An evergreen of denial is that a colder object can never make a warmer object hotter. That's the Second Law of Thermodynamics, so according to the Agendaists, the Greenhouse Effect, with greenhouse gases playing the role of the colder object, is rubbish. They neglect the fact that heating and cooling are dynamic processes and thermodynamics is not.
Eli, of course, is a dynamic bunny and knows how to add and subtract. Divide is also possible. What is happening is that one does not have just a hot body and a cold body, but a really hot body, the sun, constantly heating a colder (much), but still warm body the Earth, which then radiates the same amount of energy to space.
In elevator speak, Tyndall put it
[T]he atmosphere admits of the entrance of the solar heat, but checks its exit; and the result is a tendency to accumulate heat at the surface of the planet.Eli had a different but not as elegant elevator tweet
Today on twitter, Eli stepped through the simple math and he thought it would be a good thing to put the thread on this blog for future reference. We start with a simple case, imagine the Earth is just a plate in space with sunlight shining on it. Maybe 400 W/m^2
Using the Stefan Boltzman Law you can calculate the temperature of the plate when it reaches equilibrium (400 W/m2) = 2 σ Teq4 where σ is the Stefan Boltzmann constant 5.67 x 10-8 W/(m2 K4), factor of 2 for a two sided plate per m2. Run the numbers Teq=244 K.
Now lets add another plate. We'll color this plate green for greenhouse. It is heated by the first at a rate of 200 W/m2
But after a while, it too has to heat up and reach an equilibrium temperature. . . so as a first guess something like
That's wrong though because there are 400 W/m^2 going into the two plate system and 300 coming out. At equilibrium an equal amount of energy has to be going in as coming out So what happens??
The entire system has to heat up to reach the equilibrium condition. T1 and T2 are the equilibrium temps of the plates.
Looking at the two plate system, the energy going in is 400 W/m2 and the energy going out is σT14 + σT24 Since these will be equal at equilibrium
400 W/m2 = σ T14 + σ T24
And there also has to be an equilibrium for the energy going in and out of the green plate
σ T14 = 2 σ T24
The bunnies can rearrange the second equation to get
σ T24 = 1/2 σ T14
and substitute for σ T24 back into the first equation
400 W/m2 = σ T14 + 1/2 σ T14
400 W/m2 = 3/2 σ T14
Solving for T1 the answer is T1 = 262 K.
Without the greenhouse plate it was 244 K.
Introduction of the second plate raised the equilibrium temperature of the first by 18 K.
The Green Plate Effect
Show this to the next fool with an agenda who thinks that the Green Plate Effect violates the Second Law of Thermodynamics