First slide

Calculation of pressure

Question

In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as T^q.A good estimate for q is

Easy

A

2
B

1
C

$\frac{1}{2}$
D

$\frac{1}{4}$

Solution

Time interval between two successive collision at a face is $2 l / u .$
Number of Collisions= $\frac{u}{2 l}$
Change of momentum /collision =2mu
$\frac{u}{2 l} \times 2 mu = \frac{{mu}^{2}}{l} = F F \propto u^{2} \Rightarrow F \propto T$
Therefore , q=1

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