An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K . The mean time b

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 $6 	imes 10^{-8} \mathrm{~s}$. If the pressure is doubled and temperature is increased to 500 K , the mean time between two successive collisions will be close to\

Professor PC Thomas Classes · Answer

(a) : Mean time between\ two successive collisions\ $	au \propto \frac{1}{	ext { velocity } 	imes 	ext { number of particles }}$ per unit volume\ $\Rightarrow 	au \propto \frac{1}{\sqrt{T}} \frac{T}{P}=\frac{\sqrt{T}}{P}$\ $	herefore \quad 	au_{1}=	au_{2} \frac{P_{2}}{P_{1}} \sqrt{\frac{T_{1}}{T_{2}}}$\ $\Rightarrow \quad 	au_{2}=\frac{6 	imes 10^{-8}}{2} \sqrt{\frac{500}{300}}=\sqrt{15} 	imes 10^{-8}$ $$ \simeq 4 	imes 10^{-8} \mathrm{~s} $$