(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given the integral

integral(0,infinity)(v^3*e^(-a*v^2)dv)=a^-2/2

Calculate the average speed v(average) of molecules in a gas using the Maxwell-Boltzmann distribution function.

2. Relevant equations

v^2(average)=integral(0,infinity)(v^2*v(t)dv)

3. The attempt at a solution

I took the general approach.

integral(0,infinity)(f(v)dv)=(4/pi)*(m/(2*k*T))^(3/2)*integral(0,infinity)(v^2*e^(-mv^2/(2*k*t))dv)

However, I could not find out how to make a substitution for a in order to get the v^3 into the equation.

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# Homework Help: Maxwell-Boltzmann Distribution and average speed

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