- #1
ejensen6
- 19
- 0
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)]
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
Can this be done analytically?
Also, this function predicts a non-zero (albeit very small) probability for particles to have a speed greater than the speed of light. Is there a correction to this distribution that takes this into account?
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)]
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
Can this be done analytically?
Also, this function predicts a non-zero (albeit very small) probability for particles to have a speed greater than the speed of light. Is there a correction to this distribution that takes this into account?