First slide

Mean free path

Question

The average collision period in a gas undergoing isobaric process is

Moderate

A

Inversely proportional to temperature
B

Directly proportional to temperature
C

Directly proportional to square root of temperature
D

Independent of temperature

Solution

Average collision period, $t = \frac{1}{π d^{2} v n \sqrt{2}} \Rightarrow t \propto \frac{1}{v n}$ (v = average speed, n = number density of molecules).
$v = \sqrt{\frac{8 R T}{π M}} α \sqrt{T}$ and $n = \frac{N}{V} α \frac{1}{V}$
In isobaric process, $V α T$
So, $t α \frac{1}{v n} α \frac{V}{\sqrt{T}} α \sqrt{T}$

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