The speed of a molecule in a uniform gas at equilibrium is a random variable V whose

Chapter 6, Problem 6.29

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The speed of a molecule in a uniform gas at equilibrium is a random variable V whose density function is given by f (v) = av2 ebv2 , v > 0, where b = m/2kT and k, T , and m denote Boltzmanns constant, the absolute temperature, and the mass of the molecule, respectively. a Derive the distribution of W = mV2/2, the kinetic energy of the molecule. b Find E(W).

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