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(II) We saw in Example 8 of "Kinetic Theory of Gases" that the mean free path of air molecules at STP, $\ell_{M},$ is about $9 \times 10^{-8}$ m. Estimate the collision frequency $f,$ the number of collisions per unit time.

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$5 \times 10^{9} \mathrm{Hz}$

Physics 101 Mechanics

Chapter 18

Kinetic Theory of Gases

Temperature and Heat

University of Michigan - Ann Arbor

Simon Fraser University

University of Winnipeg

McMaster University

Lectures

02:25

(II) We saw in Example $18…

06:17

Assume that air consists o…

04:21

(a) What is the ms speed o…

01:27

Calculate the mean free pa…

01:14

(a) What is the rms speed …

05:49

(II) $(a)$ Show that the n…

02:33

Estimate the number of col…

03:50

88. Find the total number …

04:07

(II) $(a)$ The mean free p…

04:31

In the kinetic theory of g…

01:11

It is shown in the kinetic…

01:35

The average translational …

04:16

03:37

(a) Show that for a gas, …

02:49

The mean free path $\lambd…

okay. In this problem, we have air at standard temperature pressure were given its mean free path is found nine times 10 the negative eight meters and we were asked to find the collision frequency for these molecules in this ideal gas. So this is this may be perceived as cheating, but in problem 49 we derived an expression for the frequency which is f equals 16 times the pressure times the radius of our particles squared Time to square root of pi over M. Katie. This was derived in the previous problem 49. And so from that we can actually do get everything if we assume that the mass of air which we've done it in a number of problems in this chapter is about 29 times the mass of a proton. And we have standard pressure temperature. We can, uh we can do this rather easily. We also can assume that the radius of our air apartment particles is about 1.5 time. Send the native 10. This was also the cell's been done numerous times in this chapter. So I think it's very game. So we're just using this result. We can get this frequency playing in our numbers, we have 16 times standard temperature sending pressure other 1.13 10. The negative 10 to the five Pascal, that's standard pressure. 1.5 10 the negative 10 meters squared radius fruit pie over 29. 1.66 10 of the neck of 27 kilograms. The ultimate constant 1.3 a 10. The negative. 23 skin messy. And finally, our standard temperature to 93. Kelvin. Okay, Okay. Doing all those calculations, we end up with the results of 4.8 times 10 to the nine hertz, which we can approximate to the five tender. The night hurts. So for the five gigahertz and that's it kind of a short, short cat, but I think it's ah, it's valid.

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