Q 11-12-103JEE MainJEE Main 2021 (24 Feb, Shift 2)Easy
The root-mean-square speed of molecules of a given mass of a gas at 27 °C and 1 atmosphere pressure is $200\ \text{m s}^{-1}$. The root-mean-square speed of molecules of the gas at 127 °C and 2 atmosphere pressure is $\dfrac{x}{\sqrt3}\ \text{m s}^{-1}$. The value of $x$ will be ______.
Numerical value type. Enter your answer.
Answer: 400
$v_{rms} = \sqrt{\dfrac{3RT}{M}}$ depends only on temperature, not on pressure.
$$v' = 200\sqrt{\frac{400}{300}} = 200\cdot\frac{2}{\sqrt3} = \frac{400}{\sqrt3}\ \text{m s}^{-1}$$
So $x = 400$.
Solution by Sreeraj P, M.Sc Physics