JEE MAIN - Physics (2020 - 6th September Evening Slot - No. 6)
In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a
molecule varies with T as :
$$\sqrt T $$
T
$${1 \over T}$$
$${1 \over {\sqrt T }}$$
Explanation
Time (t) = $${V \over {4\pi \sqrt 2 {r^2}vN}}$$ ....(1)
Here, v = most probable speed
= $$\sqrt {{{2RT} \over {\pi M}}} $$
$$ \Rightarrow $$ v $$ \propto $$ $$\sqrt T $$
$$ \therefore $$ From (1),
t $$ \propto $$ $${1 \over {\sqrt T }}$$
Here, v = most probable speed
= $$\sqrt {{{2RT} \over {\pi M}}} $$
$$ \Rightarrow $$ v $$ \propto $$ $$\sqrt T $$
$$ \therefore $$ From (1),
t $$ \propto $$ $${1 \over {\sqrt T }}$$
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