Noworkia, Yes, that's right, on Earth, everything under pressure is really hot: I mean, I can't even pick up the gas canister I take hiking, it's so hot! And deep-sea divers have to wear protective heat equipment. More seriously, the equations you quote relate to *work done* on a gas: if I compress something, it does get hot, as work is being done on it, but then, pretty obviously, it cools down. That's why my gas canister does get cold when I use it. I really don't see how one could naively apply these to an entire planet though: as I suggested sarcastically, there are massive pressures generated under the sea, and lots of gas trapped down there, but it's not all super-heated. I thought it was pretty much settled that Venus is an example of extreme "greenhouse gas effect".
Copied from the Wiki talk page:
"The Earth has little carbon dioxide in its atmosphere but far more locked in carbonate rocks. There's enough carbon dioxide in the Earth's rocks to allow a Venus-like density if it were released. More significantly, the Earth's water has a huge volume of material (water, of course) that would become atmosphere if the Earth were to be warmed to Venus-like temperatures. Most theories hold that as the sun expands to a gas giant toward the end of its life, the Earth will slowly be warmed to temperatures around 60°C, at which point a runaway greenhouse effect will take effect, and then temperatures will skyrocket. An increasing load of water vapor will itself add density to the atmosphere (that itself raising the temperature) and accelerate the greenhouse effect, until at roughly 305°C, the critical point of water, the greenhouse effect from water vapor will no longer cause further heating. Any increased temperatures will result from the further expansion of the sun, and at another point, carbon dioxide will be released from carbonate rocks.
With an even higher pressure, the Earth would become even hotter than Venus even if the upper atmosphere clouds enough to prevent any sunlight from reaching the Earth's surface. But the Earth's seething surface will be anything but dark; its rocks will radiate heat which will likewise be prevented from escaping through the same clouds that prevent the entry of all but the dimmest sunlight.
Don't be unduly scared. This won't happen for hundreds of millions of years. So far, the Earth has a relatively thin atmosphere, much unlike that of Venus, that isn't very good at holding onto heat. We still have real winters from about 35° north and south poleward, and real nights everywhere. We are safe so far from the runaway greenhouse effect, and the carbon dioxide that would make the Earth a Hellish place is safely locked away.
Venus, in contrast, is too hot to have any carbonate rocks. It's also too hot to hold water vapor. An atmosphere as crushing as that of Venus is hot in its own right. The perfect gas law (PV=nRT) implies that temperature is proportional to pressure, and Venus has enough atmospheric pressure to be exceedingly hot in its own right.--66.231.38.97 01:20, 15 Jun 2005 (UTC)"