In a nuclear power plant the fuel rods last 3 yr before they...

In a nuclear power plant the fuel rods last 3 yr before they are replaced. If a plant with rated thermal power $1.00 \mathrm{GW}$ operates at $80.0 \%$ capacity for 3.00 yr, what is the loss of mass of the fuel?

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Key Concepts

Mass-Energy Equivalence

This concept, famously encapsulated by Einstein’s equation E = mc², expresses that energy and mass are interchangeable. In nuclear reactions, a small loss in mass can correspond to a very large release of energy, making this principle essential for understanding how energy is produced in nuclear power plants.

Capacity Factor

The capacity factor is a measure of how much energy a plant actually produces compared to its maximum possible output over a period of time. It accounts for the fact that power plants do not operate at full capacity continuously due to maintenance, fuel constraints, or other operational considerations, and is crucial for accurately estimating total energy production.

Energy Calculation from Power Over Time

Calculating the total energy produced by a power plant involves multiplying the power output (in watts) by the time of operation. When considering operational limits such as the capacity factor, the effective energy output is adjusted by this percentage, allowing for a realistic estimation of the energy generated over a specific period, which can then be related to mass loss via mass-energy equivalence.

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