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Do metal springs really store sig work as potential?

  1. Mar 27, 2007 #1
    This is a good one.

    We all know that in an ideal gas, there is no isothermal potential energy stored when you do work on the gas. Compress the gas: all the work appears as heat, and when you cool to ambient, it's all gone. Compressed ideal gas stores no work EXCEPT as heat.

    Now, less well known is that elastomers like rubber, within limits and to a good first approximation, act just like ideal gasses. They don't store elastic energy as bond potential. Which means if you stretch a rubber band, ALL the work you do on it appears as heat, and NONE of it goes into the classic kind of elastic potential energy that you're thinking of.

    In both the band and gas gases, this has an interesting corollary when they are forced to DO work-- they get cold and absorb heat from the environment. In fact, they absorb enough heat to equal the energy of the work they do.

    WHAT?? You say? What about entropy? You can't just turn ambient heat willy nilly into useful F x D work! Well, you can in a system like this where it's not reversible. When you compressed the gas or stretched the rubber, you made changes in entropy which allow you now to extract the work again using ambient heat, and let those entropy changes pay the price for you, as dG = TdS. Neat, eh?

    Now my question. What about metal springs? My faith suffered horribly enough with rubber bands! Now in reading, I find that cold-working of metals, well within their Hooke limits, produces a lot of heat. In fact, so much, that most of the work is not left in the metal. Wups. Is that true of springs, too? Do they heat up when you do work on them? What fraction of the work appears as heat? 10%? 98% I want to KNOW!

    So I went to the net and looked, and it's such a morass of student texts and theory discussions and lack of experiments, that I suspect that not many people actually DO know the answer. Most of what's written out there is from the viewpoint of profs writing what they think SHOULD happen. Stretch a spring and it *should* store the energy and not get hot. Let it do work, and the work SHOULD be extracted from pure elastic potential between the metal atom fields. And so on. Baloney. I think that CAN happen, but mostly, in real life do not. But can't prove it.

    Now, keep in mind that in answering this question, ignore how the heat is stored. We all know that in solids like metals (including springs) any heat is partitioned 50% into kinetic and 50% potential, at the microscopic level. But we seek the answers after all this has been allowed to dissipate into the environment. Does a spring which has been compressed and allowed to cool to ambient, then made to do work, cool down? Or does it just sit there at the same temp it already had, having drawn entirely on special potential energy "reserves"? You think you know, but do you REALLY? :devil:

    Steve Harris
     
    Last edited: Mar 27, 2007
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  3. Mar 28, 2007 #2

    Mentz114

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    This is an interesting question. In a good spring most of the work put into compressing it can be recovered, so it must have been stored as potential. I rely on personal experience and observation for this. In a crystal the potential could be due to a change in charge distribution.

    Another related quesion is - if the work done in compressing a spring is stored as potental, does the potential gravitate ?
     
  4. Mar 28, 2007 #3
    Ah, but the fact that the energy can be "recovered" does NOT mean it's stored as potential (I mean as field potential). I can recover the energy I store in compressed gas (after I let it cool) and NONE of that energy is stored as potential. It's all "stored" as decreased entropy, which later lets me "recover" it from the ambient heat in the room. In which case it's certainly NOT stored as anything that gravitates. The compressed gas has the same temp as the gas before I compressed it, so its mass is the same. Steve
     
  5. Mar 28, 2007 #4
    Your post confused me. :confused:

    A spring stores its energy elastically within the bonds. When I place a weight on a spring and hold it down so the spring cant 'spring' back up, the bond length between atoms inside the spring decreases. This causes an increase in the repulsive force between the atoms that pushes back up on the mass. As long as the force of the mass is not so large as to overcome the repulsive forces and break the bonds, i.e. go to strain hardening or softening of the spring, it will alway spring back no matter how long you wait.

    Springs dont dissipate heat into the enviroment just sitting there held down with a weight because they dont ever heat up to begin with.

    Cold working a material occurs when you go into the plastic region of the material. That is by no means within the elastic limit.

    http://www.engineersedge.com/material_science/cold_hot_working.htm

    Also:

    Last time I checked, rubber bands spring back when you let go. All the energy clearly did not go into heat.

    What do you mean by something "can happen, but mostly, in real life dont. It if does not happen, it does not happen. Theory invalid.
     
    Last edited: Mar 28, 2007
  6. Mar 28, 2007 #5

    Mentz114

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    Steve, so you said. But if you can recover the energy without a heat engine - it probably was not stored as heat. I think Cyrus's picture is right. Redistribution of the the charges can increase the potential energy when the material is strained.
     
    Last edited: Mar 28, 2007
  7. Mar 29, 2007 #6
     
    Last edited: Mar 29, 2007
  8. Mar 29, 2007 #7

    Integral

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    "stored work" ????? some how that term just does not seem right. I assume you mean stored energy.

    What am I missing? Let me fill a scuba tank with compressed air. As the compressor does work during the filling process there is a significant amount of heat which must be removed from the system. But how can you say there is no stored energy? Knock the valve off the end of the tank an tell me there is no stored energy?

    So fill me in, what am I missing?
     
  9. Mar 29, 2007 #8
    ===

    There is no stored energy in a scuba tank (in the limit of ideal behavior), but there is (now) only stored ability to do work, by turning some of the tank gas heat, into energy. You've made that possible that by moving entropy into a particular place (at a cost), outside the tank. But the work you do to get the gas into the tank all goes into heat that goes away long before you want to use the gas for work, so it's not located anymore in the tank, so it's not stored in the tank as energy, in ANY sense. NOT as potential. The tank and associated gas doesn't weigh any more by the amount E= deltaM*c^2, etc. It does right after you fill it, and it's still hot. But not after that heat has leaked away. Yet the capacity to do work remains, and it's not stored as potential energy. Just as potential to do work as free energy dG = TdS.
     
  10. Mar 29, 2007 #9

    Integral

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    So how do YOU define potential energy?
     
  11. Mar 29, 2007 #10
    Potential energy

    Well, it's the Lagrangian plus the kinetic energy :). Energy stored when work is done against a force field (this does NOT happen when you compress a classical gas or stretch a rubber band). Seriously, it's all those kinds of energy which show up associated with mass and gravitational fields and stress, but which are NOT due to motion. In the scuba tank that you've put compressed gas into and cooled back to ambient energy, there isn't any extra kinetic OR potential energy. The thing's ability to do work is not due to any stored potential energy, but rather due to its extra order (which happens in compression) which allows it to transform thermal energy (which in the case of an idea gas is entirely kinetic energy) into work. No potentials are actually involved at all (again, in the ideal gas limit, where by definition there are no potential interactions between molecules, and they just bounce off each other).

    Steve
     
    Last edited: Mar 29, 2007
  12. Mar 29, 2007 #11

    Mentz114

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    Steve, this is very interesting. Is the stored energy in the increased kinetic energy of the gas molecules ? No, I guess that is thermal energy...
     
  13. Mar 29, 2007 #12
    Integral: If you consider the ideal gas as consisting of rigid spheres, or even non-interacting point particles, then the only natural definition of the total energy is to sum each particle's kinetic energy. Since there aren't any interaction terms, the total energy of the ideal gas can not depend on the density of particles (and there is nothing that can appropriately be described as potential energy).

    So if you take two different volumes, each containing an equal quantity of an ideal gas and each being at the same temperature (so all particles have the same average kinetic energy individually), then each must also contain the same total amount of energy (over its respective volume). Then, you can notice that in the more compressed volume the particles reflect off the walls more often, so if you relax the confinement the two volumes will do different amounts of work on their respective containers (and afterwards, the more initially compressed one which will have less total energy than the other). Stored work is the appropriate term since, while both stored the same amount of energy, their energy is unrepresentative of their potential to do work. The ocean (being at hundreds of degrees Kelvin) has plenty of energy, yet you can't power your boat with that. I understand this is just basic thermodynamics.

    Before you knock the valve off your scuba tank, tell us where you think the energy is stored. See why "energy" is defined as "the property in a system that does not change over time", rather than "the potential to do work"?
     
    Last edited: Mar 29, 2007
  14. Mar 29, 2007 #13

    Mentz114

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    There has to be increased potential energy in the walls of the container to with stand the extra collisional forces. I don't think one can consider the gas separately from the container.
    If you do work on something and can recover the work, then energy must have been stored somewhere. I don't believe thermodynamics has the answer.
     
  15. Mar 29, 2007 #14

    berkeman

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    Um, not true. A full scuba tank does weigh more than an empty one (that's the reason your bouancy changes as you drain the tank at a given depth while you dive). The delta is the extra mass of the extra air that is stored at pressure. It has nothing to do with the temperature of the tank. I'm not sure where you got the idea that a hot scuba tank weighs more than a room temperature one.

    And if you accidentally drop a full scuba tank on a concrete floor, you will definitely see the stored potential energy of that pressure released and converted to kinetic energy.
     
  16. Mar 29, 2007 #15

    Well, if you use a tank of old (re-cooled to ambient temp) gas to do work, then the initial work you did when you compressed the gas was "stored" as heat. Whether that's heat still in the gas, or heat which escaped since you compressed it, is a matter of taste. Certainly it's conserved. But only thermodynamics (and the idea that you decreased the gas entropy when you compressed it) allows you to USE that heat, to do work. If you allow the gas to expand and do work and don't supply the heat back from the surroundings, the gas itself will cool to below ambient temp. That energy has to come from somewhere. But it's not a reversible situation. Once the gas has expanded, you have to get it back into the bottle.

    Steve
     
  17. Mar 29, 2007 #16

    Doc Al

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    Got references for these claims?
     
  18. Mar 29, 2007 #17

    Mentz114

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    Steve,
    what you say in post #15 is undoubtedly true.
    However, my gut feeling is that although the gas seems to have acquired the ability to do work, this is bestowed by the container and may not be a property of the gas. I'm still thinking about this ...
     
  19. Mar 29, 2007 #18
    Wow, Mentz! Historically, thermodynamics is one of the most important fields of physics (it's where we get the whole conservation of energy thing to begin with!), and I think it played a big part in the inception of all the modern fields of physics, yet you're still willing to contradict it (and on it's home ground no less, the like of steam engines)?

    Assume the container is "rigid". Work (done on the container) is proportional to force (ie. pressure) and distance. Since the container doesn't flex, no work is done on it, and nor does it transfer energy to the gas afterwards (except thermally).

    The idea is to compare the compressed air with the same quantity of uncompressed air, not with a vessel containing a different quantity.
     
  20. Mar 29, 2007 #19

    Mentz114

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    I wouldn't dare !

    You misunderstand me. I mean to say it is incomplete - it does not completely explain this situation, or any other.

    I should also point out that there's no such thing as a "rigid" container ( your quotes).

    My whole interest in this scenario is 'where is the energy' - not just the heat.
     
  21. Mar 29, 2007 #20

    berkeman

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    The air being pushed into the rigid container isn't moving the walls as work is done by the compressor, it's pushing against the air inside.

    PV=nRT. I stand by my previous comments.
     
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