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The efficiency of a nuclear power plant with a capacity of 800 MW is 20%. Determine the mass of nuclear fuel (Uranium-235) consumed by the power plant. Keep in mind that 200 MeV of energy is released each time the nucleus of Uranus splits.

Question

The efficiency of a nuclear power plant with a capacity of 800 MW is 20%. Determine the mass of nuclear fuel (Uranium-235) consumed by the power plant. Keep in mind that 200 MeV of energy is released each time the nucleus of Uranus splits.

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Solution

To solve this problem, we need to follow these steps:

  1. First, we need to convert the power plant's capacity from MW to Joules per second. 1 MW = 10^6 W, so 800 MW = 800 * 10^6 W = 8 * 10^8 W = 8 * 10^8 Joules/second.

  2. Next, we need to calculate the total energy produced by the power plant in one second. Since the efficiency of the power plant is 20%, the total energy produced is 8 * 10^8 Joules/second / 0.20 = 4 * 10^9 Joules/second.

  3. Now, we need to convert the energy released per fission of Uranium-235 from MeV to Joules. 1 MeV = 1.60218 * 10^-13 Joules, so 200 MeV = 200 * 1.60218 * 10^-13 Joules = 3.20436 * 10^-11 Joules.

  4. We can now calculate the number of fissions per second. This is the total energy produced divided by the energy per fission, which is 4 * 10^9 Joules/second / 3.20436 * 10^-11 Joules/fission = 1.248 * 10^20 fissions/second.

  5. The mass of one atom of Uranium-235 is given by its atomic mass (235 g/mol) divided by Avogadro's number (6.022 * 10^23 atoms/mol), which is 235 g/mol / 6.022 * 10^23 atoms/mol = 3.90 * 10^-25 g/atom.

  6. Finally, we can calculate the mass of Uranium-235 consumed per second. This is the number of fissions per second times the mass per atom, which is 1.248 * 10^20 fissions/second * 3.90 * 10^-25 g/atom = 4.87 g/second.

So, the nuclear power plant consumes approximately 4.87 grams of Uranium-235 per second.

This problem has been solved

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