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At what temperature will He atoms have the same $u_{\text {rms }}$ value as $\mathrm{N}_{2}$ molecules at $25^{\circ} \mathrm{C}$ ?
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Answer from Sia

Posted 6 months ago

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Answer

The temperature at which He atoms will have the same $u_{\text{rms}}$ value as $\mathrm{N}_2$ molecules at $25^\circ\mathrm{C}$ is $2086\mathrm{K}$.

Key Concept

The root-mean-square speed of gas particles is directly proportional to the square root of the temperature and inversely proportional to the square root of the particle's mass.

Explanation

Since the $u_{\text{rms}}$ is the same for both gases, the temperature for He must be adjusted for the difference in molar mass between $\mathrm{N}_2$ and He.

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