A town has a population of 1 million. The average electric power needed per person is 300W. 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 form each fission event on an average, find the number of events on an place every day. (b) Assuming the fission to take place largely through `U^235`, at what rate will the amount of `U^235` decrease ? Express uour answer in kg per day. (c) Assuming that uranium enriched to 3% in `U^235` will be used, how much uranium is needed per month (30 days)?

Explanation

Power required `= 10^(6) xx 300 = 3 xx 10^(8)W`
Input power, `P = (3xx10^(8))/(0.25) = 12xx10^(8)W`
(a) Let number of events/day `= n`
`(nxx200xx1.6xx10^(-13))/(24xx3600) = 12 xx 10^(8)`
`n = 3.24 xx 10^(24)`
(b) `n = (m)/(M) N_(A)`
`3.24xx10^(24) = (m)/(235) xx 6.023 xx 10^(23)`
`m = 126.4 xx 10 = 1264g//day`
`=1.264kg//day`
(c) Total `U^(235)` used in `30` days `= 1.264 xx 30kg`
Uranium enriched `3%`
Uranium needed `= 1.264 xx 30 xx (100)/(3)`
`= 1264kg`