hahahahaha. I dont know whether OPPD is a physicist or not but I sure know that you have never taken physics or math if you are offended by rearranging terms in a formula. are you even sure that OPPD believes in CAGW? so far I have only noticed him laughing at your stupidity.
I notice that you didn't answer the question either. Between you two geniuses, you should be able to answer the question I have asked.
Why would you apply any property to an equation that is already elegant? What is to be gained by doing it? What do you get that you don't get when you use the equation as it is actually written?
How about an answer?
OK, I have 5 minutes to kill.
Planck curves for two objects, one at 10C, the other at -10C. if you wanted to see how much energy was leaving the warmer object to the cooler one how would you do it? in a stripped down, complexities removed thought experiment you would simply calculate the radiation leaving the first, then calculate the radiation leaving the second, subtract them and the net result would be your answer, and depending on whether the answer was positive or negative you would know the direction.
The rate of energy emitted by an ideal surface, frequently called a blackbody, is given by the following relationship:
E = KsbT^4
where T is absolute temperature & Ksb is the Stefan-Boltzamnn constant which is 0.567 x 10-9 W/mK4
you may have noticed that there is only one (T^4) term. that is because the other term is assumed to be zero and 0^4=0. this also the reason why we must measure in the absolute temperature scale of degrees Kelvin.
we could work out both terms and subtract them, but it is easier to just subtract the T^4 terms immediately so that we only have to write the constant terms once.
what I find elegant is how the visual Planck curves so easily describe what is going on in radiation exchanges. it is easy to see why the second law is correct. the warmer object always has an excess of radiation to give to the other cooler object. as the two objects get closer together in temperature there is less and less excess (this is where polarbear's first derivative comes into play) to drive heat exchange. and when the two objects are the same temperature, it shows how there is still an exchange of radiation, just no movement of heat.
I will ask you again....what do you think happens when two objects are the same temperature? you said before that radiation could only go from a warmer to cooler object, even down to one single photon. if that is correct, then where does the radiation go?
Wow.. I see this has gotten real ugly since I left. Probably saw that coming.. Hope you've made progress.. But I don't think so.. I think we are still confusing Thermodynamics with EM Fields and Waves here..
Would I be out of line if I observed that photons don't KNOW and don't CARE if they are pointed towards a "warmer" or a "cooler" object??? Otherwise, Captain Kirk would be defenseless if the Klingon Vessel was sitting in a warm pool...