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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.84

Find the fraction of gas molecules whose velocities differ by less than δη=1.00%\delta \eta=1.00 \% from the value of (a) the most probable velocity; (b) the root mean square velocity.

Reveal Answer
2.84. (a) δN/N=(8/π)e−1δη=1.66%\delta N / N=(8 / \sqrt{\pi}) e^{-1} \delta \eta=1.66 \% (b) δN/N=123/2πe−3/2δη=1.85%\delta N / N=12 \sqrt{3 / 2 \pi} e^{-3 / 2} \delta \eta=1.85 \%
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