bob droege says
“Sorry Bryan, the flux density is found nowhere in the Wien’s displacement law.”
This is a strange comment since I did not use flux density in my equation!
My equation comes from page 1257 of University Physics by Young and Freedman 9th Edition.
In case you do not have access to physics books here is a Wiki link saying much the same thing
“From this general law, it follows that there is an inverse relationship between the wavelength of the peak of the emission of a black body and its temperature when expressed as a function of wavelength, and this less powerful consequence is often also called Wien’s displacement law in many textbooks.
λmaxT=b ”
http://en.wikipedia.org/wiki/Wien%27s_displacement_law
I hope you don’t get the impression that I think the KT97 solar intensity value is acceptable.
The division by four method satisfies the first law but violates the second LoT.
If the way you decide to balance the energy contradicts the second law then you end up with the impossible and absurd KT97 diagram.
4 times a 341W/m2 bb distribution does not equal one 1364W/m2 bb distribution.
The second law is about the ‘quality’ of the radiation as much as its quantity.
Once last try to show the difference.
Two cubic containers of volume (one cubic metre) each holding a cubic metre of water.
Water initially at say 20C
For cube A one face is irradiated by 1364W/m2 of radiation.
The other faces are totally insulated.
This cube of water will eventually reach the boiling point of water.
The maximum temperature attainable is 120C so complications beyond 100C.
Cube B is irradiated on 4 sides with 341W/m2.
The other two faces are totally insulated.
This cube of water will actually drop in temperature down to about 5C as it will radiate out more than it absorbs.