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 pressure
• C. For the gas $C$, which is typical real gas for which neither $a=0$ 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 1

Answer: (B)

For the gas $B$, $b=0$ and its dependence on P is linear at all pressure

Van der Wal's equation is

$(p+\frac{q}{v^2})(v-b)=RT$

option (C) and (D) is already graphically correct Now, (a), when $a=0,p(v-b)=RT$

$\begin{array}{c}\Rightarrow PV=RT+Pb\\ \therefore \frac{PV}{RT}=1+\frac{Pb}{RT}\\ \therefore Z=1+\frac{Pb}{RT}\mid z=\frac{PV}{RT})\end{array}$

Thus $z$ ) 1 and increases limearly with increase in Pressure.

For (b), when

$\begin{array}{cc}b=0,& (p+\frac{a}{v^2})V=RT\\ & \Rightarrow PV+\frac{a}{v}=RT\\ & \Rightarrow \frac{Pv}{RT}=1-\frac{av}{RTV}\\ & \Rightarrow z=1-\frac{av}{RTV}\end{array}$

Thus, $z<1$, The gas shows ideal -ve deviation behaviour, Hence

(b) option is only incorrect option.