Question

Nuclear Fission

If you consider all of the possible fission chains starting with U-235, the average amount of energy released per fission is about 200 MeV. A typical nuclear fission power plant produces 850 Megawatts of electrical power. Assume the plant has an overall efficiency of 30.0% (so 30% of the energy produced by fission is converted into electrical energy). Calculate the total mass of U-235 (in kg) consumed in one year.

For informational purposes, if you take the total amount of cost-effective Uranium reserves on Earth and divide by the rate at which all nuclear fission plants are currently using up Uranium, you get approximately 100 years.

Answer 1

Electrical energy output from the power pant in one year, E = Power*time taken

= 800*10^6*365*24*60*60

= 2.522*10^16 J

let Q is the heat released from the fussion reactions

30% of Q = E

0.3*Q = 2.522*10^16 J

Q = 2.522*10^16/0.3

= 8.407*10^16 J

no of fussion reactions needed, N = Q/energy released in one fussion reaction

= 8.407*10^16/(200*10^6*1.6*10^-19)

= 2.627*10^27

the amount of U-235 cosumed = N*mass of U-235 atom

= 2.627*10^27*235*1.67*10^-27

= 1031 kg <<<<<<--------------Answer