Question

The maximum speed of the molecules of a gas in a vessel is $400m/s$. If half of the gas leaks out, at constant temperature, the $rms$ speed of the remaining molecules will be-

• A. $800m/s$
• B. $400\sqrt{2}m/s$
• C. $400m/s$
• D. $200m/s$

Answer 1

The correct option is C $400m/s$

Given,

$v_{rms}=400m/s$

The RMS speed of the molecules will be

$v_{rms}=\sqrt{\frac{3RT}{M}}$. . . . . .(1)

where $R=$ universal gas constant

$T=$ temperature

$M=$ molecular weight

The RMS speed does not depend on the quantity of the gas. For a given gas and the temperature, it remains constant.

So, the RMS speed of the remaining molecules is $400m/s$.

The correct option is C.