Q. A gas mixture consists of molecules of type $1,2$ and $3,$ with molar masses $m_{1} > m_{2} > m_{3}$. $V_{rms}\ $ and $\overline{K}\ $are the$\ r.m.s.$ speed and average kinetic energy of the gases. Which of the following is true
A) $\left( V_{rms} \right)_{1} < \left( V_{rms} \right)_{2} < \left( V_{rms} \right)_{3}$ and $\left( \overline{K} \right)_{1} = \left( \overline{K} \right)_{2} = ({\overline{K}}_{3})$
B) $\left( V_{rms} \right)_{1} = \left( V_{rms} \right)_{2} \leq \left( V_{rms} \right)_{3}$ and $\left( \overline{K} \right)_{1} = \left( \overline{K} \right)_{2} > \left( \overline{K} \right)_{3}$
C) $\left( V_{rms} \right)_{1} > \left( V_{rms} \right)_{2} < \left( V_{rms} \right)_{3}$ and $\left( \overline{K} \right)_{1} < \left( \overline{K} \right)_{2} > ({\overline{K}}_{3})$
D) $\left( V_{rms} \right)_{1} > \left( V_{rms} \right)_{2} > \left( V_{rms} \right)_{3}$ and $\left( \overline{K} \right)_{1} < \left( \overline{K} \right)_{2} < \left( \overline{K} \right)_{3}$
Explanation
(a) $v_{rms} \propto \frac{1}{\sqrt{M}} \Rightarrow \left( v_{rms} \right)_{1} < \left( v_{rms} \right)_{2} < \left( v_{rms} \right)_{3}$ also in mixture temperature of each gas will be same, hence kinetic energy also remains same
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.