Q. The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at $0℃$ is $3180\ metres/second.$ The pressure on the hydrogen gas is (Density of hydrogen gas is $8.99 \times 10^{- 2}kg/m^{3},$ $1\ atmosphere = 1.01 \times 10^{5}N/m^{2}$)
A) $1.0\ atm$
B) $1.5\ atm$
C) $2.0\ atm$
D) $3.0\ atm$
Explanation
(d) $v_{rms} = \sqrt{\frac{3P}{\rho}} \Rightarrow P = \frac{v_{rms}^{2}\rho}{3} = \frac{(3180)^{2} \times 8.99 \times 10^{- 2}}{3}$
$= 3.03 \times 10^{5}N/m^{2} = 3\ atm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.