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
where: Q rad is the heat transfer rate by radiation,

 is the emissivity,

F is the surface area at absolute temperature T s,

T surr is the absolute temperature of surroundings

 is the Boltzmann constant.

 The Stefan-Boltzmann law tells us that as the temperature

Fig.13 - Lambert’s of an object increases, more radiation is emitted each second.
cosine law

E = σT 4 (1.19)

where σ is a constant, T is the temperature of an object in Kelvin and E is the

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maximum rate of radiation emitted per meter .

 Wien's law describes the maximum wavelength
that an object emits based on it's temperature.

θ
λ max = / , (1.20)
T
where λ max is the wavelength in micrometers (μm) at

which the maximum radiation emission occurs, θ is a

constant equal to 2897 μm K, and T is the temperature in
Fig.1.11 - Wien's law
Kelvin.

θ
For the Earth, T~300 K: λ max = / 300 K ~ 10 μm
θ
For the Sun, T~6000 K: λ max = / 6000 K ~ 0.5 μm
The Sun emits in shortwave radiation where as the Earth emits in longwave radiation.

The Sun emits in shortwave radiation where as the Earth emits in longwave radiation.

Lambert’s cosine law

Lambert's cosine law is the statement that the total power observed from a "Lambertian"

surface is directly proportional to the cosine of the angle Φ made by the observer's line

of sight and the line normal to the surface.

(1.21)

Utilising the Lambert’s law the total energy radiated to the hemisphere is:

(1.22)

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