The given graph represents the variations of compressibility factor `Z=PV//nRT` vs `P` for three real gases `A`, `B`, and `C`.

Identify the incorrect statements.

Options

A. for the gas A, a = 0 and its dependent on P is linear at all pressures
B. for the gas B, B = 0 and its dependence on P, is linear at all pressures
C. for the gas C, which is typical real gas for which neither a nor b = 0. By knowing the minima and the point of intersection, with `Z = 1` , a and b can be calculated
D. at high pressure, the slope is positive for all real gases.

Answer

B

Explanation

From the graph,it is cleart that value of decreases with increase in pressure. But it does not vary linearly. Actually at high pressure, P being large V will be small. As such 'b' cannot be ignord as compared to V. However, `a//V^(2)` can be ignored or neglected as compared to P in van der Waals' equation.
`(P+a//V^(2))(V-b)=RT`
`P(V-b)=RT` or `(PV)/(RT) - (Pb)/(RT) = 1`
`Z = 1+(Pb)/(RT)`
It is clear that Z is greater than 1 and increases with increase in pressure.