Chapter 21, Problem 13P

You are working on a summer job at a company that designs non-traditional energy systems. The company is working on a proposed electric power plant that would make use of the temperature gradient in the ocean. The system includes a heat engine that would operate between 20.0°C (surface-water temperature) and 5.00°C (water temperature at a depth of about 1 km). (a) Your supervisor asks you to determine the maximum efficiency of such a system. (b) In addition, if the electric power output of the plant is 75.0 MW and it operates at the maximum theoretically possible efficiency, you must determine the rate at which energy is taken in from the warm reservoir. (c) From this information, if an electric bill for a typical home shows a use of 950 kWh per month, your supervisor wants to know how many homes can be provided with power from this energy system operating at its maximum efficiency. (d) As energy is drawn from the warm surface water to operate the engine, it is replaced by energy absorbed from sunlight on the surface. If the average intensity absorbed from sunlight is 650 W/m² for 12 daylight hours on a clear day, you need to find the area of the ocean surface that is necessary for sunlight to replace the energy absorbed into the engine. (e) From this information, you need to determine if there is enough ocean surface on the Earth to use such engines to supply the electrical needs for all the homes associated with the Earth’s population. Assume the energy use for a home in part (c) is an average over the entire planet. (f) In view of your results in this problem, your supervisor has asked for your conclusion as to whether such a system is worthwhile to pursue. Note that the “fuel” (sunlight) is free.