- #1

Phys12

- 351

- 42

## Homework Statement

Assuming that we could generate Australia's electricity from a fusion reactor, that converted hydrogen to iron and turned the energy into electricity with 100% efficiency, what mass of fuel would it use per year? You may assume that this fusion reaction converts 1% of the mass into energy. Australia uses 225 billion kilo-watt hours of electricity per year which is 8.2*10^17 Joules.

## Homework Equations

E=mc^2

## The Attempt at a Solution

m = (8.2*10^17)/c^2

=> m = 10 kg (approx.)

Since the fusion converts only 1% mass into energy, I multiply the result by 100 to get 1000 kg.

While my answer is within the margin of error (the real answer is 900 kg.), my way of going about solving the problem might be wrong as the answer given is:

"Divide the energy by 1% of the speed of light squared, to get the mass needed."

What I don't understand is: why would we want to divide it by 1% the speed of light? What's the logic behind that? We obviously are not changing the speed of light, just reducing the efficiency, so, wouldn't increasing the total energy required (as I did) be a more logical approach?