Q. To what temperature should the hydrogen at 327$℃$ be cooled at constant pressure, so that the root mean square velocity of its molecules becomes half of its previous value?
A) -123$℃$
B) 123$℃$
C) $- 100℃$
D) 0$℃$
Explanation
(a) $v_{rms} \propto \sqrt{\frac{3RT}{M}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T \propto v_{rms}^{2}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \frac{T_{2}}{T_{1}} = \left\lbrack \frac{v_{2}}{v_{1}} \right\rbrack^{2} = \frac{1}{4}\ \Rightarrow T_{2} = \frac{T_{1}}{4} = \frac{273 + 327}{4}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 150\ K = - 123℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.