MCQ
To what temperature should the hydrogen at $327°C$ be cooled at constant pressure, so that the root mean square velocity of its molecules become half of its previous value ....... $^oC$
- ✓$-123$
- B$123$
- C$-100$
- D$0$
✓
Answer
Correct option: A.
$-123$
a
${v_{rms}} \propto \sqrt {\frac{{3RT}}{M}} \, \Rightarrow \,\,T \propto {v^2}_{rms}$
${v_{rms}} \propto \sqrt {\frac{{3RT}}{M}} \, \Rightarrow \,\,T \propto {v^2}_{rms}$
$\Rightarrow$ $\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{v_2}}}{{{v_1}}}} \right)^2} = \frac{1}{4}$
$\Rightarrow$ ${T_2} = $$\frac{{{T_1}}}{4} = \frac{{(273 + 327)}}{4} = 150K = - {123^o}C$
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