Maxwell Boltzmann Verteilung

We define first some constants

mhelium = 6.6465 10^-27 
boltzmannconstant = 1.3806503  10^-23

Here is the definition of the density function

f =Sqrt[2/Pi] v^2 (Sqrt[(mhelium/(boltzmannconstant  T))^3] )  Exp[-(mhelium  v^2 )/(2  boltzmannconstant T)]

Before you can plot the function you needs to be evaluated
expr /. T->80  replace the variable T by a value

Evaluate[f] /. T->80.

The "% line number" repeats the command of the line
and feeds it into the Plot function
{v,1,2000}   denotes the plot variable and the range

Plot[%4,{v,1,2000}]

Same with another Temperature

Evaluate[f] /. T->200.

Plot[%10,{v,1,2000}]

Using Show you can redraw the old  plots  or draw them on 
top of each other by giving a list.

Show[%11,%9]

Now we Integrate the density function from 0 to Infinity

Integrate[%16,{v,0,Infinity}]

Calculate the average quadratic velocity

Evaluate[v^2 f] /. T->200.

Integrate[%16,{v,0,Infinity}]
Sqrt[Integrate[%16,{v,0,Infinity}]]