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Answer :
Approximately 54.8 kg of U-235 is needed for the 25-year lifetime of a 500MW plant.
Given:
- Conversion of 1 kg of U-235 = 10^11 BTUs
- Efficiency of conversion of nuclear energy to heat = 90%
- Efficiency of the plant itself = 30%
- Lifetime of the plant = 25 years
- Power output of the plant = 500 MW
First, we need to calculate the total energy output of the plant over its lifetime:
Total energy output = Power output * Lifetime
Total energy output = 500 MW * 25 years * (365 days/year) * (24 hours/day) * (3600 seconds/hour)
Next, we need to take into account the efficiency of the plant and the conversion of U-235 to calculate the required amount of U-235:
Energy output = Conversion efficiency * Plant efficiency * Mass of U-235 * Conversion factor
Mass of U-235 = Energy output / (Conversion efficiency * Plant efficiency * Conversion factor)
The conversion factor is the energy conversion factor between BTUs and the energy unit used in the calculation (MW * years * days * hours * seconds).
Plugging in the given values:
Mass of U-235 = (Total energy output) / (0.9 * 0.3 * (10^11 BTUs/kg))
Converting the units to kilograms:
Mass of U-235 = (Total energy output * 1 BTU) / (0.9 * 0.3 * (10^11 BTUs/kg) * (1.05506 x 10^9 J/BTU) * (1 kg / 1000 g))
Finally, we can substitute the values and calculate the mass of U-235 needed:
Mass of U-235 = (500 MW * 25 years * 365 * 24 * 3600 * 1 BTU) / (0.9 * 0.3 * (10^11 BTUs/kg) * (1.05506 x 10^9 J/BTU) * (1 kg / 1000 g))
Approximately 54.8 kg of U-235 is needed for the 25-year lifetime of a 500MW plant, considering the given efficiency values and energy conversion factors.
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