Question

The total U.S consumption of electricity in a particular year was 5.0 X 10^12 kilowatt-hours. What is the mass equivalence of this amount of energy?

Answer 1

I believe we can simply use the oh so famous \(\huge E=mc^2\) to solve this question. I think the issue is the odd derived unit for energy of a kilowatt-hour (kWh). I'm not sure if we can use this unit for this equation, so I would just go ahead and attempt to convert it.

If we were to look it up, we can see that:
\[1 \ \text{kWh}=3.6 \times 10^{6} \ \text{J}\]Given this conversion, you should be able to convert and continue to easily solve for m. E and c are given.

Answer 2

@Michele_Laino

Answer 3

I think it is correct! @Aero

Answer 4

Interesting unit of energy. What's the advantage of using kWh as opposed to Joules?

Answer 5

I think, since electrical engineers prefer to use \(kWh\)

Answer 6

so, according to @Aero we can write:
\[\Delta m = \frac{E}{{{c^2}}} = \frac{{5 \cdot {{10}^{12}} \cdot 3.6 \cdot {{10}^6}}}{{{{\left( {3 \cdot {{10}^8}} \right)}^2}}} = ...{\text{Kg}}\]

Answer 7

All our electricity domestic meters read in kWh

Power stations are generally rated by their power output (kW) so their energy output is easily converted to kWh

1 kW = 1000 j/s

so in 1 hour (3600s) 1 kWh = 3,600 kJ

Answer 8

@MrNood That's really interesting! I wasn't aware of that, thank you =]