First slide

Kinetic theory of ideal gases

Question

At what temperature will oxygen molecules have the same root mean square speed as hydrogen molecules at 200 K?

Moderate

A

527 °C
B

1327 °C
C

2127 °C
D

2927 °C

Solution

$\begin{array}{l} {(V_{RMS})}_{0} = \sqrt{\frac{3 {kT}_{0}}{m_{0}}}; {(V_{RMS})}_{h} = \sqrt{\frac{3 {kT}_{h}}{m_{h}}} \\ {(V_{RMS})}_{0} = {(V_{RMS})}_{h} \\ ∴ \frac{T_{0}}{m_{0}} = \frac{T_{h}}{m_{h}} \Rightarrow T_{0} = \frac{16 \times 200}{1} = 3200 K = 2927^{\circ} C \end{array}$

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