Heat from the Sun
We are indebted to Tom Cull of Washington University for his explanation of the calculation below, although we were careful to compare his results with data reported elsewhere that the Earth receives from the Sun approximately 2 calories per minute per square centimetre of surface area. A wonderful example of mixed units, this actually equates to 1.39kW/m2. So where did this figure come from?
We need to know the surface temperature of the Sun, its radius, and the mean distance of the Earth from the Sun. The last two of these are relatively easy to research as 695,000km and 149,600,000km respectively. The temperature of the outer surface of the Sun has to be deduced from its yellow colour, which equates to a radiating surface temperature of about 5,800K.
The Stefan-Boltzmann equation for thermal radiation states that the total energy radiated per unit surface area of a black body in unit time, j*, is directly proportional to the fourth power of its thermodynamic temperature T.
where j* is in W/m2, T is in K, and σ, the constant of proportionality, is called the Stefan-Boltzmann constant and has a value of 5.67×10−8 J·s−1·m−2·K−4.
With a surface temperature of 5,800K, the Sun therefore emits 64MW/m2. If we think of a sphere around the Sun capturing the power radiated from the Sun in all directions, that sphere has a surface area which is
or 46,300 times the surface area of the Sun. So the power per unit area at the Earth’s surface reduces to a much more manageable 1.4kW/m2.
Whilst this figure is correct for the heat flux, it applies only on the sunny side of the Earth, and at the part directly in line with the Sun. At all other points, you have to correct for the angle of incidence of the light. And the figure varies with the seasons, due to the changes in angle and the Earth’s elliptical orbit. But at any season, solar gain can be very substantial . . .
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