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I Why does heat engine need to do negative work to surround?

  1. Apr 10, 2016 #1
    Every thermodynamics cycle needs to do negative work to the environment, which lower its total positive work. For example, in Carnot cycle, the most efficiency possible:

    1/ Engine receives heat from hot reservoir, expands and do positive work to surround
    2/ Surround does work to engine, compresses it and heat is rejected to cold reservoir.

    The usable work is positive work from process 1 minuses negative work in process 2, and thus limit the efficiency to n = (Th - Tc) / Th, where Th and Tc are absolute temperatures of hot and cold reservoirs.

    All thermodynamics cycles do this kind of negative work. So why don't we increase efficiency by ignoring process 2, i.e. don't do negative work by compressing gas every cycle?

    For example, let see this example, we burn oil to heat air.
    Air is heated and pressure is raised.
    Let this heated air runs through a turbine vertically, so the inlet of turbine is hot air with high pressure, and the outlet of turbine is cool ambient air with low pressure
    While hot air expands through the turbine, energy is extracted from hot air, temperature and pressure are dropped.
    Cool air is fed naturally below in the inlet of the turbine and is heated to high pressure. The cycle is completed and reapeated.

    If we assume ideal conditions, e.g. no friction... then all received heat will be converted to work. There isn't any negative work wasted to the environment, i.e. no air is recompressed like in the classical thermodynamics cycles.

    So why doesn't every thermodynamics cycle choose this approach but instead they all need to do negative work on the environment?

    What is wrong with my approach?
  2. jcsd
  3. Apr 10, 2016 #2


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    Really? You're doing all this at absolute zero temperature?
  4. Apr 10, 2016 #3


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    Those are really four processes, not two.
    The energy input from the compression isn't lost since it goes through the turbine after the compression (and after combustion or heating).

    The heat rejection has to exist because in order to make heat flow through a turbine, it has to have somewhere to go. Heat can only flow from an area of high temperature to one of low temperature (likewise for pressure).

    Consider what would happen if you tried to recover all of the energy from a hydroelectric dam. That would require stopping the water completely at the turbine, where it would pile-up. You can't do that: you have to get the water to flow away.

    There are other issues, such as with an internal combustion engine, if you didn't do the compression, you'd only be able to put in 1/10th the fuel and air, making engines 10x larger for the same input.

    For your example:
    A few problems:
    1. "heated to high pressure" doesn't make any sense. Heating increases temperature. There can be an increase in pressure as a byproduct of that, but your cycle is open, so the gas isn't constrained, so its pressure doesn't increase. Indeed, you've made this tube vertical, so you probably recognize at least part of this: gravity is providing the compression and the only thing forcing the heated air through the turbine is its own buoyancy.
    2. The outlet of the turbine can't be cool ambient air at lower pressure than it was in the turbine. There has to be a pressure and temperature difference to force the air to move through the turbine. In real life, you can make the pressure lower and the air cooler by running it through progressively larger and larger turbines, but there is of course a limit to the extra energy recovered that way.

    So your cycle does have a compressor (gravity) and does have heat rejection. You've tried to minimize them, which is fine -- you just also make your cycle not produce much work.

    This sort of device exists, by the way, it just still is a heat engine and it costs a lot of money to produce a little bit of energy because it has to be big: https://en.wikipedia.org/wiki/Solar_updraft_tower
  5. Apr 10, 2016 #4
    At least in the expansion part of Carnot cycle, all heat is transferred to work WITHOUT absolute zero, isn't it?
    It is the compression part of the cycle that does the negative work, if we don't do this part, e.g. stop the engine after its expansion, then all heat is converted to work.
    Of course, since we don't compress gas, the power is very low, but the efficiency is 100%.

    We can reject that expansion gas, and take new gas from atmosphere and repeat that step without any compression. So the cycle is:

    Take air into the cylinder, heat air in a cylinder, let it expands, reject air to exhaust and take new ambient air into the cylinder.
  6. Apr 10, 2016 #5


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  7. Apr 10, 2016 #6
    That is not a thermodynamic cycle. In a thermodynamic cycle, the initial state of the system undergoing the cycle is identical to the final state of the system. This is why it is called a cycle...
  8. Apr 10, 2016 #7
    Yes, all, even more than all, isn't it?
    Carnot cycle expansion includes isothermal and isentropic expansion.

    The heat is received in isothermal process, which is a constant temperature process, so the internal energy of gas does not change. Because the internal energy does not change, all the heat is converted to work in this isothermal reversible process. If we stop after this, we get 100% efficiency
    In the isentropic expansion, the internal energy of gas is convert to work, so, even more than 100% heat is converted to work.

    Now if we stop here, we get more than 100% efficiency. Only the compression that do the negative work.
  9. Apr 10, 2016 #8
    Thank you for your brilliant answer.

    Yes, that why, because it needs to comeback to the initial state.

    Maybe I should rephrase a better question: why do all heat engines need to work in cycles, why don't just work in a receiving heat process only, so we get 100 percent efficiency?

    For example, we have a gallon of gasoline in a car, and receive heat in the isothermal process, so all heat is converted to work. Of course that is not practical because it will require a very large volume to convert that heat to work in one push, but at least we have a very high efficient heat engine.

    But I think a more practical approach would be an engine that does not need to get back to it initial state. We burn fuel, get heat, let air expand, convert to work and reject that air. We have an infinite amount of new air, so why do we need to do negative work to get back to the initial state while we can get initial state for free by getting new ambient air?

    Thank you for your genious
  10. Apr 10, 2016 #9
    I know it, I just want to emphasis on the difference between positive and negative work parts.

    OK, so the turbine example did not deliver the message. Let say we have a Carnot engine:
    1/ Receive heat
    2/ Expand
    Now, if we stop here, we will get 100 percent efficiency. So why don't we stop here? Why do we need to do negative work to recompress the gas? We can get new air from ambient atmosphere for free.

    Of course an engine like that (without compressing air to high pressure) will have very low power per volume, but very high efficiency even in a small temperature difference.

    A good comparison, but that is the point of cold reservoir. Let see that Carnot example above, we can get 100% efficiency all the way because the infinite cold reservoir will stop pile-up heat in air.

    Thank you for looking at that example
    1/ Well, hot air increase pressure, because pressure increased, so it expands. Because it expands, its density decreases. So the buoyancy is exactly the pressure of the gas, because the hot air needs to push against the pressure of surround air
    2/ The outlet can be cool as ambient air if the turbine is large enough, but that will not be practical. So let see the Carnot example, I hope this time the message is better delivered.

    I know that compression and heat rejection is needed because the engine needs to comeback to its initial state. That is not the point of the question. The point of the question is that, why do we need to compress and reject heat to get to the initial state while we can get the initial state for free at limitless volume from ambient air?

    Thanks for this
  11. Apr 10, 2016 #10


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    We do have engines like this. We call them jet engines (or gas turbine engines if they aren't powering jet planes). The corresponding thermodynamic process is called an open Brayton cycle. I suggest looking at the thermodynamics of such a cycle to check your claim that it can deliver 100% efficiency. (Hint: it can't.)
  12. Apr 10, 2016 #11
    There are a couple confusions here, I think.

    A real engine does necessarily work on a true thermodynamic cycle. We often model real engines as thermodynamic cycles in order to compare different engines, also modeled as cycles, and ultimately with the most efficient cycle possible (Carnot). But we can also analyze an engine as an open system where, say, air and fuel come in and exhaust products leave during the production of work. But even on this analysis, efficiency is not 100%.

    For example, say I have two engines which both take in X kg of air and Y kg of fuel and both exhaust combustion products to the atmosphere while producing work. One engine is measured to produce 50 kW and the other produces 45 kW. Yet you say they are both 100%? They cannot both be 100% efficient, because if they were then both would have to produce the same power for the same input.

    In a case like this, we could calculate an efficiency based on the total available energy found in bonds of the air and fuel, alongside the thermodynamic state of the mixture, and the total amount of work delivered as a fraction of the available input energy. (An Exergy analysis does something like this.) This understanding of efficiency would allow us to compare different engine designs based on the final state of the combustion products and the amount of work per unit fuel/air consumed.
    Last edited: Apr 10, 2016
  13. Apr 11, 2016 #12


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    You can't make the other parts of the cycle go away by ignoring them: you do not get the new air from the atmosphere for free. You're hiding them from yourself with your updraft tower example, but they are still there.

    The warm air in your device doesn't leave on its own and new air doesn't replace it on its own. So you tell me: How does new air get into the bottom of this device? How does the warm air get out? It would be helpful if you wrote out the steps in your cycle and really think about what makes them happen.

    Also, the efficiency of the first two steps would only be 100% if all of the heat energy were converted to work, and it isn't/can't be.
    Last edited: Apr 11, 2016
  14. Apr 11, 2016 #13


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    Also, you aren't being very specific about how you think you could stop the cycle in the middle, but generally, all of the steps are happening simultaneously and each affects the others. A pulse jet stops between steps, but it should be obvious that:
    1. After combustion and expansion, the combustion chamber is still full of hot gas; you haven't extracted all of the energy.
    2. Unless you want to toss it in the trash after one little pop, you have to open up the inlet and let more air in; that completes the cycle.
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