How Does the Speed Distribution Function Determine Vmin and Vmax?

In summary: AV(B-V)/B^3The most probable speed is the speed for which the probability density function is the largest. In summary, 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. The minimum speed is Vmin, and the maximum speed is Vmax. The most probable speed is the speed for which the probability density function is the largest.
  • #1
reactor
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.
 
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  • #2
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
mfb said:
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
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
reactor said:
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
 

FAQ: How Does the Speed Distribution Function Determine Vmin and Vmax?

What is the Maxwell velocity distribution?

The Maxwell velocity distribution is a probability distribution that describes the speeds at which particles move in a gas or liquid at a certain temperature. It is named after the physicist James Clerk Maxwell who first described it in the 19th century.

What does the Maxwell velocity distribution tell us?

The Maxwell velocity distribution tells us the most probable speed at which particles move in a gas or liquid at a given temperature, as well as the range of speeds that are possible. It also shows that the average speed of particles increases with temperature.

What factors affect the shape of the Maxwell velocity distribution?

The shape of the Maxwell velocity distribution is affected by temperature, the mass of the particles, and the type of gas or liquid. Higher temperatures result in a wider distribution and a higher peak, while heavier particles have a lower peak and a narrower distribution.

How is the Maxwell velocity distribution related to the kinetic theory of gases?

The Maxwell velocity distribution is a key component of the kinetic theory of gases, which states that gases are made up of a large number of particles that are in constant, random motion. The distribution explains the speeds and directions of these particles and how they collide with each other and with the walls of their container.

What is the significance of the Maxwell velocity distribution in practical applications?

The Maxwell velocity distribution has many practical applications, such as in understanding gas and liquid dynamics in engineering and in the design of technologies like gas turbines and rocket engines. It also helps in predicting the behavior of gases in various environments, such as in atmospheric science and astrophysics.

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