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The mass of the fuel in a fission reactor decreases at a rate of 6.0 × 10⁻⁶ kg hour⁻ - AQA - A-Level Physics - Question 31 - 2020 - Paper 2
Question 31
The mass of the fuel in a fission reactor decreases at a rate of 6.0 × 10⁻⁶ kg hour⁻. What is the maximum possible power output of the reactor?
Worked Solution & Example Answer:The mass of the fuel in a fission reactor decreases at a rate of 6.0 × 10⁻⁶ kg hour⁻ - AQA - A-Level Physics - Question 31 - 2020 - Paper 2
Step 1
Calculate the energy released per unit mass
Answer
In fission reactions, approximately 200 MeV of energy is released per fission event. To calculate the energy released from the decrease in mass, we need to convert this energy to Joules using the conversion: 1 eV = 1.6 × 10⁻¹⁹ J. Thus,
Energy = 200 ext{ MeV} imes 1.6 imes 10^{-13} ext{ J/MeV} = 3.2 imes 10^{-11} ext{ J/kg}.
Step 2
Calculate the total power output
Answer
Given that the mass decreases at a rate of 6.0 × 10⁻⁶ kg/hour, we can convert this to kg/s to find the power output:
[ \text{Mass flow rate} = \frac{6.0 \times 10^{-6} \text{ kg}}{3600 \text{ s}} \approx 1.67 \times 10^{-9} \text{ kg/s} ] The power output (P) can be calculated using the formula: [ P = \text{mass flow rate} \times \text{energy released per unit mass} ] Substituting the values: [ P = (1.67 \times 10^{-9} \text{ kg/s}) \times (3.2 \times 10^{13} \text{ J/kg}) \approx 5.34 \text{ MW}. ] Thus, the power output is approximately 5.34 MW. However, the options provided indicate the highest possible output must be considered. Thus, we can reasonably deduce that the maximum is likely closest to the available choice D, which is 9000 MW.