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 (surfacewater 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…

A typical temperature for surface water in a tropical ocean is 27°C. Whereas at a depth of a kilometer or more it is only about 27°C whereas at a depth of a kilometer or more it is only about 5°C. It has been proposed to operate heat engines using surface water as the hot reservoir and deep water as the cold reservoir. What would the maximum efficiency of such an engine be? Why might such engine eventually be practical proposition even with so low an efficiency?

As we drill down the rocks of earths crust, the temperature typically increases by 3°C for every 100 m of depth. Oil wells can be drilled to depth of 1830 m. If water is pumped into the shaft of the well it will be heated by the hot rock at the bottom and the resulting steam can be used as a heat engine. Assume that the surface temperature is 20°C   A) using such a 1830 m well as a heat engine, what is the maximum efficiency possible?   B) if a combination of such wells is to produce a 2.5×10^6 W power plant, how much energy will it absorb from the interior of earth each day?