The Maxwell-Boltzmann probability density function f(v) is given byf(v) =

Chapter 11, Problem 25

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The Maxwell-Boltzmann probability density function f(v) is given byf(v) = v2exp(-2fJwhere m (kg) is the mass of each molecule, v (m/s) is the speed, T (K) is thetemperature, and k = 1.38 x 10-23 J/K is Boltzmann's constant. The mostprobable speed v P corresponds to the maximum value of f( v) and can bedetermined from d) = 0. Create a symbolic expression for f(v), differentiateit with respect to v and show that vP = . Calculate vP for oxygenmolecules (m = 5.3 x 10-26 kg) at T = 300 K (k = 1.38 x 10-23 J/K). Make aplot of f( v) versus v for 0 v 2500 m/s for oxygen molecules

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