Q. At constant pressure, which of the following is true?
A) $v \propto \sqrt{\rho}$
B) $v \propto \frac{1}{\rho}$
C) $v \propto \rho$
D) $v \propto \frac{1}{\sqrt{\rho}}$
Explanation
(d) Pressure due to an ideal gas is given by
$p = \frac{M}{3V}v^{2}$
Putting $\frac{M}{V} = \rho,$ the density of gas
$p = \frac{1}{3}\rho v^{2}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v = \sqrt{(\frac{3p}{\rho})}\ $
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v \propto \frac{1}{\sqrt{\rho}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.