Question

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

• A. – 123°C
• B. 123°C
• C. – 100°C
• D. 0°C

Answer 1

Answer: (A)

– 123°C

Answer 2

$v_{rms} \propto \sqrt{\frac{3RT}{M}} \Rightarrow T \propto {v^{2}}_{rms}$Ž $\frac{T_{2}}{T_{1}} = \left( \frac{v_{2}}{v_{1}} \right)^{2} = \frac{1}{4}$

Ž $T _ { 2 } =$ $\frac{T_{1}}{4} = \frac{(273 + 327)}{4} = 150K = - 123^{o}C$