First slide

Calculation of pressure

Question

In a vessel, the gas is at pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be

Easy

A

2P
B

P
C

P/2
D

4P

Solution

$As P = \frac{1}{3} \frac{m N}{V} v_{rms}^{2} . . . . . (i)$
where m is the mass of each molecule, N is the total number of molecules, V is the volume of the gas. When mass of all the molecules is halved and their speed is doubled, then the pressure will be
$P^{'} = \frac{1}{3} (\frac{m}{2}) \times \frac{N}{V} \times {(2 v_{rms})}^{2} = \frac{2}{3} \frac{m N}{V} v_{rms}^{2} = 2 P . . . . . (u \sin g (i))$

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