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

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Heat & Thermodynamics

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

2 7^{\circ} C

and 1 atmosphere pressure is

200 ms^{- 1}

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

12 7^{\circ} C

and 2 atmosphere pressure is

\frac{x}{3} ms^{- 1}

. The value of

x

will be.

Answer: 400

Solution

The root mean square speed

v_{r m s} = \frac{3 R T}{M}

is fixed by the temperature alone, so the change of pressure has no effect. With

T_{1} = 300

K and

T_{2} = 400

\frac{v _{2}}{v _{1}} = \frac{T _{2}}{T _{1}} = \frac{4}{3} = \frac{2}{3}

v_{2} = 200 \times \frac{2}{3} = \frac{400}{3} m s^{- 1}

. Comparing with

\frac{x}{3} m s^{- 1}

gives

x = 400

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Integer answer

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