AskPablo: OTEC and Engine Efficiency

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.
Please note that I have a new URL, If you are currently linking to AskPablo on, please change it. My column will continue to be a part of, but we want to get past on Google (it’s a horse betting site, don’t ask why).
Pablo Päster, MBA
Sustainability Engineer

17 responses

  1. Nick, The truth is that it does not apply directly to transportation engines since we are talking about electricity generations here. But similar methods can be used to determine the maximum engine efficiency of a vehicle. Our vehicle engines are around 30% efficient. Based on the theoretical maximum efficiency we can’t go much higher. The majority of vehicle efficiency improvements are not through engine efficiency improvements. What we can do is to prevent the combustion of fuel when it is not needed (when stopped, going down hill), prevent the loss of energy (aerodynamics, tires, transmission, braking), and teach people to drive more efficiently (by not driving and taking public transit). I think I should save all this fun for another time though…

  2. Sorry got cut off… what I meant to ask it – what exactly are you measureing here? In the coal plant example are you telling me the amount of the coal’s potential energy that is getting wasted as heat? How so? The coal has potential energy, it gets burned, it heats water, the water gets really really hot and blasts through a turbine which turns producing electricity. Then the steam get’s shot out a smokestack of some kind. So… what are you measureing at the other ened? The coolant water that gets used to chill the spinning turbine? What if you put the coal plant in the arctic with an endless supply of 32 degree water – does this make the burning of coal more efficient in the arctic? How?

  3. Ah, I see… What we are measuring is the efficiency of turning coal (or any other fuel), which has a certain chemical potential energy, into work (turning a turbine), which generates electricity. So, when a power plant is 35% efficient, 65% of the energy in the fuel become waste (heat, noise, light) and is of no use to us.
    A power plant in the arctic would be more efficient (you can try this out yourself with the Carnot equation) but the efficiency gained would be lost in transmission to a population center.

  4. Anything that does not contribute to the intended output is waste/inefficiency. You can have heat from combustion, heat from friction, heat from radiation but you can also have sound from friction, sound from a rapid release of energy (explosion, collision), etc. According to the 1st law of thermodynamics nothing can be created or destroyed. Fuel becomes heat, light, sound, and carbon emissions. Nothing is lost, even though we cannot harness certain “non-product outputs.”

  5. Thomas, Thank you for bringing this up. Finding uses for what would otherwise be waste is a key part of sustainability. Cogeneration, the generation of electricity and hot water (for heating or domestic use), is a very smart way to maximize the efficiency of fuel use.
    It seems that you are an authority on OTEC plants. Would you like to share any news or technology updates with us? I am sure that my column left out a few things. Thanks!

  6. So, when a power plant is 35% efficient, 65% of the energy in the fuel become waste (heat, noise, light) and is of no use to us.

    The 65% you mention is of no use from a electrical generation point of view, but can of course be used to heat housing or other facilities, or can be used for other purposes.
    To see how that works see:

    In Scandinavia, modern Combined Heat and Power plants can reach as high as 90-95% in their energy use during the winter time. Nearly nothing goes to waste. In hotter climates one can use the waste heat for other purposes, for example to improve the efficiency of a seawater desalination plant.

    Best regards

    Thomas, Editor at OTEC News,

  7. Thank you Pablo for bringing up the “efficiency” question. I once worked for a VP of Engineering that insisted solar was far less efficient than Diesel…he designed machines, and didn’t pay for fuel.
    The NELHA example provides a similar situation in connection with OTEC efficiency.
    NELHA was and is a subscale pilot plant which established that the minimum practical size of an OTEC plant for power production would be 30 MegaWatts. It is interesting that the US Navy, today, is building an OTEC plant at Diego Garcia. The proposed OTEC facility will be designed to provide 7 MW of electrical power and 1.25 million gallons of potable water per day for the island. No threat to the petro-establishment by the Navy!
    On the other hand, NOAA never looked at anything but electrical energy production efficiency. The plant is the second largest exporter in Hawaii, now. Exporting what? Bottled “Deep Ocean” water!
    Exploiting the varied outputs of an OTEC plant might be very profitable in combination. Distilled water, Oxygen, Nitrogen, Hydrogen, or Ammonia, Methanol. Using cogeneration equipment presently available. At the very least, it could solve potable water problems in small island nations as no other technology can.
    Please see for a few examples.

  8. Hello, a question about “arctic OTEC”: I saw somewhere the idea to utilize the temperature gradient between arctic under-ice seawhater (+1c) and the air above the ice (-40c). Would that be at all feasible for an OTEC-plant? olle

    1. yes, if you have a working fluid that boils and condenses within those artic temperatures. Also , need to be considere; thermodynamic properties (heat contents), safety, flamablity etc type issues. how practical also (dont operate at vacuum)

      1. Actually, research is being done on this at Runde Centre in Norway. I don’t know how far tey have come yet though. Also, I guess that there might be environmental issues concerning pumping lots of water where the ice is currently melting, but that’s just my thinking…

        Petter Dessne, OTEC Africa (

  9. OTEC is the best form of alternative energy. It doesn’t link to any congressional disadvantages. Any negative disadvantage would be outweighed by the OTEC plant built at Diego Garcia. This plan would be perfect to ensure the United State’s energy security. OTEC is critical to reduce dependence on foreign oil. We must develop OTEC before the year 2010 in order to avoid the implications of loss of energy dependence, continued reliance on foreign oil, and bickering politics over alternative energies. This plan trades off for the need for environmentally destructive forms of alternative energies such as nuclear power.

  10. I’ve been wondering the same for quite some time, olle holm. I live near the artic (James Bay, actually) and I don’t see it being commercially viable but it’s a nice dream. One technical problem I see is that the pipe you send under the ice to carry the antifreeze fluid would quickly develop a thick crust of ice all around it because the coolant would be well below 0*C. That’s if the ice tension and movement forces don’t rip away the pipe in the first place. If someone could overcome all these problems, though, in some remote communities where electricity costs like $0.80/kW*h, there might be potential for part of the year, but it would be too seasonal in most parts… maybe it could be something for the scientists living in Antartica. I guess you could overcome the problem of pipe destruction from ice by passing the pipes through the ground where diving below sea-level, assuming the ground doesn’t shift too much. For the problem of ice build-up on the pipes, you could reduce or avoid that by having crazy long pipes that follow the ocean floor very far or something. Not enough consummers at the poles to attract serious attention from the business community, but it could be a niche industry for a wizard of the North of South.
    Anyways, I saw a cool show on Discovery channel last night about a pump to lift deep ocean water with a buoy oscillating on the waves and a valve at the bottom of the long tube. That reminded me of OTEC and of how the Japanese had difficulty producing net energy because of what it took to lift the deep water with a pump. Because the scientists on the show were hoping to create an artificial ocean bloom to capture carbon dioxide and fight global warming, it was obvious that one revenue stream could be the sell of carbon credit. Along with that and electricty from an OTEC system that works, because on the show the bloom attracted a bunch of small fish and even a whale-shark, another revenue stream could be fisheries, some time of deep-sea fish farm of sorts, an asset in a world running out of fish. Then of course if the process allowed it you could generate and sell clean water to nearby islands and even trace amounts of precious minerals. Sounds like a challenge for me… if only I lived near the tropics.

    1. Guillaume,

      You are perfectly right – OTEC holds a lot of “extras”, including trapping C02 and retrieving ammoniak and hydrogen (for use in cars).

      At OTEC Africa we concentrate on fresh water. A 10 MW plant would cost less than USD 100 million to place outside Tanzania or Kenya and would produce electricity for about 100,000 people and generate 35,000 cubic metres of fresh water on a daily basis!

      But as you said, these “extras” could be highly valuable to countries near the equator, which is really good.

      /Petter Dessne, OTEC Africa

  11. Sadi Carnot  described an engine in his book “reflect on the motive power of fire.” The disadvantage of its construction is the fact that it offers a moving heat source while Robert Stirling built an engine in which heat sources are fixed  and gas moves between the two sources to the aid of a mover. (Except for the engine Alpha). Both engines have in common four cycles of transformations:  isothermal and adiabatic (Carnot) and isothermal and isochoric ( Stirling).
    The Carnot engine was reported as impossible to builtvery early “This cycle is theoretically impossible, since the perfect adiabatic and  perfect isothermal  are impossible to obtain.” Steam engine and various heat engines J. Dejust (1899) “). Who speaks perfect engine? The Stirling engine and Ericsson engine are they perfect?​​. The best imperfect of hot air engines is the Carnot engine because it does not require a regenerator, the main imperfection Stirling engine (dead volume vs. efficiency). There are many architectures to held the Carnot cycle. here’s one here: Make this architecture and you have the hot-air engine the least imperfect.
    I was told it would be less powerful than a Stirling equal size. Not true! Heat transfer occurring in isothermal processes that are the same on both engines (with and T.cold identical and identical mass of the same gas). The best of both is the one with the least amount of dead volumes; Carnot!. It was not done because no one had seriously thought.

    The discussion is now open.

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