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I know how difficult it is for most people to understand global heating and the carbon dioxide greenhouse effect. Over the years, I went from fairly easy acceptance of the scientific research, then a period of critical uncertainty as I gained some understanding of the complexity of the problem, and then firm acceptance of anthropogenic global warming as I realized how inevitable it was under the present inputs into the global system.
It is perhaps useful to compare the situation on Earth with our so-called "sister planet", Venus, almost the same size as Earth but with an atmosphere 96.5% carbon dioxide, using the Ideal Gas Law.
Reduced to basic form, the Ideal Gas Law is expressed as:
PV = NkT, where
P = pressure, V = volume, N = number of particles in the volume, k = Boltzmann's Constant, and T = temperature.
For Earth, the average pressure at planetary surface is 101.3 kilopascals or 101 300 Joules of energy per cubic metre.
The surface density of the atmosphere is 1.225 kilogrammes per cubic metre. The atmosphere consists mainly of diatomic molecules of nitrogen and oxygen -- 80% nitrogen and 20% oxygen.
The average molecular mass of these is 28.8 -- giving the average molecule a mass of 4.820 x 10^-26 kg. Dividing 1.225 kg by 4.820 kg, one arrives at 2.541 x 10^25 particles per cubic metre.
Boltzmann's Constant = 1.381 x 10^-23 Joules per degree Kelvin.
Dividing PV by the particle number and Boltzmann's Constant, we get a temperature of 288 K, or in more familiar terms, 15 degrees Celsius.
This is very close to the measured surface temperature of the Earth, but it is not precise. Actually, in the absence of carbon dioxide and other greenhouse gases, the temperature would be at or below the freezing point of water, and the oceans would be a solid block of ice.
The main problem in using the Ideal Gas Law for the Earth is that the Earth is not a good approximation to a thermodynamic ideal "black body".
The situation is much different when one turns to the planet Venus, which much more closely approximates an ideal black body. Its atmosphere is quite uniform and well mixed, and its cloud cover is also uniform. Venus has the highest albedo (reflectivity) of all the planets in the Solar System -- it immediately reflects fully 70% of all the solar radiation which it receives. Only 30% of solar radiation contributes to warming the planet. The situation is exactly reversed for the planet Earth. The Earth has an albedo of only 30%, and 70% of incident radiation is absorbed by our planet. It is important to remember these facts.
The surface pressure of Venus is 92 times that of the Earth -- a pressure of 9 319 600 Joules per cubic metre.
The surface density of the Venusian atmosphere is 53 times that of the Earth -- 65 kg per cubic metre. Dividing 65 kg by the mass of a carbon dioxide -- 7.310 x 10^-26 kg -- gives the particle number per cubic metre: 8.90 x 10^26.
Again, dividing PV by the particle number and Boltzmann's Constant gives a temperature of 482.9 K, or 209.7 degrees Celsius.
That is more than 300 K less than the measured surface temperature of 787 K (514 degrees Celsius).
The reason Venus is so much hotter than one would calculate by pressure alone IS BECAUSE OF THE CARBON DIOXIDE GREENHOUSE EFFECT!!!
Naturally, the first thing a global warming Denialist would think of is that Venus is a third closer to the Sun than the Earth is, receiving a little more than twice the radiation as the Earth does, and so would of course be warmer.
This plausible chain of thought is totally fallacious!!
Remember, Venus has an albedo of 70%!
Believe it or not, Venus absorbs less radiation from the Sun than the Earth does!
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