Speed distribution function

[Niko84]

Homework Statement

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

Homework 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

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 = $$\int^{V}_{0}v*4\pi*v^{2}*f(v)dv$$ ?

Please help with the solution or link to a similar problem solution.

 

[malawi_glenn]

Why do you invlove Maxwell-Boltzmann Distribution? Your given speed distrubtion was
dN_v=k*dv if U>v>0
dN_v=0 if v>U

Thus, you have for U>v>0: dN / N = k dv and for v >U: dN / N = 0

For a Maxwell-Boltzmann speed distribution you have $\dfrac{dN}{N } = f(v) dv = 4\pi v^2\left( \dfrac{m}{2 \pi kT} \right)^{3/2} e^{-mv^2 / 2kT} \, dv$

You want to make sure your speed distribution is normalized, e.g. $\int_0^\infty f(v) dv = N$
Which will turn to $\int_0^U k dv = N$ for your distribution.