First slide

Rms speed

Question

Gas at pressure P_o is contained in a vessel. If the masses of all the molecules are halved and their speed doubled, the resulting pressure P will be equal to

Moderate

A

$4 P_{0}$
B

$2 P_{0}$
C

$P_{0}$
D

$P_{0} / 2$

Solution

We know that $P_{0} = \frac{1}{3} (\frac{mn}{V}) {V_{rms}}^{2}$
If $m = m / 2 and v_{rms} = 2 v_{rms}$ , then
$P = \frac{1}{3} (\frac{mn}{2 V}) {(2 v_{rms})}^{2} = \frac{1}{3} (\frac{mn}{V}) 2 {v_{rms}}^{2} = 2 P_{0}$

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