# Speed distribution function

1. Feb 1, 2009

### Niko84

1. The problem statement, all variables and given/known data

The speed distribution function of a group N particles is given by:
dNv=k*dv if U>v>0
dNv=0 if v>U

1) find k in terms of N and U.
2) draw a graph of distribution function
3) compute the average and rms speed in terms of U.
4) compute the most probable speed

2. Relevant equations

f(v)=$$\left[\frac{m}{2\pi\kappa*T}\right]^{\frac{3}{2}}*exp\left(-\frac{mv^{2}}{2\kappa*T}\right)$$ - Maxwell-Boltzmann distribution

$$\frac{dn_{v}}{n}$$=4$$\pi*v^{2}*f(v)*dv$$ - speed distribution function

3. The attempt at a solution

1) k=4$$\pi*n*v^{2}*f(v)$$ - so I can draw a graph of the distribution function.
2) which function and how should I integrate in order to obtain k in terms of N and U?
3) is average speed = $$\int^{V}_{0}v*4\pi*v^{2}*f(v)dv$$ ?