OTECs are unusual in that the heat that can be provided at the hot side of...

 

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OTECs are unusual in that the heat that can be provided at the "hot" side of the heat engine (temperature Tsurface) is practically unlimited because it is provided by ambient surface water. (In more conventional heat engines, the hot-side heat is valuable because it is created by burning fuel.) Instead, it is the cold deep-ocean water (temperature Tdeep) that is a limited resource because it needs to be pumped up to the surface. If we want to extract as much power as possible from the cold water pumped up to the surface, we need to use the cold water efficiently. 25C 5 C OTEC The efficiency you found in part (a) can only be achieved if the cold water is not allowed to heat up at all during the operation of the heat engine, which means that the mechanical power produced by OTEC should be very small. If you want to produce the most work from a given mass of cold water, you would want to use the cold water as a heat sink of a Carnot engine for as long as you can. Of course, the more you run it, the more heat is rejected to the initially cold water, raising its temperature. Eventually, the temperature of this initially cold water will rise all the way to a temperature of the warm water, at which point the efficiency of the Carnot engine will drop to zero. Derive a formula for the maximum amount of work that can be produced by one kg of cold water. Assume that the specific heat of water is Cp = C = 4.2 kJ/K/kg and independent of temperature. OTECs are unusual in that the heat that can be provided at the "hot" side of the heat engine (temperature Tsurface) is practically unlimited because it is provided by ambient surface water. (In more conventional heat engines, the hot-side heat is valuable because it is created by burning fuel.) Instead, it is the cold deep-ocean water (temperature Tdeep) that is a limited resource because it needs to be pumped up to the surface. If we want to extract as much power as possible from the cold water pumped up to the surface, we need to use the cold water efficiently. 25C 5 C OTEC The efficiency you found in part (a) can only be achieved if the cold water is not allowed to heat up at all during the operation of the heat engine, which means that the mechanical power produced by OTEC should be very small. If you want to produce the most work from a given mass of cold water, you would want to use the cold water as a heat sink of a Carnot engine for as long as you can. Of course, the more you run it, the more heat is rejected to the initially cold water, raising its temperature. Eventually, the temperature of this initially cold water will rise all the way to a temperature of the warm water, at which point the efficiency of the Carnot engine will drop to zero. Derive a formula for the maximum amount of work that can be produced by one kg of cold water. Assume that the specific heat of water is Cp = C = 4.2 kJ/K/kg and independent of temperature.