Question

The given graph represents the variation of $Z$ (compressibility factor $=\frac{PV}{nRT}$ ) versus $P$, for three real gases $A,B$ and $C.$ Identify the only incorrect statement.

• 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 dependence on $P$ is linear at all pressures.
• C. $C$ is less compressible than expected from ideal behaviour.
• D. At high pressure, the slope is positive for all real gases.

Answer 1

Answer: (C)

van der Waals equation is $\left(P+\frac{a}{V^2}\right)(V-b)=RT$

When $a=0,P(V-b)=RT$ or $PV=RT+Pb$

i.e., $Z=1+\frac{Pb}{RT}.$ Thus, $Z>1$ and increases with increase of

pressure. Hence (a) is correct.

When $b=0,\left(P+\frac{a}{V^2}\right)V=RT$ or $PV+\frac{a}{V}=RT$

i.e., $Z=1-\frac{a}{RTV}$. Thus, $Z<1$ and decreases with increase of pressure. Hence, $(b)$ is correct.

Statement $(d)$ is also correct. $C$ shows negative deviation, it implies $C$ is more compressible than expected from ideal behaviour