### 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