A town has a population of 1 million. The average electric power needed per person is 300 W . A reactor is designed to supply power to this town, with an aimed efficiency of 25 % for converting thermal power into electric power. Assuming an average of 200 MeV of thermal energy is released from each fission event, and that uranium enriched to 3 % in ²³⁵ U will be used, how much uranium is needed per month ( 30 days)?

Step-by-step solution

Total electric power required for the town is: P_e = 10^6 300 W = 3 10^8 W Given the efficiency of 25 % , the total thermal power required is: P_ th = P_e = 3 10^8 0.25 = 1.2 10^9 W Total thermal energy required in 30 days is: E = P_ th t = 1.2 10^9 (30 24 3600) = 3.1104 10¹⁵ J Energy released per fission of ²³⁵ U is: E_f = 200 MeV = 200 10^6 1.6 10⁻¹⁹ J = 3.2 10⁻¹¹ J Number of fissions required per month is: N = E E_f = 3.1104 10¹⁵ 3.2 10⁻¹¹ = 9.72 10²⁵ Mass of ²³⁵ U required is: m₂₃₅ = N N_A 235 g = 9.72 10²⁵ 6.0