This is apparently a "E = mc² " question. This is the famous equation
that relates energy and mass. When I get the answer, we're all going to
swoon "ooooo" when we see how little mass it represents.
OK. So first we have to change kilowatt-hours into the equivalent number
of joules:
1 watt = 1 joule per second
1 hour = 3600 seconds
(5 x 10¹² kw-H) · (10³ watt/kW) · (1 [joule/sec]/watt) · (3600 sec/hr)
= (5 x 10¹² · 10³ · 1 · 3600) joules = 1.8 x 10¹⁹ joules .
The other number we need is 'c' ... the speed of light.
That's 3 x 10⁸ m/s . c² = 9 x 10¹⁶
Now we're ready to use E = m c² :
1.8 x 10¹⁹ = (m) · (9 x 10¹⁶)
Divide each side
by (9 x 10¹⁶) : m = (1.8 x 10¹⁹) / (9 x 10¹⁶)
= 200 kg .
And there you are. That's the amount of mass that needs to be
converted to energy in order to deliver the total consumption of
electrical energy in the USA for a year. Nice of them to pick a
number that works out so roundly.
That's it. 200 kilograms. A mass that weighs about 440 pounds
on Earth. It doesn't matter what kind of substance it is. It could be
rock, paper, scissors, water, Jello, it doesn't matter. If you could
convert a couple of NFL quarterbacks to pure energy ... and I sure
wish you could ... you'd have it right there.
