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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.85

Determine the gas temperature at which (a) the root mean square velocity of hydrogen molecules exceeds their most probable velocity by Δv=400 m/s\Delta v=400 \mathrm{~m} / \mathrm{s} (b) the velocity distribution function F(v)F(v) for the oxygen molecules will have the maximum value at the velocity v=420 m/sv=420 \mathrm{~m} / \mathrm{s}.

Reveal Answer
 (a) T=m(Δv)2k(3−2)2=380 K (b) T=mv22k=340 K\text { (a) } T=\frac{m(\Delta v)^{2}}{k(\sqrt{3}-\sqrt{2})^{2}}=380 \mathrm{~K} \text { (b) } T=\frac{m v^{2}}{2 k}=340 \mathrm{~K}
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