Saturday, October 01, 2005

Explaining the greenhouse effect to your mom....)Part I(

has been a hard thing to do, so don't expect miracles folks. Conventional wisdom, CW says, that it is simple to explain what the greenhouse effect is not, the thing that keeps greenhouses warm and heats up your car in the in the summer. The CW for those two cases is that you cut off convection, exchange of atmospheric gases between the inside and the outside, and as a result the inside of the greenhouse and the car warms as solar energy pours in through the windows. OTOH, says the CW, that ain't the greenhouse effect, the thing that keeps the surface of the earth mostly toasty, or at least about 25 C toastier then it would be without.

I am going to show that what happens in the greenhouse and your car is much like what happens in the earth's atmosphere, and the CW misses something important. This posting will grow and hopefully change under the influence of comments. Eventually we might port it elsewhere, like Wikipedia but I don't want to throw this into that scrum without some preliminary doodling.

Let us start by discussing your car in the summer sun. You have to balance the flow of energy in with a flow of energy out. Assuming the sun is constant, any physicist will tell you that there are only three ways to ditch energy: Conduction, convection, and radiation. A chemist will throw in exothermic phase changes and reactions.

If your car is sitting in the sun with all the windows open, energy from the sun's radiation flows into the car and either is reflected out (off the white seats) or absorbed (off the black ones). For the sake of this thought experiment, assume that the car was sitting in a garage with the garage door opened and had reached an equilibrium temperature with the air around it.

Pull it out of the garage. As seats absorb energy from the sun, they will become warmer and heat the air next to them. The air inside is now a bit hotter than the air outside. The flow of energy into the car is balanced by flows of energy out of the car both from exchange of air and radiation through the open window but also the air inside heats the windows and surface of the car which then radiate faster. For the purpose of this argument we will make the usual spherical elephant assumption and postulate an all glass auto. On net the air in the car will be a bit warmer than that outside in order to maintain the balance.

As the sun's radiation pours in this process heats the windows and body of the car. The wavelength region that the warm seats and the body of the car radiate in is the infrared which cannot pass through the glass, but the glass can radiate back into the car and, on the other side, into the air.

Now close the windows. The rate at which energy flows into the car decreases as convection is cut off. The immediate rate of energy flow out by radiation stays the same, therefore the rate of energy flow into the car exceeds the rate of energy flow out of the car, and....the air in the car warms. As the air in the car warms, the interface between the atmosphere and the car, the glass also warms, as things warm, the rate of radiation increases as the fourth power of the temperature, so the hotter glass radiates at a faster rate. The air in the car stops heating when the temperature is high enough that the energy radiated from the glass surface out into the air (half goes back into the car) exactly balances the energy radiated into the car from the sun.

If you want a hydraulic analogy, imagine a pipe with water flowing through it. Now narrow one part of the pipe. The flow out of the pipe will decrease, but if the flow into the pipe remains constant, the pressure in the pipe will increase until the balance between the flow in and the flow out is restored.

Does anyone see where I am going??


Anonymous said...

Looks good so far, I think UV apsorption by the glass further heating the windows might be the next largest contribution not outlined, but I'm thinking my mom might feel a bit lost after the word convection was used. :)

Anonymous said...

Hi Eli: First, I agree with your comment about the surface temps (on Deltoid) but Jenkins seemed to place more faith on the UAH data.

Anyway, to the matter at hand. I liked the approach you have taken. Too many have dismissed the greenhouse analogy too quickly and I think that it does explain a great deal. The car should be familiar to most so you are starting with an advantage.

However my teaching side would not let me comment without some criticism (constructive I hope). First, it is a trivial point, but I have always used the number of 33C as what greenhouse gases have increased surface temperatures by. Second, I would point out the following sentence, it seems a bit clunky.

As the air in the car warms, the interface between the atmosphere and the car, the glass also warms, as things warm, the rate of radiation increases as the fourth power of the temperature, so the hotter glass radiates at a faster rate.

Last, I might remove or rehash the hydraulic example. I know what you mean and you are clear about it, but the old saying goes that a little knowledge is a dangerous thing. I can see that some might be confused by thinking you are talking about Bernoulli’s equation and thus the pressure should go down.

Anyway, the above is offered free of charge and worth every bit of it. Feel free to use, modify and ignore any or all of it.


William M. Connolley said...

Oho, your own blog. Hello.

I strongly suggest you read the wiki page, and the refs therein, including to Wood's early paper (greenhouses with walls transparent to IR heat up just the same). The wiki greenhouse effect page had about the longest revert war in known history over this very topic.

I don't see anything in what you've written that overturns the CW. Maybe I read carelessly.

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