A nuclear reactor using 235 U generates 250 MW of electrical power. The efficiency of the reactor (i.e. efficiency of conversion of thermal energy into electrical energy) is 25%. What is the amount of 235 U used in the reactor per year? The thermal energy released per fission of 235 U is 200 MeV.
Text Solution
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Sol. Rate of electrical energy generation is 250 MW = 250 × 10 6 W (or Js –1 ), therefore electrical energy generated in 1 year is
(250 × 10 6 Js –1 ) × (365 × 24 × 60 × 60 s) = 7.884 × 10 15 J.
Thermal energy from fission of one 235 U nucleus is 200 MeV = 200 × 1.6 × 10 –13 = 3.2 × 10 –11 J. Since the efficiency is 25%, the electrical energy obtained from the fission of one 235 U nucleus is
E 1 = 3.2 × 10 –11 × 
= 8.0 × 10 –12 J.
Therefore, the number of fissions of 235 U required in one year will be
N = 
= 9.855 × 10 26 Number of moles of
235 U required per year is
n = 
= 1.636 × 10 3 .
Therefore, mass of 235 U required per year is
m = 1.636 × 10 3 × 235 = 3.844 × 10 5 g = 384.4 kg.
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