- #1

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**v**and

**v'**colliding is described as:

What is f(

**v**,

**v'**) here? Is it the velocity distribution function? If so, isn't it simply the fraction of molecules with velocities

**v**and

**v'**?

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- Thread starter unscientific
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- #1

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What is f(

- #2

Simon Bridge

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It may be a bit confusing because it is expressed as a small range of velocities.

- #3

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It may be a bit confusing because it is expressed as a small range of velocities.

How did they get the exponential expression for f(

And it is implied that the probability of both of them colliding is the product: f(

Then on its own, what does f(

- #4

Simon Bridge

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$$p(\vec v^2) = \sqrt{\frac{\alpha^3}{\pi}}e^{-\alpha \vec v^2}$$ ... comes from the distribution of kinetic energies perhaps (as ##K\propto v^2##) ...

You may find the following approach easier:

http://physics.bu.edu/~redner/542/refs/reif-chap12.pdf

- #5

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$$p(\vec v^2) = \sqrt{\frac{\alpha^3}{\pi}}e^{-\alpha \vec v^2}$$ ... comes from the distribution of kinetic energies perhaps (as ##K\propto v^2##) ...

You may find the following approach easier:

http://physics.bu.edu/~redner/542/refs/reif-chap12.pdf

I have verified that the book meant f(

Why is the product of f(

- #6

Simon Bridge

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Did you read the link I gave you?

- #7

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Did you read the link I gave you?

Yeah, nothing is said about the relation between probability of collision and distribution of velocities.

Collision time, probability of collision and mean free path was explained, but it didn't relate them to the distribution of velocities?

- #8

Simon Bridge

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Is the distribution of relative velocities not related to the P(v,v') ?

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