I What is the significance of calculating the average value of cos?

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1. Feb 12, 2017

srhelfrich

In kinetic theory, the number of molecules hitting a unit area of a surface per unit time with speeds between v and v + dv and angles between \theta and \theta + d \theta is found to be a function of sin(theta) and cos(theta). There will often be a practice problem asking to show that the average value of cos(theta) for these molecules is 2/3.

My question is why the expected value wouldn't be zero instead of 2/3? What is the significance of finding this average value?

2. Feb 12, 2017

Svein

Check the average value of |cos(θ)|.

3. Feb 12, 2017

Staff: Mentor

What is the range of values of θ? Are you considering molecules that hit one side or both sides of the wall?

4. Feb 12, 2017

srhelfrich

I understand that it works out mathematically. I also figured out that theta is measured with respect to the normal of the wall so now I see why it shouldn't be zero.

But what is the significance of finding the average value? Why is this something we would be interested in calculating?

5. Feb 12, 2017

srhelfrich

Yeah, I just realized the range is from 0 to pi/2. The angle is measured wrt the normal of the wall.

6. Feb 12, 2017

srhelfrich

Sure, the math works.

But why is it significant?

7. Feb 12, 2017

Staff: Mentor

What about molecules coming in from one side of the normal, versus coming in from the other side of the normal?