A typical nuclear reactor generates 1000 MW (1000 MJ/s) of electric energy. In doing so, it produces 2000 MW of 'waste heat' that must be removed from the reactor to keep it from melting down. Many reactors are sited next to large bodies of water so that they can use the water for cooling. Consider a reactor where the intake water is at 18°C. State regulations limit the temperature of the output water to 30°C so as not to harm aquatic organisms. How many liters of cooling water have to be pumped through the reactor each minute?
Verified step by step guidance
1
Calculate the total amount of heat that needs to be removed per second. This is given as 2000 MW, which is equivalent to 2000 MJ/s.
Determine the specific heat capacity of water, which is approximately 4.186 J/g°C. This value is crucial as it indicates how much energy is required to raise the temperature of water by one degree Celsius per gram.
Calculate the temperature difference between the intake and output water, which is 30°C - 18°C = 12°C. This will help in determining the amount of energy absorbed by each gram of water.
Use the formula for heat transfer, Q = mcΔT, where Q is the heat energy transferred, m is the mass of water in grams, c is the specific heat capacity, and ΔT is the change in temperature. Rearrange the formula to solve for m (mass of water required per second).
Convert the mass of water from grams to liters (since 1 gram of water is approximately equal to 1 mL, and 1000 mL is equal to 1 liter) and then convert the flow rate from per second to per minute by multiplying by 60.