year period of operation , the plant delivers 200,000 MWd of electric power to the utility grid. During this time the plant was down as follows: 30 days for refueling; 50 days for maintenance and repairs. Calculate the plant capacity and plant availability during the year. (5 Marks) Question 3: Briefly explain the following terms as used in a nuclear reactor: (i) specific burnup, and (ii) fractional burnup. (4 Marks) 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) Question 5: Briefly explain the control of nuclear chain reaction. Your explana- tion should include:

Question 1:<br />To calculate the plant capacity and plant availability during the year, we need to determine the total number of days the plant was operational and the number of days it was down for refueling and maintenance.<br /><br />Plant capacity refers to the maximum power output that the plant can deliver to the utility grid during its operational period. In this case, the plant delivers 200,000 Mild of electric power to the utility grid during the year.<br /><br />Plant availability is the percentage of time the plant is available to operate during the year. It can be calculated by dividing the number of operational days by the total number of days in the year and multiplying by 100.<br /><br />Given that the plant was down for 30 days for refueling and 50 days for maintenance, the total number of days the plant was down is 80 days. Since there are 365 days in a year, the number of operational days is 365 - 80 = 285 days.<br /><br />Therefore, the plant capacity is 200,000 Mild of electric power, and the plant availability is (285/365) * 100 ≈ 78.1%.<br /><br />Question 3:<br />(i) Specific burnup: Specific burnup refers to the amount of energy produced per unit mass of fuel consumed in a nuclear reactor. It is usually measured in megawatt-days per kilogram (MWd/kg) or megajoules per kilogram (MJ/kg). Specific burnup indicates the efficiency of the fuel in producing energy during the fission process.<br /><br />(ii) Fractional burnup: Fractional burnup is the ratio of the actual energy produced by the fuel to the theoretical maximum energy that could be produced if all the fuel atoms were fissioned. It is a measure of the effectiveness of the fuel in terms of energy production. Fractional burnup is usually expressed as a percentage and ranges from 0% to 100%.<br /><br />Question 4:<br />To calculate the specific burnup and fractional burnup of the fuel at shutdown, we need to determine the total energy produced by the reactor and the mass of the fuel consumed.<br /><br />Given that the reactor operates at a power level of 2 GW for 720 days, the total energy produced can be calculated as:<br /><br />Energy produced = Power level * Time<br />Energy produced = 2 GW * 720 days = 1,440 GW-days<br /><br />The mass of the fuel consumed can be calculated as:<br /><br />Mass of fuel consumed = (Enrichment percentage / 100) * Total mass of fuel<br />Mass of fuel consumed = (3/100) * 100 metric tons = 3 metric tons<br /><br />Therefore, the specific burnup can be calculated as:<br /><br />Specific burnup = Energy produced / Mass of fuel consumed<br />Specific burnup = 1,440 GW-days / 3 metric tons = 480 MWd/kg<br /><br />To calculate the fractional burnup, we need to know the theoretical maximum energy that could be produced if all the fuel atoms were fissioned. Assuming that the theoretical maximum energy is 3,200 MWd/kg, the fractional burnup can be calculated as:<br /><br />Fractional burnup = (Specific burnup / Theoretical maximum energy) * 100<br />Fractional burnup = (480 MWd/kg / 3,200 MWd/kg) * 100 ≈ 15%<br /><br />Question 5:<br />The control of a nuclear chain reaction is crucial to ensure the safe and efficient operation of a nuclear reactor. It involves regulating the rate of the fission process to prevent an uncontrollable chain reaction or a meltdown.<br /><br />One method of controlling the nuclear chain reaction is through the use of control rods. Control rods are made of materials that can absorb neutrons, such as boron or cadmium. By adjusting the position of the control rods within the reactor core, the number of neutrons available for further fission reactions can be controlled. When the control rods are inserted deeper into the reactor core, more neutrons are absorbed, slowing down the chain reaction. Conversely, when the control rods are withdrawn, fewer neutrons are absorbed, allowing the chain reaction to proceed more rapidly.<br /><br />Another method of controlling the nuclear chain reaction is through the adjustment of the fuel composition. By changing the enrichment level of the fuel, the number of fissile atoms available for fission can be altered. Increasing the enrichment level increases the number of fissile atoms, leading to a faster chain reaction. Decreasing the enrichment level reduces the number of fissile atoms, slowing down the chain reaction.<br /><br />In summary, the control of a nuclear chain reaction is achieved through the use of control rods and the adjustment of the fuel composition. These methods allow operators to regulate the rate of the fission process and maintain a stable and controlled nuclear reaction.