Question 4: Consider a thermal reactor that is loaded with 100 metric tons of uranium dioxide UO_(2) fuel. The fuel is enriched to 3w/o of {}^235U The reactor operates at a power level of 2 GW for 720 days before it is shut down for refueling. Calculate the specific burnup and fractional burnup of the fuel at shutdown. (6 Marks)

To calculate the specific burnup and fractional burnup of the fuel at shutdown, we need to follow these steps:<br /><br />1. Calculate the total energy generated by the reactor during its operation.<br />2. Calculate the mass of uranium consumed during the reactor's operation.<br />3. Calculate the specific burnup.<br />4. Calculate the fractional burnup.<br /><br />Let's start with step 1:<br /><br />1. Calculate the total energy generated by the reactor during its operation:<br /><br />The power level of the reactor is given as 2 GW, which means it generates 2 gigawatts (GW) of power. The reactor operates for 720 days before it is shut down for refueling.<br /><br />To calculate the total energy generated, we need to convert the power level to energy using the formula:<br /><br />Energy = Power × Time<br /><br />First, we need to convert the time from days to hours:<br /><br />720 days × 24 hours/day = 17,280 hours<br /><br />Now, we can calculate the total energy generated:<br /><br />Energy = 2 GW × 17,280 hours = 34,560 GW-hours<br /><br />Since 1 GW-hour is equal to 3.6 × 10^9 joules, we can convert the energy to joules:<br /><br />Energy = 34,560 GW-hours × 3.6 × 10^9 joules/GW-hour = 1.2424 × 10^14 joules<br /><br />2. Calculate the mass of uranium consumed during the reactor's operation:<br /><br />The fuel is enriched to 3% of 235U, which means that 3% of the uranium dioxide fuel is 235U.<br /><br />Mass of 235U = 0.03 × 100 metric tons = 3 metric tons<br /><br />3. Calculate the specific burnup:<br /><br />Specific burnup is defined as the total energy generated divided by the mass of uranium consumed.<br /><br />Specific burnup = Energy / Mass of 235U<br /><br />Specific burnup = 1.2424 × 10^14 joules / 3 metric tons = 4.1413 × 10^11 joules/metric ton<br /><br />4. Calculate the fractional burnup:<br /><br />Fractional burnup is defined as the specific burnup divided by the energy released per fission of 235U.<br /><br />The energy released per fission of 235U is approximately 200 MeV, which is equal to 3.2 × 10^-12 joules.<br /><br />Fractional burnup = Specific burnup / Energy released per fission of 235U<br /><br />Fractional burnup = 4.1413 × 10^11 joules/metric ton / 3.2 × 10^-12 joules/fission = 1.29 × 10^23 fissions/metric ton<br /><br />Therefore, the specific burnup of the fuel at shutdown is 4.1413 × 10^11 joules/metric ton, and the fractional burnup is 1.29 × 10^23 fissions/metric ton.