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

[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?

 

[Svein]

Check the average value of |cos(θ)|.

 

[jtbell]

My question is why the expected value wouldn't be zero instead of 2/3?

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

 

[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?

 

[srhelfrich]

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

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

 

[srhelfrich]

Check the average value of |cos(θ)|.

Sure, the math works.

But why is it significant?

 

[jtbell]

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

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