The MaxwellBoltzmann distribution, plotted in Fig. 17.4, is given by N1v2 v = 4pN a m
Chapter 17, Problem 76(choose chapter or problem)
The MaxwellBoltzmann distribution, plotted in Fig. 17.4, is given by N1v2 v = 4pN a m 2pkT b 3/2 v2 e -mv2 /2kTv where N(v)v is the number of molecules in a small speed range v around speed v, N is the total number of molecules in the gas, m is the molecular mass, k is Boltzmanns constant, and T is the temperature. Use this equation to show that the most probable speed for a gas moleculethe speed at the peak of the curves in Fig. 17.4is 22kT/m. Note that the thermal speed (Equation 17.4), which is the average molecular speed, is a factor of 23/2 or about 20% greater than the most probable speeda fact that reflects the long, high-energy tail of the MaxwellBoltzmann distribution.
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