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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.87

At what temperature of a nitrogen and oxygen mixture do the most probable velocities of nitrogen and oxygen molecules differ by \(\Delta v=30 \mathrm{~m} / \mathrm{s} ?\)

Reveal Answer
T=mN(Δv)22k(1−mN/m0)2=0.37kKT=\frac{m_{\mathrm{N}}(\Delta v)^{2}}{2 k\left(1-\sqrt{m_{\mathrm{N}} / m_{0}}\right)^{2}}=0.37 \mathrm{kK}
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