Physics HL · Chapter 24: Nuclear Fission
24.4 Reactor Power, Fuel Use, and Efficiency
Scale from per-fission energy to plant-level electrical output, then estimate fuel use over operational timescales.
Estimated time: 48 minutes
From MeV per Fission to MW at Plant Scale
A common exam move is to mix microscopic and macroscopic units. Keep a clear bridge: convert MeV per fission to joules per fission, determine total fission count required for the desired thermal energy, and then map thermal-to-electrical output using efficiency. Unit discipline is the main source of marks in these long calculation chains.
eta = rac{P_{ ext{electrical}}}{P_{ ext{thermal}}},qquad E_{ ext{fission}}( ext{J}) = Q( ext{MeV}) imes 1.602 imes10^{-13}
Use efficiency first to recover thermal power demand before converting to fission count.
Fuel Mass Consumed Over Time
Once fission count is known, divide by Avogadro's constant to get moles consumed, then multiply by molar mass to obtain kilograms. For gigawatt-class reactors, yearly fuel use is often on the order of 10^3 kg of fissile material. That number feels surprisingly small compared with fossil-fuel plants, and that contrast is one of the central quantitative arguments for fission energy density.
Power Output, Capacity Factor, and Real Operation
Real plants do not run at full nameplate output every hour of the year. Maintenance cycles, demand-following, and regulatory shutdown windows reduce delivered annual energy. In exam-style estimations this is often ignored unless a capacity factor is explicitly provided. In engineering contexts, capacity factor strongly affects fuel logistics and lifecycle emissions comparison.
Simulation: Fuel Burn and Output Scaling
Set electrical power, thermal efficiency, runtime, and per-fission energy to estimate fission count, fuel mass consumed, and equivalent fossil CO2 avoided.
Thermal power needed
2.29e+3 MW
Fission events
2.65e+27
Fuel mass used
1.03e+3 kg
Coal CO2 avoided
5.75e+6 t
Test Yourself
A plant delivers 800 MW electrical with 35% efficiency for one year. If each fission releases 170 MeV, estimate the U-235 mass used.
Hint: Find thermal power first, then total energy over one year, then fission count and moles.