Question

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

The correct option is A $4\times {10}^{-8}s$

$t\alpha \frac{Volume}{Velocity}$
Volume $\alpha \frac{T}{P}$
$\therefore t\alpha \frac{\sqrt{T}}{P}$
$\frac{t_1}{6\times {10}^{-8}}=\frac{\sqrt{500}}{2P}\times \frac{P}{\sqrt{300}}$
$t_1=3.8\times {10}^{-8}$
$\approx 4\times {10}^{-8}$