Q. Gas at a pressure $P_{0}$ in contained is a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure $P$ will be equal to
A) $4P_{0}$
B) $2P_{0}$
C) $P_{0}$
D) $\frac{P_{0}}{2}$
Explanation
(b) $v_{rms} = \sqrt{\frac{3P}{\rho}} = \sqrt{\frac{3PV}{m}} \Rightarrow v_{rms} \propto \sqrt{\frac{P}{m}}$
$\Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{P_{1}}{P_{2}} \times \frac{m_{2}}{m_{1}}} \Rightarrow \frac{v}{2v} = \sqrt{\frac{P_{0}}{P2} \times \frac{m/2}{m}} \Rightarrow P_{2} = 2P_{0}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.