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f(v) = av²e-bu*, v>0, where a is a constant and b = , with m being the mass of the molecule, T the temperature of the gas, and k Boltzmann's constant. Find the distribution of W = mv² , the kinetic energy of the molecule. Also find the expected value of the kinetic energy. SS

f(v) = av²e-bu*, v>0, where a is a constant and b = , with m being the mass of the molecule, T the temperature of the gas, and k Boltzmann's constant. Find the distribution of W = mv² , the kinetic energy of the molecule. Also find the expected value of the kinetic energy. SS

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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6. The speed of a molecule of gas at equilibrium is a random variable V with pdf f(v) = av²e-bv². v > 0, where a is a constant and b = , with m being the mass of the molecule, T the temperature of the gas, and k Boltzmann's constant. Find the distribution of W = my², the kinetic energy of the molecule. Also find the expected value of the kinetic energy.
Transcribed Image Text:6. The speed of a molecule of gas at equilibrium is a random variable V with pdf f(v) = av²e-bv². v > 0, where a is a constant and b = , with m being the mass of the molecule, T the temperature of the gas, and k Boltzmann's constant. Find the distribution of W = my², the kinetic energy of the molecule. Also find the expected value of the kinetic energy.
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