This week I am looking into the theoretical maximum efficiency of a heat engine. Then I will focus on a technology that harnesses ocean water to generate electricity.
The ideal engine runs on the Carnot cycle. According to our friends at Wikipedia “it is the most efficient cycle possible for converting a given amount of thermal energy into work.” In a Carnot cycle there is a heat source (flame, sunlight) and a cooling source (water, cold air). The definition of Carnot efficiency is 1 – Temp.Cold /Temp.Hot, where temperature is in Kelvin.
Let’s look at an example: Let’s say that the University of Hawaii wants to take advantage of the temperature difference between water on the surface of the ocean and deep ocean water. To figure out the maximum efficiency that they could achieve they find the temperatures at the surface, 80F ( 299.6K), and the temperature at the ocean floor, 50F (283K), and plug them into the formula (1 – 283K/299.6K = 0.06, or 6%). 6% is pretty low, but is not bad (Solar PV is only around 15%). But, of course the Carnot cycle is the theoretical maximum, based on a reversible cycle, and the actual efficiency would be quite a bit lower. The formula for an unreversible cycle is very similar, just take the square root of the 283K/299.6K bit. This gives us a more realistic 2.8%. It is just our luck that someone has tried this sort of thing out in real life. And as is frequently the case, the actual efficiency is lower than the theoretical. The Ocean Thermal Energy Conversion (OTEC) plant Keahole Point in Hawaii is only about 1-3% efficient. Even at such poor efficiency one study estimates the cost to be around $0.07 per kWh. Ocean water is, after all, a free and renewable resource.
The same equations can be used for other power plants, such as a coal-fired power-plant. Assume that the cooling water from the river is at 25C (298K) and that the burning coal can make steam at 550C (823K). The Carnot theoretical maximum efficiency would be around 63.8%, the unreversible maximum efficiency would be 39.8%, while the actual efficiency of a coal-fired power plant is around 35%. Nuclear Power Plants are around 30% efficient.
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Pablo Päster, MBA