Maxwell velocity distribution

  • Thread starter reactor
  • Start date
  • #1
2
0
Dear
I have problem with determine the minimum speed in this problem , I think the the maximum speed equal to the average speed and the most probable speed can be obtain by derive equation and equally to zero .Is my solution correct?

The speed distribution function for N particles in a fixed volume is given by f (V) = AV(B - V)/B^3,
where V (>0) is the particle speed, and A and B are positive constants. Determine:
(a) The minimum speed Vmin and maximum speed Vmax.
b) The most probable speed where the probability density function is the largest.
 

Answers and Replies

  • #2
35,646
12,213
I think the the maximum speed equal to the average speed
If that would be true, all particles would have to have the same speed.

I have problem with determine the minimum speed in this problem
What is the minimal V where f(V) is not zero?
If you don't see that, make a sketch of f(V).

and the most probable speed can be obtain by derive equation and equally to zero
Right.
 
  • #3
2
0
If that would be true, all particles would have to have the same speed.

What is the minimal V where f(V) is not zero?
If you don't see that, make a sketch of f(V).

Right.

the minimum when B=v=0 and what about the maximum
 
  • #4
35,646
12,213
the minimum when B=v=0
Why B=?
A and B are parameters, you cannot set their values.

and what about the maximum
Did you draw the sketch I proposed? Do you see the maximum?
 
  • #5
Andrew Mason
Science Advisor
Homework Helper
7,686
403
Dear
I have problem with determine the minimum speed in this problem , I think the the maximum speed equal to the average speed and the most probable speed can be obtain by derive equation and equally to zero .Is my solution correct?

The speed distribution function for N particles in a fixed volume is given by f (V) = AV(B - V)/B^3,
where V (>0) is the particle speed, and A and B are positive constants. Determine:
(a) The minimum speed Vmin and maximum speed Vmax.
b) The most probable speed where the probability density function is the largest.
First of all, this is not a Maxwellian distribution. The distribution is determined by this equation.

The minimum speed is the speed for which the distribution f(V) < 1. Since we don't know the values of A and B you cannot really determine that so assume it is very close to f(V) = 0.

How is the maximum related to the rate of change of f(V) with respect to V?

AM
 

Related Threads on Maxwell velocity distribution

  • Last Post
Replies
1
Views
594
Replies
26
Views
1K
  • Last Post
Replies
3
Views
962
  • Last Post
Replies
9
Views
6K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
3
Views
2K
Top