Watt conversion from mg??

Question

A Watt (W) is a unit of power equal to 1J/s. A kilowatt is 1000 watts. How many kilowatt hours (1000 watts/s for one hour) of energy would be produced by the complete conversion to energy of 0.59 mg of matter?

Answer 1

5.9 x 10^-7 x (3 x 10^8)^2 = 5.3 x 10^10 J

5.3 x 10^10/(3600 x 10^3) = 1.5 x 10^4 kWh

Answer 2

"Complete conversion to energy" means Einstein's mass-energy equivalence equation: e=mc^2

so mass is 0.000753 g, and c is 3 E 10 cm/sec, c^2 therefore 9E20 cm^2/sec^2.

Multiply that out, and you get: 6.7 E17 g*cm^2/sec^2.

g*cm2/sec2 is the unit of energy called an erg. But the question asks for KWHr. It's an exercise in energy conversion and the result is that one erg is only 2.77 E-14 KWHr.

So multiplying by that, you get the final result that the mass conversion gives 18,611 Kilowatt Hours.

Or 18.6 Megawatts for an hour. A nice little power plant.

By the way that amount of mass, if water, is a little bitty drop that you could see, but if it were any smaller you probably couldn't.