Question

If the mean free path of a gas is $\lambda$ at one atmospheric pressure, then its value at 5 atmospheric pressure will be (temperature is assumed to be constant)

• A. $\lambda$
• B. $5\lambda$
• C. $\frac{3}{2}\lambda$
• D. $\frac{\lambda }{5}$

Answer 1

The correct option is D $\frac{\lambda }{5}$

the maxwell's mean free path equation is

$\lambda =\frac{1}{\sqrt{2}\pi d^{2}n}d=$ diameter of molecule

or $\lambda =\frac{1}{\sqrt{2}\pi d^2\cdot \frac{P}{kT}}P=nkT$

or $\lambda \propto \frac{1}{P}$

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{P_2}{P_1}$

or $\frac{\lambda }{{\lambda }_2}=\frac{5}{1},{\lambda }_1=\lambda =$ mean free path at

1 atmosphere ${\lambda }_2=\frac{\lambda }{5}$

Ans Option (D).