Jul
11
2007

Venus and Mars are alright tonight: They may not teach us much about conditions on Earth, but they provide hours of entertaining temperature conversion!  Photo of Venus (left) from NASA; photo of Mars (other guy) from the Library of Congress.
Venus and Mars are alright tonight: They may not teach us much about conditions on Earth, but they provide hours of entertaining temperature conversion! Photo of Venus (left) from NASA; photo of Mars (other guy) from the Library of Congress.

As Science Buzz's resident global warming skeptic, I've taken a lot of shots at Al Gore over the years. Today, however, I find myself in the unusual position of having to defend him against unfair attacks. Somewhat.

In an editorial last Sunday, Gore stated:

“Consider this tale of two planets. Earth and Venus are almost exactly the same size, and have almost exactly the same amount of carbon. The difference is that most of the carbon on Earth is in the ground - having been deposited there by various forms of life over the last 600 million years - and most of the carbon on Venus is in the atmosphere.

As a result, while the average temperature on Earth is a pleasant 59 degrees, the average temperature on Venus is 867 degrees. True, Venus is closer to the Sun than we are, but the fault is not in our star; Venus is three times hotter on average than Mercury, which is right next to the Sun. It's the carbon dioxide.”

This got a bunch of bloggers to thinking. George Reisman went to a NASA website and found an interesting comparison:

PLANET Venus Earth Mars
CO2 IN ATMOSPHERE 96% 0%* 95%
AVERAGE TEMPERATURE 867˚F 59˚F -81˚F

*Not quite true: Earth’s atmosphere is 0.035% CO2.

So, planets with lots of carbon in their atmosphere can be either broiling hot or icy cold.

(Another writer, Evan Kayne, complained (seventh item) the comparison isn't fair; Reisman didn’t take into account the fact that the atmosphere on Mars is only 1.3% as thick as Earth’s. James Taranto of the Wall Street Journal re-did the calculations, and concluded that frigid Mars still has 34x as much CO2 per cubic foot of atmosphere as the Earth does.)

So far, Al isn't looking too good. But then, blogger David Downing thought he'd discovered another problem. According to the NASA site, Mercury has an average temperature of 452˚ Kelvin, while Venus has an average temp of 726˚ Kelvin. That’s only 1.6 times hotter, a far cry from what Gore had claimed!

Wait a minute. What’s this “Kelvin” scale and why is Downing using it? Well, all temperature scales measure energy. And on the Kelvin scale, 0 degrees means “no energy AT ALL.”

This makes it very easy to compare the energy in different systems. In Celsius, 0 degrees doesn’t mean “zero energy;” it means “the amount of energy in frozen water” -- which may seem chilly to you and me, but at a molecular scale, it’s got plenty of heat. (0 degrees Fahrenheit is apparently the amount of energy in a mix of ice, water, and ammonium chloride.) Comparing 25˚F to 50˚F is tricky, because the scale doesn't stop at 0. As any Minnesotan knows, it goes wayyyyy lower than that!

(It’s kind of like saying “Mike is five years older than me; Vic is 10 years older than me; therefore, Vic is twice as old as Mike.” That would only be true if I were 0 years old. If I were, say, 47, then Mike would be 52 and Vic would be 57, and the differences would be much less impressive.)

So, Downing assumed Gore must have been working in Fahrenheit, and believed that if Venus is 867˚F and Mercury is 289˚F, then Venus is three times hotter. Ha ha, what a silly mistake! I was all prepared to poke fun at Al for this glaring error, until I realized – Mercury isn’t 289˚F. According to NASA, it’s a toasty 354˚F.

So, where did Al get 289˚F? I looked in a bunch of sources -- no one was even close. Wikipedia listed Mercury at a mere 26˚F. (The side facing the Sun broils; the side turned away freezes; this is an average.)

But then I noticed -- 26˚F is 270˚K. And Wikipedia lists Venus at 735˚K . Using the proper Kelvin scale, that works out to 2.7 times hotter than Mercury. Not quite 3 times, but in the ballpark. And, to be fair, Wikipedia gives Mercury a range of temperatures, and “3x hotter” fits comfortably within that range.

So, it turns out Gore was closer to being right than he’s given credit for. He WAS working in the proper Kelvin scale. He was just relying on figures from Wikipedia rather than from NASA.

I don’t know if all this has taught us anything about global warming. But man, have I learned a lot about planetary atmospheres, temperature scales, and math! Thanks, Al!

UPDATE: Evan Kaye had claimed that the atmosphere on Mars is only 2% as thick as Earth's. James Taranto, using figures from the NASA site linked to above, calculated that it is actually 1.3% as thick as Earth's. We have corrected the figure.

Your Comments, Thoughts, Questions, Ideas

Mr. Time Waster Guy's picture
Mr. Time Waster Guy says:

Hi!

Interesting post. I just wanted to quantify some more of the things you were talking about. I hope you don't mind me sharing the results with you. Caveat Emptor: IANAP (I am not a physicist - I stopped at Astronomy 100 :P )

A more relevant bit of information here is how hot a planet is relative to its black body temperature. Black bodies absorb all incoming energy (none is reflected or passes through) and emit that energy at a rate relative to their temperature. It is possible to compute what one black body's temperature given another black body of known temperature.

Given that we can see light being reflected by the planets in the solar system we can assume that they are not perfect black bodies. If they don't trap any of their heat due to some greenhouse-like effect or have an elevated temperature from some other cause they should be cooler than their ideal black body temperature.

The sun can be assumed to be so hot that contributions to its heat from incoming energy are negligible so it can be considered in isolation from the planets. We can also call it an approximate black body - this is a rough approximation but it is common in astronomy to consider stars to be black bodies.

Given the sun as a black body we can then compute what the ideal equilibrium black body temperatures of the planets should be. The surface temperature of a planet relative to its black body surface temperature could then be an indication of the greenhouse effect of its atmosphere. However it is also possible that a high surface temperature could indicate a body that is not at equilibrium and is cooling, or it could point to some other heat source.

Here is a table of some calculations I have made. The equation I used and all other data are from wikipedia. Distances are relative to the sun and the sun has a radius (RSun) of 6.96*105km and a temperature (TSun) of 5780K.


Hover over image to enlarge

Mercury looks too cold, but given that it has no atmosphere and is reflective the TT/BBT ratio may be just right. Consider also that there is no average surface temperature statistic listed in its wikipedia entry so the True Temperature might be very wrong.

It seems clear that Venus is considerably warmer than it should be. Notice also that Venus should only be 1.2 times warmer than Earth, but it is instead 2.56 times warmer. This deviation is larger than that of any other planet.

Mars and Earth are also slightly too warm - given that they reflect visible light they should be colder than an ideal black body. Mars retains less heat than Earth, but still has a warmish surface in spite of its thin atmosphere. That could be the result of its high CO2 level.

posted on Wed, 07/11/2007 - 11:04pm
Anonymous's picture
Anonymous says:

What on earth is the matter with you people? First, it doesn't even occur to you that Mars' atmospheric pressure might be germane. Then, you decide it's 2% of the earth's. It's not. It's 0.5%.

posted on Mon, 07/16/2007 - 10:48am
Gene's picture
Gene says:

It did occur to us that Mars' atmospheric pressure might be germane; that's why we discuss it in the original post.

According to the NASA site linked to in the post, Mars' atmosphere is 1.3% as thick as Earth's. We had cited the incorrect 2% figure (since corrected), but the calculations on how much CO2 surrounds each planet were made using the correct figure.

posted on Mon, 07/16/2007 - 11:38am
Anonymous's picture
Anonymous says:

Venus isn't hot because it's 97% CO2, it's hot because it's atmosphere is 90 times the mass of Earth's.

(Note, any greenhouse gases will do. On Earth, it's mostly water vapour.)

The fundamental problem here is that the Warmenistas have been lying about how the Greenhouse Effect is supposed to work. It doesn't work by trapping infra-red, it works because of pressure.

First, when you compress air, it gets hot, and when you let it expand, it cools. This results in the air cooling with altitude - for every 6 km you go up, it cools by 1 degree C. Second, the heat coming in has to balance the heat going out, and the heat radiates out at the 'top' of the atmosphere, where the air above is too thin to stop it escaping any more. To maintain heat balance, the top of Earth's atmosphere must be at about -20 C on average, and the increase of temperature with pressure means that the surface is about 34 C warmer, or about 14 C (global average). Doubling CO2 raises the height of the 'top' of the atmosphere about 150 m, and hence warms the surface about 1 C. (This is then claimed to be trebled by feedbacks.)

Venus has a thicker atmosphere, so instead of the effective top being 5 km up (it's actually spread over the bottom 10 km fairly evenly on Earth), it's about 50-60 km up. And with no water, it increases about 10 C per km, meaning the surface is 500-600 C warmer than the cloud tops. Actually, the cloud tops are at about the same temperature and pressure as Earth's surface (it's even been proposed that colonists could live there in balloons), and the 'top of atmosphere' temperature where it radiates to space is about 30 C cooler (!) than Earth's, because of the higher albedo of Venus. Hence, the surface is very hot.

Simple physics, and no 'runaway' necessary.

posted on Tue, 02/03/2009 - 5:32pm
You aren't correct sir!'s picture
You aren't correct sir! says:

I'm not sure about some of that.

I hope someone corrects me if I'm off the mark here—I don't need to be right, I just want to know if the science is on the level—but I really don't think that's how the greenhouse effect theory works.

When you compress air, doesn't it get cooler? Have you ever held a tank of compressed air, or a CO2 canister? It's always cold. Gas expands as it heats, and contracts as it cools, because there's less energy and less molecular activity, right? If heat were all about pressure, wouldn't the bottoms of the oceans be the hottest places above the Earth's mantle? (They aren't.) I suppose that for a gas to be cold (when it's compressed) it has to release the energy that it had, but that heat just has to radiate away, right? Because you can't lose energy (from being compressed), and keep the same energy (to be hot). Totally confused here.

I don't follow your second point either, about Earth maintaining a heat balance. Do you mean that the planet can't absorb more heat than it radiates back off?

I'm not sure that "Warmenistas" are lying to anyone. It just sounds like you have a fundamental disagreement with atmospheric scientists on how physics works.

posted on Tue, 02/03/2009 - 6:19pm

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