Final answer:
The amount of exhaust heat discharged per hour by the nuclear power plant operating at 68% of its maximum theoretical efficiency can be calculated using the Carnot efficiency equation. The rate of electric energy production and the temperatures of the hot and cold reservoirs are used to find the Carnot efficiency, which is then used to calculate the rate of heat transfer to the environment. Finally, the rate of heat transfer is converted to the amount of exhaust heat discharged per hour.
Step-by-step explanation:
To find the amount of exhaust heat discharged per hour by a nuclear power plant, we need to use the given information about the plant's efficiency and the rate of electric energy production. The maximum theoretical efficiency of the plant is 68% according to the Carnot efficiency equation. We can use this efficiency along with the temperatures of the hot and cold reservoirs (680°C and 400°C, respectively) to calculate the Carnot efficiency. Once we have the Carnot efficiency, we can find the rate of heat transfer to the environment by subtracting the plant's efficiency from the Carnot efficiency. Finally, we can calculate the amount of exhaust heat discharged per hour by converting the rate of electric energy production (1.5 GW) to joules per hour and using the heat transfer rate.
The formula to calculate the Carnot efficiency is:
Carnot efficiency = 1 - (T_cold / T_hot)
Using the given temperatures:
Carnot efficiency = 1 - (400 / 680) = 0.41176
The rate of heat transfer to the environment is:
Heat transfer rate = (Carnot efficiency - plant efficiency) * rate of electric energy production
Heat transfer rate = (0.41176 - 0.68) * 1.5 * 10^9 J/h = -4.811*10^8 J/h (rounded to 2 significant figures)