UPDATE: Commenter 'Gord,' source of the analysis in the post originally here entitled Why 'Science of Doom' doesn't understand the 1st Law of Thermodynamics, was away from email for a few days and unable to respond to claims in the discussion. I unfortunately misinterpreted that he had dropped out of the discussion and therefore took it down with a "mea culpa." Gord is now back and thus I have put the discussions back up to allow further debate.
Although this debate is irrelevant to AGW for the reasons below, there is merit to continuing the discussions for those interested.
The Science of Doom 'thought experiment' does not prove anything relevant to the Kiehl/Trenberth (K/T) Earth energy budget or the earth/atmosphere system as claimed since
1. The atmosphere cannot behave as both an ideal gas and as a solid PVC blackbody (Science of Doom said elsewhere on this site, "...I realize you are right. As my example is made out of PVC and the atmosphere is made out of gas the example shows nothing useful.")
2. Limitation of conduction and convection by PVC has no relevance to the radiative transfer budget of K/T, which Science of Doom claims is supported by his thought experiment
3. The energy source ["sun"] should be located outside the sphere
4. The energy source should be intermittent ["day & night"], not continuous. Better yet, the source could be continuous outside the sphere as long as the sphere continously rotates.
The K/T Earth energy budget shows
1. The incoming solar radiation (the only energy source) is 342 Wm-2
2. The earth surface radiation is 390 Wm-2, i.e. 48 Wm-2 more than the only energy source.
3. Another 102 Wm-2 is being lost from the earth surface via evapotranspiration and convection that is not limited by PVC or anything else, and conduction is not a part of the budget. Thus, we now have an energy source of 342Wm-2 creating 492 Wm-2 leaving the earth surface even without limiting convection and conduction as in the SoD example. An additional 30 Wm-2 is reflected from the Earth surface for a new total of 522 Wm-2 leaving the Earth surface.
4. Even if greenhouse gases could behave like a mirror, they cannot add energy to the system, and explain how
342 Wm-2 in becomes 522 Wm-2 out
Why conventional Greenhouse Theory Violates the 1st Law of Thermodynamics
U Mass thinks greenhouse gases can add energy to the system
And this explains why Earth energy budgets that don't incorporate greenhouse gases at all do balance whereas the K/T budget is described by it's creator Kevin Trenberth as "a travesty" that doesn't balance.