Does Pressure Alone Account for Hot Planet Surfaces?

(c) 2020 by Barton Paul Levenson

The idea that the surface temperatures of planets can be explained by their surface atmospheric pressure was originated, to my knowledge, by crackpot internet blogger Tony Heller, a/k/a "Steve Goddard," in 2010. It was immediately echoed by crackpot physicist Lubos Motl, who should have known better, and was most recently repeated in 2017 by former forest rangers Ned Nikolov and Karl Zeller (the latter of whom really is a retired meteorologist--again, someone who should have known better). Their argument goes roughly like this. There is something called the ideal gas law:

where

• P is the pressure of an ideal gas (measured in pascals, Pa, in the SI metric system),
• V is the volume under discussion (cubic meters m³),
• n the number of kilomoles of gas present--a kilomole is just a number, about 6.022 x 10²⁶,
• R the "Universal Gas Constant" (8,314.4598 joules per kilomole per kelvin, J kmol^-1 K^-1), and
• T is the absolute temperature (in kelvins K).

Consider sea-level conditions on Earth. A cubic meter holds about 0.042293 kilomoles of air molecules, pressure averages 101,325 Pa, and temperature 288.15 K. It all works out! And clearly, if you were to double P, and everything else stayed constant, T would double! So Venus, which is much hotter than Earth, must be hotter due to its high air pressure alone, without any silly talk of a greenhouse effect.

Except, of course, that everything else does not stay constant. An atmosphere is not bound by a container, so its "volume" (or rather, its density) can change with pressure and temperature, and when that happens, you realize you have no way to predict temperature from pressure alone. R is the only constant in the equation; everything else is up for grabs, and you have to know P, V, and n to know T. In other words, pressure by itself tells you nothing at all.

And if the atmosphere of Venus had, indeed, been heated by some enormous compression event, would it still be hot?

Consider a tire. If you've ever inflated a tire, you know the tire feels hot after being pumped full of air. Increasing the pressure has increased the temperature. But is it still hot an hour later? Usually it is not. Because objects radiate away heat.

The atmosphere of Venus is 96.5% carbon dioxide. Carbon dioxide (CO₂) is an excellent absorber of infrared radiation, and that means it is an equally excellent radiator of infrared radiation. Sunlight can only heat Venus to 227 K, a value set by its local solar constant and its albedo, or reflectivity. If the Venus atmosphere had been heated by compression, so that its surface temperature reached the present 735.3 K, it would have lost all that heat in something like 1,000 years, and Venus would now be at a uniform temperature of 227 K again, all the way down to the surface.

If pressure alone could produce enough heat to warm the surfaces of planets above the radiative equilibrium temperature, they would have to do so constantly, to replace the heat lost by radiation. It would mean heat was being generated out of nowhere. Planetary atmospheres would then be perpetual motion machines of the first kind. The first law of thermodynamics--energy can neither be created nor destroyed--prevents such machines from existing in the real world.

So if someone tells you pressure accounts for the high surface temperatures of planets, and not the greenhouse effect, tell them to pick up an introductory physics book and read through it. People like Lubos Motl and Karl Zeller presumably did so, once upon a time, but since then they seem to have forgotten some of the details.