The root-mean-square speed of molecules of a given mass of a gas at...

The root-mean-square speed of molecules of a given mass of a gas at

27 ° C

and

1

atmosphere pressure is

200m{s}^{- 1} .

The root-mean-square speed of molecules of the gas at

127 ° C

and

2

atmosphere pressure is

\dfrac{x}{\sqrt{3}}m{s}^{- 1} .

The value of

x

will be __________.

Correct answer

Step-by-step solution

{v}_{rms} = \sqrt{\dfrac{3RT}{M}}⇒ {v}_{rms} ∝ \sqrt{T}⇒ \dfrac{\left({v}_{rms}\right)2}{\left({v}_{rms}\right)1} = \sqrt{\dfrac{T2}{{T}_{1}}}= \sqrt{\dfrac{400}{300}}= \dfrac{2}{3} $</p><p>\left({v}_{rms}\right)2 = \dfrac{2}{3}\left({v}_{rms}\right)1= \dfrac{2}{3} \times 200⇒ \left({v}_{rms}\right)2 = \dfrac{400}{3}ms^{- 1}$ .

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