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Calculation: lightning's radiant heat energy relative to the Sun
We calculate lightning's heat energy relative to the Sun's as follows:
The energy radiated by a hot object per second is proportional
to the fourth power of the absolute temperature and is expressed by this
equation:
P = e σ A T4
where e is the emissivity of the object (e = 1 for ideal
radiator), σ = 5.6703 x 10-8
watt/m2
and A is the surface area of the radiating body.
Thus, for each second, the ratio of the energy radiated by the Sun (Ps) to that radiated by lightning is (Pl)
is given by
Ps / Pl =
10-4
As / As
assuming that the lightning temperature is 10 times the Sun's
temperature and that both are ideal radiators.
The Sun's surface area is 0.609 x 1019 m2.
The surface area of a typical lightning bolt is 314 m2, assuming a
bolt length of 100 m and a diameter of 2 m.
Thus Ps / Pl
= 7.66 x 1016 ~ 1017
Only one billionth of the Sun's radiant energy reaches Earth.
So the Sun's radiant energy that reaches Earth is 108 times a
lightning's bolt radiant energy per unit second.
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