Boltzmann Transport Equation (part II), Transport examples

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The following three questions refer to the material you were to read in preparation for the lesson. Questions one and two require you to write a three or four sentence response. Number three is a multiple choice question. Click in the appropriate circle.

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1.

In class last time, we touched on the "relaxation time approximation" for the Boltzmann transport equation. Basically, to use this approximation, we say:

In your own words, try to explain what this equation means. We'll discuss this more in class.
Also, consider an example of diffusion. Why do you think the characteristic (or "relaxation") time, _c, should be of the order of the time between collisions?

2.

In Lesson 41's class, we're going to consider the variation of temperature in the Earth's crust when the temperature of the Earth's surface is varied periodically with time. We will approximate the Earth as a semi-infinite medium (z>0) and think of the temperature at the surface of the Earth (a plane at z=0) as varying with time. (Yes, we're going back to a flat Earth model!) We'll approach the problem by using plane waves -- we'll think of heat waves or diffusion waves that are very highly damped (so that they are hardly waves at all) as they enter the Earth's surface.

Before we actually do this analysis in class, think about estimating a characteristic depth or "penetration depth" that would be an approximate measure of how far the heating at the surface penetrates into the Earth.

Please make a guesstimate (based on your everyday life observations, and a little bit of physics insight) for the value of the "penetration depth" for

the daily ("diurnal") cycle of heating of the ground by the sunlit sky and cooling of the ground by the night sky and
the annual cycle due to the summer/winter effect.

Please explain your thoughts. On what parameters do you think this penetration depth depends?

3.

Warning: Although this may seem "off the wall," it actually has practical considerations and is relevant to 421...
When constructing a house, the most energy efficient thing to do is to put the heating elements

in the centers of the rooms.
against the walls.
wherever they look best.

Below is a space for your thoughts, including general comments about today's assignment (what seemed impossible, what reading didn't make sense, what we should spend class time on, what was "cool", etc.):

You may change your mind as often as you wish. When you are satisfied with your responses click the SUBMIT button.
I received no help from anyone on this assignment.

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