Question

The value of compression factor of a van der Waals gas at critical point is?

• A. $8/27$
• B. $27/8$
• C. $3/8$
• D. $8/3$

Answer 1

Answer: (C)

$3/8$

Solution:- (C) $\frac{3}{8}$

As we know that, compression factor $\left(Z\right)$ is given by-

$Z=\frac{PV}{RT}$

Whereas,

$P=$ pressure

$V=$ molar volume of the gas

$R=$ Universal gas constant

$T=$ temperature

At critical point-

$P=\frac{a}{27b^2}$

$V=3b$

$T=\frac{8a}{27Rb}$

$\therefore Z=\frac{\left(\frac{a}{27b^2}\right)3b}{R\left(\frac{8a}{27Rb}\right)}$

$\Rightarrow Z=\frac{3}{8}$

Hence the value of compression factor of a van der Waals gas at critical point is $\frac{3}{8}$.