The Relentless Pseudo-science of WUWT
The Steel Greenhouse as proposed by Willis Eschenbach and published twice on the “Watts Up With That” website is a misinterpretation of the fundamental rules of physics governing the radiative transfer of energy.
Below are 2 statements of this fundamental principle from 2 modern physics references.
It is trivial to use this fundamental principle to prove the “Steel Greenhouse” proposition as proposed and its ability to double the energy flux is a complete fallacy.
“The energy an object absorbs comes from its environment, which consists of other bodies that radiate energy. If an object is at a temperature T, and its surroundings are at a temperature T0, the net energy gained or lost each second by the object as a result of radiation is –
Pnet = A ξ σ (T4 – T04).”
College Physics 7th Edition
“While a body at absolute temperature is radiating, its surroundings at temperature Ts are also radiating, and the body absorbs some of this radiation.
If it is in equilibrium with its surroundings, T = Ts and the rates of radiation and absorption must be equal.
For this to be true, the rate of absorption must be given in general by H = A ξ σ Ts 4. Then the net rate of radiation from a body at temperature T with its surroundings at temperature Ts is:-
Hnet = A ξ σ (T4 – Ts4).”
Sears and Zemansky’s – University Physics With Modern Physics – Young and Freedman.
The “Steel Greenhouse” proposal is a sphere with an internal source of energy capable of causing it to radiate at 235 Watts per square metre.
A steel shell is then closely “fitted” and it is claimed this action causes the sphere to increase in temperature until it emits double the original flux at a temperature that is approximately 1.1892 (the fourth root of 2) times its original temperature.
It is assumed ξ is unity.
Let’s analyse this proposal from first principles.
Let r be the radius of the Sphere.
Let R be the radius of the Shell.
Let T be the original temperature of the Sphere, T1 be the temperature of the Shell and Ts be the temperature of the surroundings.
A of the Sphere is 4 π r2.
Let Q be the rate of energy lost by the Sphere initially:-
Q = A ξ σ (T4 – Ts4) = 4 π r2 ξ σ (T4 – Ts4) = 4 π r2 σ (T4 – Ts4) as ξ is unity.
Let Q’ be the rate of energy loss by the Sphere after the Shell is fitted:-
Q’ = A ξ σ (T4 – T14) = 4 π r2 ξ σ (T4 – T14) = 4 π r2 σ (T4 – T14) as ξ is unity.
Let Q’’ be the rate of energy loss by the Shell:-
Q’’ = A ξ σ (T14 – Ts4) = 4 π R2 ξ σ (T14 – Ts4) = 4 π R2 σ (T14 – Ts4) as ξ is unity.
We are now in a position to solve for T1. Note we do this without making any erroneous assumptions about its value. This represents real scientific method not pseudoscience.
As Q’’ = Q’ the solution is
T14 = (r2 T4 + R2Ts4)/ (R2 + r2)
Setting Ts to zero as there is no energy other than the internal energy of the sphere and making the approximation that r ≈ R we have the inescapable conclusion that
T14 (the temperature of the Shell) = (r2 T4 + R2Ts4)/ (R2 + r2) ≈ (r2 T4 + 0)/ (r2 + r2)
That is –
T14 (the temperature of the Shell) ≈ T4 (the original temperature of the Sphere) /2
Q was quoted as 235 watts per square metre and therefore T is ~254 Kelvin
This means T1 is ~213 Kelvin with a flux of 117.5 Watts per square metre.
Thus the true energy balance is the Sphere emits 235 Watts per square metre and receives 117.5 Watts per square metre from the Shell for a net result of 117.5 Watts per square metre radiated.
The Shell is at a temperature of 213 Kelvin and emits 117.5 Watts per square metre in all directions. The net 117.5 Watts per square metre received from the Sphere maintains the Shell temperature hence its ability to continue to radiate – this is the Shell’s only energy source after all.
I think you will find all authoritative sources confirm this result.
Anyone who thinks the 117.5 from the Shell to the Sphere has to be added to the 235 from the Sphere’s internal source simply hasn’t been following and obviously cannot understand real science.
This is accounted for in the energy balance I presented above but it is also implicit in what we started with – the fundamental equation of energy transfer.
Hnet = A ξ σ (T4 – Ts4).
If T > Ts – that is the difference is positive – then net energy transfers from the object. The equation says that absolutely.
If T = Ts – that is the difference is zero – then there is no net energy transfer from the object or the surroundings. The equation says that absolutely.
If T < Ts – that is the difference is negative – then net energy transfers from the surroundings to the object. The equation says that absolutely.
Thus for the “Steel Greenhouse” we have proven that T – the temperature of the sphere – is greater than T1 – the temperature of the shell – without the need for pseudoscience.
The equation says that net energy transfers from the Sphere to the Shell.
This derivation from first principles and the fundamental equation eloquently demonstrates the impossibility of a back radiation heating effect as proposed for Steel Greenhouses.
The model as presented is fallacious.
References
Essentials of College Physics 7th Edition Raymond A Serway, Chris Vuille
University Physics with Modern Physics 13th Edition Young and Freedman
Physics for Scientists and Engineers Sixth Edition Paul A Tipler and Gene Mosca
Problems and Solutions on Thermodynamics and Statistical Mechanics (Major American Universities Ph.D. Qualifying Questions and Solutions) Volume 5 Edited by Young-Kuo Lim
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