Question

A nuclear power plant operates at 40.0% efficiency with a continuous production of 1072 MW of usable power in 1.00 year and consumes 1.10×106 g of uranium-235 in this time period. What is the energy in joules released by the fission of a single uranium-235 atom? Express your answer numerically in joules per atom.

Answer 1

We know that
Power = work / time, we are looking for joules/atom so we need to get to joules from power. Joules is the unit of work, so let's solve for work:

Work = Power x Time, however time needs to be in seconds (SI unit), and we have it in years, so let's solve for seconds:

1 yr (365 days/yr) (24 hrs/day) (60 min/hour) (60 seconds / min) = 31536000 seconds

The plant only operates at 40 % efficiency, we need the true power however. X(0.40) = 1072 MW.

X = true power = 2680 MW = 2680 x 10^6 Watts.

Finally, we can solve for our energy (work):

P = W / T PT = W = (2680x10^6) (31536000) = 8.45 x 10^16 joules, that's a lot of energy.

Half way! This is the amount of energy supplied by ALL of the U-235, we need it on a per atom basis:

8.45x10^16 joules / 1.10x10^6 g U-235 (235 g / 1 mol) ( 1 mol / 6.02x10^23 atoms)

= 2.99 x 10^-11 joules / atom of U-235

Hope that makes sense! Good luck.