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

For oxygen:
$v_{rms} = \sqrt{\frac{3 {kT}_{0}}{m_{0}}}$
For hydrogen:
$v_{rms} = \sqrt{\frac{3 {kT}_{h}}{m_{h}}}$
The value of v_rms will be the same if
$\begin{array}{l} \frac{T_{0}}{m_{0}} = \frac{T_{h}}{m_{h}} \\ or T_{0} = \frac{m_{0}}{m_{h}} \times T_{h} = 16 \times 200 \\ = 3200 K = 2927^{\circ} C \end{array}$
Hence the correct choice is (4).

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