Surface temperatures of Venus are around 500 degrees C, some 485 degrees hotter than Earth (15 degrees C). Although Venus has for decades been cited as a severe example of the "runaway greenhouse effect" [http://www.esa.int/Our_Activities/Space_Science/Venus_Express/Greenhouse_effect_clouds_and_winds] for one example, there are problems with this theory [http://theendofthemystery.blogspot.gr/2010/11/venus-no-greenhouse-effect.html],
[http://www.perthnow.com.au/news/opinion/miranda-devine-perth-electrical-engineers-discovery-will-change-climate-change-debate/news-story/d1fe0f22a737e8d67e75a5014d0519c6], and [http://science.nasa.gov/science-news/science-at-nasa/2012/22mar_saber/]. In fact, it appears that it is Venus' dense atmosphere which accounts for most of the temperature diffence [https://en.wikipedia.org/wiki/Atmosphere_of_Venus-venus-atmosphere.html].
I was interested in using the Arrhenius equation to calculate how much greenhouse warming did contribute to Venus' lead-melting surface temperature. This equation can be summarized as
delta T = k * ln(C/C0).
In this case, I will use C = concentration of CO2 in Venus' atmosphere, and C0 as the concentration in Eath's atmosphere, and k as approximately 2. Thus
2 * ln(90/0.0025) = 21 degrees C, or only 4% of the temperature difference between Earth and Venus! This, it is important to add, does not include greenhouse cooling at the top of the atmosphere by CO2 deflecting incoming infrared, an effect that might reduce greenhouse heating by 80% or more.
Incidentally, if you want to know how hot Earth would get if the entire atmosphere were pure CO2 (2500 times greater), the same equation yields about a 10 degree rise (overlooking cooling and other effects of such high CO2 levels).
I said that the density of the Venusian atmosphere is responsible for (most of) its temperature. There is a simple method of demonstrating this, although under the conditions we will consider there are some serious caveats to this method. If you have ever studied gases in high school or college, you may have seen the equation
PV = nRT,
otherwise known as the ideal gas equation, where PV is the pressure times the volume of the gas, and nRT is the number of mols of gas (6.203E23 = molecules/mol), R is the ideal gas constant, and T is the temperature (in kelvins). This is where one caveat comes in: in principle there is no such thing as an "ideal gas", but most gases under Earthlike conditions come close enough for the equation to provide a reasonable approximation. On Venus, however, things are trickier.
You probably know that when you compress a gas, its temperature rises, and vice versa. (Bear in mind, you can compress with a constant pressure, which means P does not change.) Starting with Earth's atmosphere (for it is closest to an ideal gas), we rearrange the equation above equation to:
T = PV/nR, where we treat P/nR as a single constant, called K. Then T(e) = K*V(e), and T(v) = K*V(v). Then, again rearranging, we have T(v)/T(e) = V(v)/V(e) (K's cancel). If you reduce the volume V(e) to the same density of V(v) -- a factor of about 90 -- then T(v) = 90*T(e).
Here, we run into our caveat, because the density of the Venusian gas is 90 times that of Earth's, and the temperature is about 2.67 times that of our planet (not 90). Gas at such high density and temperature behaves in a highly non-ideal fasion; in fact, at the surface of Venus the carbon dioxide isn't even a gas anymore, but what's known as a "super critical" fluid, which absorbs much more heat than regular gases under Earth-like conditions.
Another factor comes into play here. All gases, especially gases at high densities, are excellect heat insultors, due to conduction and convection. I can think of no better example than our sun (or any star), in which a photon generated at the core takes thousands (or is it millions?) of years to reach the top of the atmosphere (the photosphere, the part we see) before zipping off into space at the speed of light. Given that stars are almost entirely hydrogen and helium, non-greenhouse gases, that is clearly not the reason for this phenomenon.
