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 dependence on P is linear at all pressures
B. For the gas B `b = 0` and its denpendence on P is linear at all pressures
C. For the gas C, which is a 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

C

Explanation

van der Waal's equation is `(P + (a)/(V^(2))) (V - b) = RT` when a = 0,
`P (V - b) = RT " or " PV = RT + Pb`
or `(PV)/(RT)`, i.e., `Z = 1 + (Pb)/(RT)`
Thus `Z gt 1` and increases with increases of pressure. Hence (A) is correct
When `b = 0, (P + (a)/(V^(2))) V = RT` or
`PV + (a)/(V) = RT " or " (PV)/(RT)`, i.e., `Z = 1 - (a)/(RTV)`.
Thus `Z lt 1` and decreases with increases of pressure. Hence (B) is correct.
Statement (C) is also correct.
Hencce the only wrong statement is (D) because for the real gas (B) the slope is negative at all pressure.