Kinetic Theory

JEE Main level, single correct, medium

62 of 168

Question 62 of 168

An ideal gas is enclosed in a cylinder at pressure of 22 atm and temperature, 300K.300K. The mean time between two successive collisions is 6×10−8s.6\times {10}^{-8}s. If the pressure is doubled and temperature is increased to 500K,500K, the mean time between two successive collisions will be close to:

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Answer: (D) 4x10−8s4x{10}^{-8}s

τ=12nπd2vavg\tau =\dfrac{1}{\sqrt{2}n\pi {d}^{2} {v}_{avg}}

Where n=n= number of molecules per unit volume.

τ∝VT⇒τ∝TP\tau \propto \dfrac{V}{\sqrt{T}}\Rightarrow \tau \propto \dfrac{\sqrt{T}}{P}

τ2τ1=T2T1.P1P2⇒τ2=6×10−8×5000300×24\dfrac{{\tau }_{2}}{{\tau }_{1}}=\sqrt{\dfrac{{T}_{2}}{{T}_{1}}}.\dfrac{{P}_{1}}{{P}_{2}}\Rightarrow {\tau }_{2}=6\times {10}^{-8}\times \sqrt{\dfrac{5000}{300}}\times \dfrac{2}{4}

≈4×10−8s\approx 4\times {10}^{-8}s

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