Question

An ideal gas is enclosed in a cylinder at pressure of $2$ atm and temperature, $300 \,K$. The mean time between two successive collisions is $6 \times 10^{-8} s$. If the pressure is doubled and temperature is increased to $500\, K$, the mean time between two successive collisions will be close to:

• A. $4 \times 10^{8}S$
• B. $3 \times 10^{6}S$
• C. $2 \times 10^{7}S$
• D. $0.5 \times 10^{8}S$

Answer 1

Answer: (A)

$t \propto \frac{Volume}{velocity}$
vloume $\propto \frac{T}{P}$
$\therefore \, \, \, t \, $ \propto $\frac{\sqrt{T}}{P}$
$\frac{t_1}{6 \times 10^{-8}} \, = \frac{\sqrt{500}}2P{} \, \times \, \frac{P}{\sqrt{300}} $
$t_1 \, = \, 3.8 \times \, 10^{-8}$
≈ $4 \times \, 10^{-8}$