An electric power plant that would make use of the temperature gradient in the ocean has been proposed. The system is to operate between 20.0°C (surface water temperature) and 5.00°C (water temperature at a depth of about 1 km).
The first question asks What is the maximum efficiency of such a system? which I found to be 5.1168%.
The second part asks If the electric power output of the plant is 65.0 MW, how much energy is taken in from the warm reservoir per hour? And they want the answer in TJ/hr.
My work:
I did 5.1168 * 65MW * 3600sec/hr * 10^12 (mw to TJ conversion) = 1.1973312 x 10^18 but that didn't give me the correct answer. Plus, I'm not sure if the online hw want's me to round or not.
To calculate the energy taken in from the warm reservoir per hour, you need to use the formula:
Energy = Efficiency * Power
Where:
Efficiency is the maximum efficiency of the system (5.1168% or 0.051168).
Power is the electric power output of the plant (65.0 MW).
To convert the power from MW to joules per hour (TJ/hr), you need to consider the following conversions:
1 MW = 1,000,000 J/s
1 hour = 3600 seconds
1 TJ = 10^12 J
Therefore, the correct calculation would be as follows:
Energy = 0.051168 * 65.0 MW * (3600 seconds/hour) * (10^12 J/TJ)
Energy ≈ 1.191168 TJ/hr
So, the amount of energy taken in from the warm reservoir per hour is approximately 1.191168 TJ/hr.