Figure displays the plot of the compression factor `Z` veres `p` for a few gases

Which of the following statements is//are correct for a van-der waals gas:

Options

A. The plot I is applicable provided the vander waals constant a is negligible.
B. The plot II is a applicable provided the vander waals constant `b` is negligible.
C. The plot III is applicable provided the vander waals constants `a` and `b` are negligible.
D. The plot IV is applicable provided the temperature of the gas is much higher than its critical temperature

Answer

A, B, C

Explanation

The vander waals equation of state is: (for 1 mole of gas)
`(P +(a)/(V_(m)^(2))) (V_(m) -b) = RT`
When a is negligible, then
`Z = (pV_(m))/(RT) = 1+(b)/(RT) P`
that is `Z` increases with increaser in `p`.
when `b` is negligible, then
`Z = (pV_(m))/(RT) = 1 - (a)/(VRT)`
increasing `p` implies decreases in `V`, which is turn, implies increase in the value of `a//VRT` and hence decrease in the value of `Z`.
The curve IV is applicable provided temperature of the gas is near bit larger than it's critical temperature Hence, teh choice (a),(b) and (c ) are correct.