Q.17 A nuclear power plant generates 1000 Megawatts (MW) of electrical power and used half of its fuel
supply in 5 years. The reactor uses 235 U with 33% efficiency for the conversion of heat released by
nuclear fission to electrical power. Each atom of 235 U releases 200 MeV of energy. How many tons
of 235 U did the reactor start with? (1 ton = 1000 kg; Avogadro number = 6.023 × 1023 mol –1 )
Step-by-Step Solution
1. Calculate thermal power first. Electrical output is 1000 MW (\(10^9\) W), so thermal power \(P_{th} = \frac{10^9}{0.33} \approx 3.03 \times 10^9\) W.
2. Determine total thermal energy over 5 years. Time \(t = 5 \times 3.156 \times 10^7\) s \(\approx 1.578 \times 10^8\) s, so energy \(E_{th} = P_{th} \times t \approx 4.78 \times 10^{17}\) J.
3. Convert fission energy to joules. Each ²³⁵U fission releases 200 MeV \(= 200 \times 10^6 \times 1.602 \times 10^{-13} \approx 3.204 \times 10^{-11}\) J.
4. Find fissions needed. Number of fissions \(N = \frac{E_{th}}{3.204 \times 10^{-11}} \approx 1.492 \times 10^{28}\).
5. Compute initial mass. Atoms fissioned equal \(N\); mass fissioned \(m_f = \frac{N \times 235}{6.023 \times 10^{23}} \approx 5.82\) g (0.00582 kg). Since half fuel used, initial mass \(m_0 = \frac{0.00582}{0.5} = 0.01164\) kg \(\approx 1.164 \times 10^{-5}\) tons (or 0.012 tons).
Key Physics Concepts
- Fission Energy Conversion: 200 MeV to joules uses \(1.602 \times 10^{-13}\) J/MeV.
- Thermal vs. Electrical: Divide output by efficiency (0.33).
- Mass Calculation: \(\frac{\text{fissions} \times 235}{N_A \times 0.5}\) for initial fuel.
Common Pitfalls Explained
Students often forget efficiency (underestimate thermal energy) or time conversion (365.25 days/year). Using exact \(3.204 \times 10^{-11}\) J/fission avoids rounding errors. Real plants use enriched fuel, but this assumes pure ²³⁵U fission.
CSIR NET Exam Tips
Practice similar problems: scale power, handle half-life-like usage (here operational), cite constants precisely. Answer: ~0.012 tons aligns with benchmarks (~1 ton/year for full burn).[web:11][web:12]
