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The Maxwell-Boltzmann distribution, plotted in Fig. 17.4, is given by
where N(v) Δv is the number of molecules in a small speed range Δv around speed v, N is the total number of molecules in the gas, m is the molecular mass, k is Boltzmann’s constant, and T is the temperature. Use this equation to show that the most probable speed for a gas molecule—the speed at the peak of the curves in Fig. 17.4—is
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