First slide

Kinetic theory of ideal gases

Question

The rms velocity of the molecules in a sample of helium is ${(\frac{5}{7})}^{t h}$ of that of the molecules in a sample of hydrogen. If the temperature of hydrogen gas is $0 ° C$ , the temperature of the helium sample is nearly equal to

Moderate

A

4K
B

$0 ° C$
C

$273 ° C$
D

$100 ° C$

Solution

$\begin{array}{l} v_{RMS} = \sqrt{\frac{3 RT}{M}} \\ {(v_{RMS})}_{He} = \frac{5}{7} {(v_{RMS})}_{H} \Rightarrow \sqrt{\frac{3 {RT}_{He}}{M_{He}}} = \frac{5}{7} \sqrt{\frac{3 {RT}_{H}}{M_{H}}} \\ \Rightarrow T_{He} = \frac{25}{49} \frac{M_{He} T_{H}}{M_{H}} = (\frac{25}{49}) \frac{4}{2} (273) K \approx 273 K = 0^{\circ} C \end{array}$

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