In the previous two posts (first, second) we have looked at the climate alarmist’s “steel greenhouse” which they mathematically solve in such a way as to lead to what they think is an alarming behaviour about temperature, which they call a radiative greenhouse effect. Well, they should call it a “radiative greenhouse effect”, but they actually only ever call it a “greenhouse effect” thus sowing confusion over how a real greenhouse functions (physical stoppage of convection) vs. how their solution functions (via radiation which can’t be stopped) which is not like an actual greenhouse. The steel greenhouse is a perfect model for demonstrating the non-existence, the thermodynamic impossibility, of the radiative greenhouse effect of climate alarm.
In the first post we demonstrated the correct solution which utilizes the complete set of laws of thermodynamics, and this solution quite clearly mathematically proved the non-existence of the alarmist radiative greenhouse effect. In the second post we examined the alternative climate alarmist solution which we identified only partially uses the law of conservation of energy in such a way that it then ignores the full statement of the First Law of Thermodynamics which is the actual law about conservation of energy.
The alarmist solution invents an alternative accounting of energy flows which treats all energy to behave like heat and thus to be able to raise any object’s temperature no matter the source of the energy. This is contradictory to the actual statement of the First Law which specifically states that an object can only raise in temperature if it receives heat, where heat is then defined only as the balance difference of energy intensity between two objects, that is, the energy which spontaneously flows from hot to cold, thus disallowing the energy from a cooler body to raise the temperature of a warmer body. The alarmists go to create this solution because they dispense with the thermodynamic concepts and definitions of heat and specifically of thermodynamic equilibrium, and thus their solution is thermodynamically incomplete and hence does not connect to reality. Logically, they are thus required to come up with a solution which is impossible, and this we can now immediately mathematically prove.
From the last post in equation 4, the mathematical solution for the temperature of the shell showed that it would be
1) Tsh4 = PspO/4πRsh2σ
So, if the shell had the radius of the sphere, then the solution shows that the shell would have the same temperature of the sphere because the temperature of the sphere by itself is simply
2) Tsp4 = PspO/4πRsp2σ
That is all well and good, and is what you would expect for the shell. This is the same result in both the alarmist’s solution and the correct solution from the first post. That is, the temperature of the sphere is given simply by its internal power generation spread over emission from its surface, and if the shell is identical with the surface of the sphere then the shell must equate to the surface of the sphere and hence have the temperature of the sphere. However, the ontological error of their non-utilization of the complete and proper set of thermodynamic laws is exposed when we look at their solution for the temperature of the sphere (equation 6 from the last post):
3) Tsp4 = (Psp0/4πσ)((Rsp2 + Rsh2)/Rsp2Rsh2)
Let us make the shell radius the same as the sphere radius, i.e., Rsh2 = Rsp2, and then equation 3 becomes
4) Tsp4 = 2PspO/4πRsp2σ
Equation 4 should have been identical to equation 2 since what we’re doing in equations 3 and 4 is the exact same thing as in equations 1 and 2, i.e., making the shell radius the same as the sphere radius. Instead what we have is a contradiction, a paradox, i.e. an impossibility, thus indicating that something has gone fatally wrong – there is a factor of two in equation 4 which should not be there.
At the stage of arriving at the equation 1 above in the previous two posts, everything is OK. The flaw in the alarmist’s radiative greenhouse effect physics comes in after that, when they develop a solution with a mathematics which does not utilize the definition and concepts and maths of heat flow and thermodynamic equilibrium. What else can happen but deriving an equation which contradicts and hence disproves itself when the premises going into the solution aren’t based in the mathematical laws of physics and the logic of reality, i.e. the logic of that which can exist?
Remember, this is their solution, their mathematics which they create by ignoring the definition and equations for heat flow and thermodynamic equilibrium, their result, and their own paradox which exposes their radiative greenhouse effect scheme as false.
It is finished. And they are finished.