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A container holds N molecules of gas A (each of mass m) and 2N molecules of gas B (each of mass 2m), both at the same temperature T. The mean square speed of gas B molecules is v², and the mean square speed of the x-component of velocity of gas A molecules is w². What is the ratio w² / v²?

1. 1
2. 2
3. 1/3
4. 2/3

Correct answer: 1/3

Solution

By equipartition, the mean square of each velocity component equals kT/M where M is particle mass, and mean square speed = 3kT/M. For gas A: w² = kT/m. For gas B: v² = 3kT/(2m). So w²/v² = (kT/m)/(3kT/2m) = 2/3.

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