Question

The compressibility factor for a gas under critical conditions is:

• A. $\frac{3}{8}$
• B. $\frac{8}{3}$
• C. 1
• D. $\frac{1}{4}$

Answer 1

The correct option is A $\frac{3}{8}$

We know that,
$Z=\frac{PV}{RT}$
$P_c,V_c,T_c$​ are critical pressure, volume and temperature.
$\Rightarrow =\frac{P_C{V}_C}{R{T}_C}$
By substituting, $P_c=\frac{a}{27b^2},V_c=3b,T_c=\frac{8a}{27Rb}$
$=\frac{a}{27b^2}\times 3b\times \frac{1}{R}\times \frac{27Rb}{8a}=\frac{3}{8}$