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By what factor does the temperature of a gas increase when the rms speed of its molecules in a fixed-volume container is doubled from 5 * 10⁴ cm/s to 10 * 10⁴ cm/s?

1. 2 folds
2. 4 folds
3. 8 folds
4. 16 folds

Correct answer: 4 folds

Solution

The rms speed v_rms = sqrt(3RT/M). So v_rms is proportional to sqrt(T), which means T is proportional to v_rms². If v_rms increases from 5*10⁴ cm/s to 10*10⁴ cm/s (doubled), then T increases by a factor of (10/5)² = 4.

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