Question

The temperature should the hydrogen at $327 \, ^\circ C$ be cooled at constant pressure so that the root mean square velocity of its molecules becomes half of its previous value is

• A. $-123^\circ C$
• B. $123 \, ^\circ C$
• C. $-100 \, ^\circ C$
• D. $0^\circ C$

Answer 1

Answer: (A)

$v_{r m s} \propto \sqrt{\frac{3 R T}{M}}$
$\Rightarrow \, \, \, T \propto v_{r m s}^{2}$
$\Rightarrow \, \, \frac{T_{2}}{T_{1}}=\left[\frac{v_{2}}{v_{1}}\right]^{2}=\frac{1}{4} \, \Rightarrow T_{2}=\frac{T_{1}}{4}=\frac{273 + 327}{4}$
$ \, \, =150 \, K=-123℃$