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Reverse osmosis perpetual motion machine

  1. May 12, 2009 #1

    The original problem was as follows:

    Closed-loop system, with complete isolation.
    Salt water is green, fresh water blue,
    porous plug (AB) is red.

    Fresh water spills into the salt water column
    at C if the fresh water is lifted
    higher than the salt water,
    maintaining continuous flow.

    Can this really happen?

    The theory that i worked out is that the pressure in the bottom of any of the columns is Pressure = density x constant of gravity x height

    The density of pure water is 1000 kg/m^3, while the density of salt water is 1025 kg/m^3. This means that the pressure at the bottom of a salt water column is 2.5% higher than the fresh water.

    The osmotic pressure needed to drive water from the salty side to the fresh side is 1450kPa, or around 14.5 bar.

    If both columns are around 6km high, the osmotic pressure at the bottom of:
    the salt water tank is 1025 * 9.8 * 6000 = 60.27 MPa, or 602.7 bar
    the fresh water tank is 1000 * 9.8 * 6000 = 58.8 MPa, or 588 bar

    The difference in pressure is 14.7 bar, enough to counter the 14.5bar requirement for reverse osmosis. The salt column's pressure now pumps fresh water into the fresh water column.

    If the freshwater feeds back into the saltwater column, after perhaps passing a waterwheel that generates power, this becomes a perpetual motion machine.

    some considerations noted: the saltwater will not become diluted by the fresh water pouring over at the top since the salt never leaves the column through the semi-permeable membrane

    I know it doesn't really work due to thermodynamics, but i can't figure out why in terms of fluid dynamics and statics. Please tell me why it doesn't work, i cant figure it out.
  2. jcsd
  3. May 12, 2009 #2
    This is surely the best perpetual motion machine I have ever seen. I have puzzled over it for a long time and sadly I must report that I have uncovered a flaw.

    The column is very high and therefore the density of salt cannot be a constant. Just like the density of air is only 35% at the top of Mount Everest, the density of salt is accordingly lower at the top of your column. At the same time, the density is higher at the bottom of the column...high enough to overcome the gravitational differential and suck fresh water in through the porous plug, rather than the other way around.
  4. May 12, 2009 #3
    Water is not nearly as compressible as air, it is almost completely incompressible. Yet it's true that neither water nor salt-water is truly incompressible, but it doesn't really play a role in this problem since water and salt-water both increase their densities with pressure at the same relative rate.

    Furthermore, the 2.5% difference in density is never countered, even if the compressiveness of the liquids were to prove to be very slightly different:
    "The low compressibility of water means that even in the deep oceans at 4000 m depth, where pressures are 4×10^7 Pa, there is only a 1.8% decrease in volume.", from Wikipedia.

    I'm sorry to say, but you haven't managed to convince me.
  5. May 12, 2009 #4


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    Gold Member

    Deos this machine do any useful work? Is that not a requirement of at least one class of PMMs?
  6. May 12, 2009 #5
    Uh, the water is going to diffuse in the opposite direction.
  7. May 12, 2009 #6
    When the water from the pure side spills over at C, it can perhaps turn a waterwheel.

    Well, the idea is that the increased density of the salt-water will perform reverse osmosis. Have a look at the numbers.
  8. May 12, 2009 #7


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    Staff: Mentor

    This problem appears to have stumped the author of the site you got that pic from. I suspect the answer has something to do with the energy associated with the chemical process of osmosis, which unfortunately, I don't fully understand. Perhaps a chemist can verify this, but a temperature change across the membrane either due to the chemical process or the thermodynamics of flow through a nozzle could provide the answer.

    This hints at it, but unfortunately, I can only get the abstract:
    http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000075000011000997000001&idtype=cvips&gifs=yes [Broken]

    This implies to me that if you don't return that potential energy to the salt water (ie, you extract it with a turbine), the entire system will cool continuously until the water freezes.
    Last edited by a moderator: May 4, 2017
  9. May 12, 2009 #8
    Where are you getting your numbers (for the osmotic pressure between water at high compression and brine at high compression)?
  10. May 12, 2009 #9
    His numbers are fine.
  11. May 12, 2009 #10
    This I understand. I know the laws of thermodynamics will not allow a perpetual motion machine. What i want to know is the reasons why this will not work in terms of what is really going on, that is, in terms of fluid statics and osmosis.

    Well, according to http://en.wikipedia.org/wiki/Osmotic_pressure, the osmotic pressure should simply be linear to the molarity (and temperature, but that is constant anyway). I looked up the water potential pressures in a table that i cannot find for the moment, but here is a diffrent example: http://books.google.se/books?id=oAF...5uWhCw&sa=X&oi=book_result&ct=result&resnum=2. This is for sucrose, but all that it might be different from salt is in its van't Hoff factor, but since we are considering salt-water with pure water, neither this plays a role.

    Simply put, the molarity is the only thing that plays a role, and it serves to put a relatively lower osmotic pressure on the side with higher molarity.
    Last edited by a moderator: May 4, 2017
  12. May 12, 2009 #11


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    Gold Member

    Free refrigeration! :biggrin:
  13. May 12, 2009 #12
    If osmotic pressure is independent of absolute pressure, then I would guess conway is right: that the energy extracted will be insufficient to mix the saline gradient.
  14. May 12, 2009 #13
    Well, yeah, even if this machine ends up freezing over, it still did free useful work, which is also thermodynamically impossible. Hence, we have a problem.

    Yet I am still more concerned with the explanation that foils this plan without simply stating "There is no free lunch".
  15. May 12, 2009 #14


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    You're asking for an explanation without an explanation. Turbines and nozzles are thermodynamic devices, so the explanation of how they affect the system has to include thermodynamics. And I gave the explanation (I'm just not certain it is correct! :biggrin: ):

    -When a fluid passes through a nozzle or a turbine, it loses energy, so unless that energy is returned to the system, it will continuously cool.

    Now that I think about it, though, I'm not sure you even really need the chemistry of it - the thermodynamics would seem to be enough (though I haven't done the math to see if the energies are really equal...).
  16. May 12, 2009 #15
    Yes it seems to be that osmotic pressure is independent of absolute pressure, it was one of my first ideas to try to uncover the answer, but to no avail. You mean that the pressure exerted will not be enough to work backwards against the saline gradient, or did i misunderstand you?

    Anyway it seems that, given that the osmotic pressure is independent, the pressure difference at those depths generated by difference in densities should be enough to make the process run in the correct (impossible) direction.
  17. May 12, 2009 #16
    Hehe, well, i might be into a hopeless pursuit, but simply saying "No device can make free energy" feels kind of an unsatisfactory explanation, when the hydro-statics and osmotic mechanisms all declare that the pure water should rise above the salt-water, period. And thus generate potential energy out of nowhere.

    There must be something in terms of fluid statics or the mechanisms of osmosis that I have neglected for the theory to converge with thermodynamics. And this neglected theory is what I'm trying to recover here.
  18. May 12, 2009 #17


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    Staff: Mentor

    No, it isn't. The system is then essentially just a charged battery.
  19. May 12, 2009 #18
    The problem becomes that when the risen water at point C goes to the level where it pours back into the salt-water, it is still in the same "charged" state, while water is pouring.
  20. May 12, 2009 #19


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    Staff: Mentor

    I didn't say that! I didn't specifically invoke any of the laws of thermodynamics in my explanation!
    Well that's kinda the point: if the system is cooling, then they are converting heat energy to potential energy. There is no violation implied in that unless you try to extract energy from it indefinitely. It looks like this:

    Without a turbine:

    heat energy input - mechanical potential energy output = 0
    That's a conservation of energy statement

    With a turbine:
    heat energy input - mechanical potential energy output - mechanical kinetic energy output < 0
    That says the energy will decrease continually, a violation of conservation of energy. The water freezing is a manifestation of it.
  21. May 12, 2009 #20
    Again with the Clausius statement Russ? A battery that can recharge itself from ambient thermal energy is unacceptable.
    That's just being obtuse; The fact that a problem can sometimes be solved by parroting global arguments does not alter the fact it always can also be solved purely by integration of local forces.
    Last edited: May 12, 2009
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