A model fission plant delivers 1.000 × 10^8 W of electrical power at efficiency 32%. Each fission has total initial rest mass exceeding total final rest mass by 0.188 u, including all reaction products in the accounting. Use 1 u c² = 931.5 MeV, 1 eV = 1.602 × 10⁻¹⁹ J and 1 u = 1.661 × 10⁻²⁷ kg. Assume every event consumes one uranium-235 nucleus of mass 235 u and all released energy enters the thermal system. Find energy per fission, fission rate and mass of uranium-235 actually fissioned in 24 hours. Explain why this is not the total fuel mass a real plant must load.

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Energy 175.1 MeV = 2.805 × 10^-11 J per fission; rate 1.114 × 10^19 s⁻¹; uranium-235 fissioned 0.3757 kg per day. The positive mass defect releases energy E_f = Δmc² = 0.188 × 931.5 = 175.1 MeV. Converting mega-electronvolts to joules gives 2.805 × 10^-11 J per event. Electrical efficiency is η = P_electric/P_thermal, so required thermal power is P_electric/η = 3.125 × 10^8 W. Efficiency must be expressed as a fraction, not its percentage number. The event rate is thermal power divided by energy per event: rate = 1.114 × 10^19 s⁻¹. Multiplying rate by ηE_f recovers the specified electrical power. Over 24 hours, multiply the rate by 86400 s and by the mass 235(1.661 × 10⁻²⁷) kg per nucleus. The consumed uranium-235 mass is 0.3757 kg. This counts nuclei actually fissioned under the idealized assumptions. Real fuel includes other isotopes, structural material and uranium that remains unfissioned; loading, burnup and neutron losses therefore prevent equating this result with total fuel inventory.

From mass defect to electrical output · set 4

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