Solar Energy On how the Sun emits energy as radiation, and how the Earth receives it.

Outline  Blackbody radiation and the Sun. –Wien’s law –Stefan-Boltzmann law –The temperature and spectrum from the Sun.  The Earth as receiver –The Solar Constant –The wobbly Earth –The Atmospheric Filter and albedo –The absorbing/reflecting surface –Blackbody re-emission.

Blackbody Spectrum and Temperature

Wien’s law  A blackbody emits the greatest percentage of its energy at a single wavelength, called λ max.  That wavelength depends on the blackbody’s temperature, according to Wien’s law. – λ max =.0029 m*K / T(K)  Example: –If T = 500 K, λ max =.0029 m*K / T(K) = 5.8 x m –Looking at our EM chart, that is in the Infrared.

The Sun’s spectrum

The Sun’s temperature  From the graph, –λ max =.5  m or 5 x m or 5000 . –Then Wien’s law says: λ max =.0029 m*K / T(K) or T(K) =.0029 m*K / 5 x m = 5,800 K  The temperature of the Sun’s surface is 5,800 K!  It’s spectrum is centered in the Visible range (44%), with a long tail in the Infrared, and a significant amount of Ultraviolet, as well.

Stefan-Boltzmann Law  The power (energy per time) per area emitted by a blackbody is also a function of Temperature.  Stefan-Boltzmann law: –Power / Area =  T 4 –  = 5.67 x W/m 2 *K 4 –Example: Our body temperature is T = 310 K –If we were a blackbody, we would emit 500 W per square meter of area. Actually, we emit far less because we are not close to being a blackbody. We end up emitting around 1,000 food calories in a day.

Power radiated by the Sun  T sun = 5800 K  P/A = Power / Area =  T 4 – = 64 MW / m 2 –The Sun emits enough energy per square meter to supply all the energy needs of a small city!

But what do we get out of it?  Solar constant = 1360 W/m^2. –93 million miles away! –Earth’s tilt! –Atmospheric absorption.

Earth’s tilt

Atmospheric absorption