Search any question & find its solution
Question:
Answered & Verified by Expert
To what temperature should the hydrogen at $327^{\circ} \mathrm{C}$ be cooled at constant pressure, so that the root mean square velocity of its molecules becomes half of its previous value?
Options:
Solution:
1318 Upvotes
Verified Answer
The correct answer is:
$-123^{\circ} \mathrm{C}$
$v_{\mathrm{ms}} \propto \sqrt{\frac{3 R T}{M}}$
$$
\begin{array}{ll}
\Rightarrow & T \propto v_{\mathrm{rms}}^{2} \\
\Rightarrow & \frac{T_{2}}{T_{1}}=\left[\frac{v_{2}}{v_{1}}\right]^{2}=\frac{1}{4} \\
\Rightarrow & T_{2}=\frac{T_{1}}{4}=\frac{(273+327)}{4} \\
& =150 \mathrm{~K}=-123^{\circ} \mathrm{C}
\end{array}
$$
$$
\begin{array}{ll}
\Rightarrow & T \propto v_{\mathrm{rms}}^{2} \\
\Rightarrow & \frac{T_{2}}{T_{1}}=\left[\frac{v_{2}}{v_{1}}\right]^{2}=\frac{1}{4} \\
\Rightarrow & T_{2}=\frac{T_{1}}{4}=\frac{(273+327)}{4} \\
& =150 \mathrm{~K}=-123^{\circ} \mathrm{C}
\end{array}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.