First slide

Rms speed

Question

The root mean square speed of molecules of a given mass of a gas at 27°C and 1 atmosphere pressure is 200 ms^-1. The root mean square speed of molecules of the gas at 127°C and 2 atmosphere pressure is $\frac{x}{\sqrt{3}} {ms}^{- 1}$ . The value of x will be ______

Easy

A

400
B

300
C

200
D

100

Solution

$v_{mo} = \sqrt{\frac{3 RT}{M}} v_{mo} = \sqrt{T} \frac{{(v_{rmo})}_{2}}{{(v_{rmo})}_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{400}{300}} = \frac{2}{\sqrt{3}} {(v_{rmo})}_{2} = \frac{2}{\sqrt{3}} {(v_{rmo})}_{1} = \frac{2}{\sqrt{3}} \times 200 {(v_{rmo})}_{2} = \frac{400}{\sqrt{3}} m / s = 400$

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