Question

A town has a population of 1 million. The average electric power needed per person is 300 W. A reactor is to be designed to supply power to this town. The efficiency with which thermal power is converted into electric power is aimed at 25 %. (a) Assuming 200 MeV of thermal energy to come from each fission event on an average, find the number of events that should take place every day. (b) Assuming the fission to take place largely through ${}^{235}U$, at what rate will the amount of ${}^{235}U$ decrease ? Express your answer in kg per day. (c) Assuming that uranium enriched to 3% in ${}^{235}U$ will be used, how much uranium is needed per month (30 days) ?

Answer 1

(a) Total power used by town in one day

= $300\times {10}^6\times 60\times 60\times 24$ Joule

Energy generated in one fission

= $200\times {10}^6\times 1.6\times {10}^{-19}$

= $3.2\times {10}^{-11}$ Joule

Electrical power,

= $3.2\times {10}^{-11}\times \frac{25}{100}$

$8\times {10}^{-12}$ Joule

Let no of fission be N

So, $N\times 8\times {10}^{-12}$ Joule

= $300\times 86400\times {10}^6$

N = $3.24\times {10}^{24}$

(b) Number of moles required per day

= $\frac{3.24\times {10}^{24}}{6.023\times {10}^{23}}=5.38$ mole

So number of moles not required per day

= $5.38\times 235$

= 1264.3 gm = 1.2643 kg.

(c) Total uranium needed per month

= $1.264\times 30$ kg

Let xgm of uranium enriched 803 % is used

So, x $\times \frac{3}{100}=1.264\times 30$

x = 1264 kg.