Question

A nuclear power plant operates at 40.0% efficiency with a continuous production of 1012 MW of usable power in 1.00 year and consumes 1.04×106 g of uranium-235 in this time period. What is the energy in joules released by the fission of a single uranium-235 atom?

Answer 1

First, let's considerate the following.

1 W -------- 1 J/s,

1012 MW -----------1012 MJ/s

WE just want the power in jouls only, so, we know that the plant operates in one year so:

1012 MJ/s * 1 yr * 365 d / 1 yr * 24 h / 1 d * 3600 s / 1 h = 3.19x10¹⁰ MJ

We also know that the efficiency is 40% so:

3.19x10¹⁰ * 0.40 = 1.28x10¹⁰ MJ

With the molecular weight of Uranium that is 235 g/mol, calculate the moles and atoms of U:

1.04x10⁶ g * (1 mol / 235 g) * (6.02x10²³ atoms / 1 mol) = 2.66x10²⁷ atoms.

Finally to calculate the energy per fission:

E = 1.28x10¹⁰ / 2.66x10²⁷ = 4.80x10^-18 MJ / atom * 1x10⁶ J / MJ = 4.8x10^-12 J

Hope this helps.....