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^-1The 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 ______

Moderate

A

400
B

300
C

200
D

100

Solution

$\begin{array}{l} v_{r m s} = \sqrt{\frac{3 RT}{M}} \\ v_{r m s} \propto \sqrt{T} \\ \frac{{(v_{rm s})}_{2}}{{(v_{rm s})}_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{400}{300}} = \frac{2}{\sqrt{3}} \end{array}$
$\begin{array}{l} {(v_{rm s})}_{2} = \frac{2}{\sqrt{3}} {(v_{rm s})}_{1} = \frac{2}{\sqrt{3}} \times 200 \\ {(v_{rm s})}_{2} = \frac{400}{\sqrt{3}} m / s \Rightarrow x = 400 \end{array}$

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