Maxwell Boltzmann Distribution

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I don't know how to integrate the Maxwell-Boltzmann distribution without approximation or help from Maple.

Given the Maxwell-Boltzmann distribution:

f(v) = 4*pi*[m/(2*pi*k*T)]^(3/2)*v^2*exp[(-m*v^2)/(2*k*T)]

Observe the appearance of the Boltzmann factor exp[(-m*v^2)/(2*k*T)] with E = 1/2(mv^2)

Assuming a fixed temperature and mass, one can simplify this equation:

f(v) = a*v^2*exp[-bv^2]
a = 4*pi*[m/(2*pi*k*T)]^(3/2)
b = m/(2*k*T)

In order to calculate the fraction of particles between two speeds v1 and v2, one should evaluate the definite integral:

∫f(v)dv

Here is an link to integral-tables, http://integral-table.com/
How would I solve this problem for let's say a certain amount of moles with hydrogen between two different velocities? Best regards, Tor
 

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  • #2
SteamKing
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What have you tried in terms of integrating the M-B distribution?
 
  • #3
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What have you tried in terms of integrating the M-B distribution?
I've just put in some values to calculate how many atoms gets affected from let's say 400-401 m/s for hydrogen. I'm not sure what solution to pick for this kind of integration, that's what I'm asking. To calculate between higher speeds like 400-500 m/s, an integration is needed.
 
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