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  • The root mean square speed of molecules of a given mass of a gas at 27o C and 1 atmosphere pressure is 200 ms -1. The root mean sqaure speed of molecules of the gas at 127o C and 2 atmosphere pressure is <img alt="\frac

The root mean square speed of molecules of a given mass of a gas at 27o C and 1 atmosphere pressure is 200 ms -1. The root mean sqaure speed of molecules of the gas at 127o C and 2 atmosphere pressure is \frac{x}{\sqrt{3}} ms -1. The value of x will be ______.
Option: 1 100
Option: 2 200
Option: 3 300
Option: 4 400

Answers (1)

best_answer

The rms velocity of gas molecules,

  v_{\text {rms }} \propto \sqrt{T} \ \ \ \left[as \ \ v_{\text {rms }}=\sqrt{\frac{3 R T}{m}}\right]

So

\begin{aligned} \frac{\left(\mathrm{v}_{\mathrm{rms}}\right)_{1}}{\left(\mathrm{~v}_{\mathrm{rms}}\right)_{2}} &=\sqrt{\frac{T_{1}}{T_{2}}} \\ \Rightarrow \frac{200}{\left(v_{r m s}\right)_{2}} &=\sqrt{\frac{300}{400}}=\sqrt{\frac{3}{4}} \\ \Rightarrow\left(v_{r m s}\right)_{2} &=\frac{2}{\sqrt{3}} \times 200 = \frac{400}{\sqrt{3}} \mathrm{~m} / \mathrm{s} \end{aligned}

So

x=400

Posted by

avinash.dongre

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