# 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?