Arguments
The 2nd law of thermodynamics and the greenhouse effect
Posted on 22 October 2010 by TonyWildish
Skeptics sometimes claim that the explanation for global warming contradicts the second law of thermodynamics. But does it? To answer that, first, we need to know how global warming works. Then, we need to know what the second law of thermodynamics is, and how it applies to global warming. Global warming, in a nutshell, works like this:
The sun warms the Earth. The Earth and its atmosphere radiate heat away into space. They radiate most of the heat that is received from the sun, so the average temperature of the Earth stays more or less constant. Greenhouse gases trap some of the escaping heat closer to the Earth's surface, making it harder for it to shed that heat, so the Earth warms up in order to radiate the heat more effectively. So the greenhouse gases make the Earth warmer - like a blanket conserving body heat - and voila, you have global warming. See What is Global Warming and the Greenhouse Effect for a more detailed explanation.
The second law of thermodynamics has been stated in many ways. For us, Rudolf Clausius said it best:
"Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature."
So if you put something hot next to something cold, the hot thing won't get hotter, and the cold thing won't get colder. That's so obvious that it hardly needs a scientist to say it, we know this from our daily lives. If you put an ice-cube into your drink, the drink doesn't boil!
The skeptic tells us that, because the air, including the greenhouse gasses, is cooler than the surface of the Earth, it cannot warm the Earth. If it did, they say, that means heat would have to flow from cold to hot, in apparent violation of the second law of thermodynamics.
So have climate scientists made an elementary mistake? Of course not! The skeptic is ignoring the fact that the Earth is being warmed by the sun, which makes all the difference.
To see why, consider that blanket that keeps you warm. If your skin feels cold, wrapping yourself in a blanket can make you warmer. Why? Because your body is generating heat, and that heat is escaping from your body into the environment. When you wrap yourself in a blanket, the loss of heat is reduced, some is retained at the surface of your body, and you warm up. You get warmer because the heat that your body is generating cannot escape as fast as before.
If you put the blanket on a tailors dummy, which does not generate heat, it will have no effect. The dummy will not spontaneously get warmer. That's obvious too!
Is using a blanket an accurate model for global warming by greenhouse gases? Certainly there are differences in how the heat is created and lost, and our body can produce varying amounts of heat, unlike the near-constant heat we receive from the sun. But as far as the second law of thermodynamics goes, where we are only talking about the flow of heat, the comparison is good. The second law says nothing about how the heat is produced, only about how it flows between things.
To summarise: Heat from the sun warms the Earth, as heat from your body keeps you warm. The Earth loses heat to space, and your body loses heat to the environment. Greenhouse gases slow down the rate of heat-loss from the surface of the Earth, like a blanket that slows down the rate at which your body loses heat. The result is the same in both cases, the surface of the Earth, or of your body, gets warmer.
So global warming does not violate the second law of thermodynamics. And if someone tells you otherwise, just remember that you're a warm human being, and certainly nobody's dummy.
This post is the Basic Version (written by Tony Wildish) of the skeptic argument "The 2nd law of thermodynamics contradicts greenhouse theory".
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Effective temperature of an object is defined as the actual temperature of an isothermal perfect black body with the same surface area and same radiative power output. For the Earth this temperature does not depend on its IR emissivity, neither on the IR emissivity of any atmospheric ingredient. It is perfectly determined by ASR (Absorbed Shortwave Radiation), that is, short wave (visible & near IR) albedo and incoming solar radiation flux.
Outgoing longwave radiation is not only uneven, but neither it is thermalized perfectly, because at such low temperatures no material approximates a black body and due to the semitransparent nature of atmosphere radiation escaping to space originates in different layers with vastly different temperatures. Therefore it is a tricky business to assign (radiative) temperature to each and every point of the globe.
Nevertheless it can be done. If it's useful or not, is another matter entirely.
If the surface of the globe is divided up into a grid, having measured the distribution of OLR (Outgoing Logwave Radiation), effective temperature can be calculated for each gridcell, then one can take the (area weighted) average of these temperatures. As <T>4 ≤ <T4>, the finer the grid the smaller this average will be. A decreasing series bounded from below is convergent, therefore with a fine enough grid we can calculate a well defined unique average temperature for the globe as it is seen from the outside.
This temperature is much smaller than the oft quoted -18°C, it is certainly somewhere below -30°C. In defining the atmospheric greenhouse effect it also has the advantage of having a chance to be the correct choice to compare average surface temperature against, because comparing average temperatures to an effective temperature hardly makes sense in the first place (like apples to oranges).
Is the atmospheric greenhouse effect more than 45°C then (instead of 33°C)?
One also wonders what is the correct choice for surface? I know we live at the bottom of the atmosphere, so the special surface separating it from the rest of the globe is important for us. However, at least from the 16th century on we are moving away from an anthropocentric viewpoint, not by pure chance, but it has turned out the Universe is not centered around mankind after all, at least not in any trivial sense.
So the correct question to ask is "Which surface is the important one for the climate system?"
The question put this way has a unique straightforward answer: the upper surface of crust. The interface between the atmosphere and ocean is a busy one, both material and heat flows are several orders of magnitude higher there than those between the crust and atmosphere/hydrosphere combined. The whole AGW issue is started by the realization of a small, but in a geological sense still fast flow of the element carbon from crust to atmosphere effected by industry. It can be considered a "forcing" precisely because this interface is usually much more "closed" than the one between air and ocean.
So when talking about "average surface temperature" we'd better compute it along a true boundary surface of the climate system, that is, along the surface of land and bottom of ocean. This average would be less than 7°C and much more stable than the usual one.
In this case is the atmospheric greenhouse effect 25°C? or 37°C?
I have no idea if average temperature of the globe as it is seen from space is increasing, decreasing or just fluctuating around some value. Neither do I know if among the several possible definitions of atmospheric greenhouse effect which one has a trend and in what direction. But it would certainly be interesting to know.
Average temperature is probably not as important as some say. Entropy fluxes could be calculated in a similar, although slightly more complicated manner (one would need spectral resolution as well) and that would be way more informative than average temperature at an arbitrary interface.
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