Energy from the Sun

The Earth receives heat from the Sun by way of sunlight, a form of electromagnetic radiation.
•Because the Earth is surrounded by a vacuum it can not lose heat by conduction or convection.
•The only way in which it can lose heat is by radiation.
•The Earth receives ~ 1,368 W/m2 of solar radiation from the Sun.
•This is the energy that would be received by a disk as shown.
•Since the planet is a sphere, the area of the disk (πr2) receiving this energy needs to be divided by the surface area of the Earth’s sphere (4πr2) to find the energy per square meter on the sphere.
•That is, the surface area of a sphere is 4 times the area of one side of a disk so the quantity of energy impinging on the surface of the Earth is:   Es = 1368/4 = 342 W/m2

The common method to calculate the Temperature of the Earth is to give the absorptivity of the Earth a value of aE = 0.7 and then to consider the Earth a black-body eE = 1 when calculating the IR emission as shown below In Summary: The qouted temperature of the Earth without a GreenHouseeffect (-18deg C) is entirely fictitious and is brought about by a simple miscalculation – how is it that this figure is widely quoted in the scientific literature?

•The Stefan Boltzmann model assumes a well defined surface of a homogenous material from which energy is irradiated.
•The Earth does not have a well defined surface due to its atmosphere, clouds etc.
•Energy is irradiated from the surface of the Earth (Tave = 15oC) and from the atmosphere (T =  -50 oC to 15 oC)
•The value obtained 6 oC is a reasonable value for the effective radiative temperature of the Earth

2 Responses to Energy from the Sun

1. iya says:

Kirchhoff’s law does not apply, because its frequency specific.
The incoming solar spectrum is very different from the outgoing thermal spectrum.
Earth’s albedo is 0.3, i.e. absorptivity 0.7, otherwise it would not be so bright when viewed from space, but the emissivity of the surface is close to 1.

• wstannard says:

Hi Again Iya

Yes, you are right about Kirchoff (but a = e is often a reasonable place to begin..)…

The emissivity of the surface may be close to 1 but what about the emissivity of the atmosphere where most of the energy radiated into space originates?
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