Q. Consider a gas with density $\rho$ and $\overline{c}$ as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity $v,\ $then the pressure exerted by the gas is
A) $\frac{1}{3}\rho{\overline{c}}^{2}$
B) $\frac{1}{3}\rho(c + v)^{2}$
C) $\frac{1}{3}\rho\left( \overline{c} - v \right)^{2}$
D) $\frac{1}{3}\rho\left( c^{- 2} - v \right)^{2}$
Explanation
(a) Pressure of the gas will not be affected by motion of the system, hence by
$v_{rms} = \sqrt{\frac{3P}{\rho}} \Rightarrow {\overline{c}}^{2} = \frac{3P}{\rho} \Rightarrow P = \frac{1}{3}\rho{\overline{c}}^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.