Question

QUESTION 15

A nuclear power plant operates at 40.0% efficiency with a continuous production of 1042 MW of usable power in 1.00 year and consumes 1.07×10⁶ 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

Convert year into seconds

(1 yr) x (365 days/yr) x (24 hr/day) x (60 min/hr) x (60s / min) = 31536000 s

Efficiency of the plant = 40%

Actual power of the plant = 1042/0.40 = 2605 MW

Energy released by uranium-235

= (2605x10^6 W) x (31536000) s

= 8.215 x 10^16 J

Moles of U-235 = mass/molecular weight

= (1.07×10^6 g) / (235 g / 1 mol) = 4553.19 mol

Number of atoms = (4553.19 mol) /(1mol/6.02x10^23atoms)

= 2.742 x 10^27 atoms

energy released by a single uranium-235 atom

= (8.215 x 10^16 J) / (2.742 x 10^27 atoms)

= 2.995 x 10^-11 joules / atom

Or
= 3.00 x 10^-11 joules / atom