Final answer:
The question as posed would lead to a calculation showing that the uranium fuel has overproduced energy based on the fractions of isotopes found in natural uranium. Only a fraction of uranium undergoes nuclear fission, therefore we can't accurately compute the remaining uranium without exact isotopic proportions.
Step-by-step explanation:
To calculate the amount of uranium left after operating a nuclear power plant for 25 years, we need to first find the total energy produced. The power plant produces 5GW (5x10^9 J/s) of power and runs for 25 years. To convert this to a total energy reading we can use the following approach:
1 year has approximately 31,536,000 seconds, so 25 years would be about 788,400,000 seconds. Therefore, the total energy produced in 25 years is 5x10^9 J/s * 788,400,000 s = 3.942x10^18 J.
Uranium 235 has an energy density of about 80 TJ/kg (terajoules per kilogram), or 80x10^12 J/kg. So, the energy produced from 1kg of Uranium will be 80x10^12 J. Hence, the mass of Uranium consumed in 25 years can be calculated as:
3.942x10^18 J / 80x10^12 J/kg = ~49,275 kg
However, this is much greater than the initial mass of uranium fueled to the power plant, which indicates an error. The energy output exceeds what is expected from the given input because the question overlooks the fact that only a small fraction of uranium, specifically U-235 isotope, undergoes nuclear fission which is responsible for energy production. Therefore, it would be better to ignore this kind of oversimplification for real nuclear power plant situations.
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