We want to calculate how many molecules collide with the surface per unit time and per unit surface area. We will use the same technique we used in computing the pressure against a surface except now there is no momentum exchange, we only want to count the collisions.

Once again we consider a portion of the wall of area,
*A*, and a molecule which impinges on the wall with *x*-component
of velocity, *v _{x}*, and we consider what happens in a small
time interval &Delta

(1)molecules. The number of these molecules which have velocity,

(2)Then the total number of collisions is obtained by summing this number of collisions over all positive

(3)In Equation 3 we have used the definition of the average of the absolute value of

(4)and the fact that is an even function of

(5a, b, c)So, to find the number of collisions per unit time per unit area, we divide the number of collisions in Equation 3 by the area and by the time interval, &Delta

(6)We will show later that

(7)where

(8)The bottom line is that

(9a, b)We will refer to the expression in Equation 9b as

We will have to leave our equations in the form of Equation
9b because we do not yet have the form of the velocity probability distribution
function, *f*, in Equations 2, and 3. As soon as we learn the form
of *f* we will be able to write equations such as Equation 9b in terms
of temperature, molecular masses, and so on.

WRS

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