I had a discussion with someone about why Venus is so much hotter than Earth. Is it because Venus is 96.5% CO2, which is acting as a "heat trap"? Or can the higher temperature be explained by other causes?
I made the point that, being closer to the Sun, the radiant energy received by Venus is about 88% higher than Earth (67 million miles away vs. 92 million, average, and intensity increases as the square of distance). The Earth has an average temperature of 287K, while Venus has an average temperature of 855K. Therefore, 1.88 * 287K = 541K is the least that the temperature of Venus should be, simply because it's closer to the sun.
But the discrepancy makes one wonder -- if Venus is still subject to heat trapping, how else does the temperature get up to 855K?
I made a hand-waving argument that the higher surface pressure on Venus (80 atmospheres) should have an effect because of the higher heat capacity of the denser atmospheric gas. I argued from the chemistry formula PV = nRT, and, while it points in the right direction, doesn't give a correct answer within an order of magnitude.
So I considered whether the higher molecular density of CO2 on Venus is a factor. I checked this: Carbon has an atomic weight of 12, Nitrogen 14, Oxygen 16. Average molecular weight of CO2 is 12+32 = 44. But the weighted average for Venus's atmosphere is 43.44 (96.5% CO2, 3.5% N2). Earth's atmosphere is 78.1% N2, 20.9% O2 and 0.9% Ar. Monoatomic argon has an atomic weight of 36. Average molecular weight of Earth's atmosphere is 28.91.
Multiplying my original estimate of the Venusian temperature times a density correction factor, I get 541K * (43.44 / 28.91) = 813K as the estimated surface temperature of Venus. This is pretty close to the actual surface temperature of Venus, 855K. It still leaves a little room for heat trapping effects, though. T'would be interesting to re-do the calculation based on the isotopic distributions (different number of neutrons) in the N2, O2, etc (they will have a big effect), or the amount of monoatomic vs diatomic species (ie, O vs O2, N vs N2) to see if the answer gets better or worse.
I wouldn't publish this reasoning in a scientific journal without more work, but it's worth pondering. Simple formula that gives reasonably correct results sometimes have valid foundations when analyzed more deeply. Better than a lot of the crap you'll read in professional journals, anyway.
Postscript (12/6/09): Venusians Discredit Robb
I re-did this calculation, and now my numbers aren't quite adding up. The situation is more complex than I assumed. My biggest error is that temperature increases only as the fourth root of solar power (per Stefan's Law of Radiancy), but I also got a wrong value of the average Venusian temperature, which should be 737K (I accidentally converted "F" to "K"), but I'm still unsure -- some reports give close to 900K as an equatorial surface temperature, and the "average" numbers I find on the web are all over the map, from 673K to 755K.
I did, however, find that the ratio of heat capacity to thermal conductivity of a gas is relatively independent of pressure and temperature, so that supports using my molar mass hypothesis without corrections for P and T, but the calculated surface temperature is still coming out too low (508K). This points to at least a higher thermal resistance of the Venusian atmosphere, as compared to Earth. This makes sense from several aspects -- the high concentration of CO2, and the fact that the atmosphere of Venus is 94 times heavier than Earth. Heat capacity is roughly proportional to mass, but as I said, so is thermal resistance. A small difference of two big numbers can make a big difference.
I tried to find high temperature CO2 thermal conductivity data to incorporate this, but couldn't. However, the higher thermal resistance is supported by a Venusian blackbody temperature of 231K (per Nasa) as compared to Earth's 254K. Even correcting thermal resistance based on the ratio of blackbody temperatures (and solar fluence closer to the sun) I still only get up to 644K for the average Venusian surface temperature.
Another aspect -- the much more massive Venusian atmosphere is almost twice as high as Earth's -- this would increase the thermal resistance, and temper the blackbody radiation. Trap more heat.
Another aspect -- the only atmospheric composition data I could find apparently only applies to the surface. No information on what it is at 15.9km or higher.
Another factor I learned is that much of the excess heat could be coming from the core of Venus (the surface was reportedly molten only 500 million years ago), and with the high atmospheric thermal resistance, that would raise surface temperatures significantly. So, in conclusion, I have too little data to really make a good calculation. The devil's in the details. Sigh.