Question

The root mean square speed of a definite amount of ideal gas molecules placed in a container having piston will be doubled if:

• A. pressure is doubled at constant volume
• B. pressure is made four times at constant volume
• C. volume is made four times at constant pressure
• D. volume is increased by 41.4% at constant pressure

Answer 1

Answer: (B), (C)

pressure is made four times at constant volume
volume is made four times at constant pressure

The formula of root mean square speed = $\sqrt{3RT/M}$ where M = molecular mass and T is the absolute temperature.

Now for ideal gas, PV = nRT. So substituting RT in the above equation, $c_{rms}=\sqrt{3PV/nM}$.

So if we take the pressure four times then $c_{rms}$ will get doubled same for volume also.

So the correct options are B and C