those conditions?

• In order to make comparisons you have to specify other conditions i.e temperature and volume. so do the other conditions remain same or not? – user99496 Oct 3 '20 at 12:09

The van Der Waal equation is $$\left(p+\frac a{V_\mathrm m^2}\right)(V_\mathrm m-b)=RT$$ Here $$V_\mathrm m$$ is molar volume. When pressure is low and temperature is very high, we can qualitatively say that the molar volume will be very large. Due to this the volume occupied by the molecules (given by $$b$$) becomes insignificant.
The pressure is low but the molar volume $$V_\mathrm m$$ is very large and thus the term $$\frac a{V_\mathrm m^2}$$ comes out to be much much lower than the already low pressure. $$p+\frac a{V_m^2}\approx p$$ and $$V_\mathrm m-b\approx V_\mathrm m$$ Thus the gas shows ideal behavior at low pressure and high temperature.