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The Solar Temperature *****

Estimate the solar temperature using
- the solar radiation intensity on the earth of 1.4 kilowatts per square meter. (
m,
m)
- and the solar spectrum which peaks at about 500 nm.

First we compute the power radiated per unit area on the solar surface.

We compare this to the expectation as a function of temperature.

and get

Lets assume that
peaks at 500 nm as one of the graphs shows.
We need to transform
.
Remember
for distribution functions.

This peaks when

is maximum.

Lets set
and solve the equation

I solved this iteratively starting at y=5 and got
implying

If we take
nm, them
.

That's agrees well.

Jim Branson
2013-04-22