Quote:
Originally Posted by julianh72
I'm pretty sure Eratosthenes was talking about the potential fusion energy contained in a rain-drop, not the kinetic energy of a falling raindrop.
0.05 mL = 50 mg of water (i.e. 20 raindrops per gram).
Molecular weight of H2O is 18 (2 x Hydrogen = 2, 1 x Oxygen = 16), so a drop of rainwater contains about 2/18 x 50 mg = 5.5 mg of hydrogen.
About 0.7% of the mass of fusing hydrogen is converted to energy in the process of combining 4 hydrogen nuclei to make one helium nucleus.
E = mc^2 = (0.7% x 5.5E-6 kg) x 3E8 x 3E8 = 3.5 TJ per raindrop
(I guess Eratosthenes must have assumed slightly larger raindrops than 0.05 mL each to arrive at his 9 TJ figure!)
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I doubt that very much given that his calculation for the energy to lift 28 Gl of water is based on the formula for gravitational potential energy
PE= mgh.
I'm pretty sure he had the same idea in mind with rain drops otherwise changing the subject from rest mass energy to gravitational potential energy midstream in a thread seems quite unusual to me.
But then again what do I know....