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 ``^235U`, at what rate will the amount of ``^235U` decrease ? Express uour answer in kg per day. (c) Assuming that uranium is needed per month (30 days)?

Answer

A, B, C, D

Explanation

(a) Total power used by town in one day
`= 300 xx (10^6) xx 60 xx 60 xx 24 Joule`
Energy generated in one fission
`= 200 xx 10^(6) xx 1.6 xx 10^(-19)`
`= 3.2 xx (10^(-11))` Joule
Electrical power,
`= 3.2 xx 10^(-11) xx 25/100`
` = 8 xx 10^(-12)` Joule
Let no of fission be N
So, `N xx 8 xx 10^(-12)`
` = 300 xx 86400 xx 10^6`
`N = 3.24 xx 10^(24)`
(b) Number of moles required per day
`= (3.24 xx 10^(24))/(6.023 xx 10^(23)) = 5.38 mole`
So number of moles not required per day
`= 5.38 xx 235`
`= 1264.3 gm = 1.2643 kg.
(c) Total uranium needed per month
` = 1.264 xx 30 Kg`
Let xgm of uranium enriched `803%` is used.
`So, x xx 3/100 = 1.264 xx 30`
`x = 1264 kg. `