I have a question about an experiment that seems to violate the law of conservation and energy. I’m hopeful that you will be able to dispel my misunderstanding.
Suppose you take a metal spring wound to its capacity, thereby storing potential energy in the spring. Suppose then that you immerse the spring in a bath of acid so that it dissolves into the acid in a uniform way so that the tension in the spring is not released because one part dissolves faster than the rest of the spring.
What then has become of the potential energy in the spring?
Look at it on a microscopic level - what is the potential energy stored in the spring? It’s individual molecules that are stretched out of their rest position in the metallic lattice. When they are dissolved out of the bulk metal, each of those individual molecules gives up a little energy to the surrounding solution as heat.
Suppose that the acid happened to eat through one area of the spring quickly and it goes sproinggg… The released energy is tranfered to mechanical energy which then becomes heat in stirring the acid.
A similar thing will happen on a molecular level. The spring energy is stored in intra-molecular displacements and as these are released by the acid, heat (or chemical reaction activity) will be added to the solution.
You’re imagining the spring is continuous but really it’s discrete. The spring is composed of a specific number of atoms, held together with chemical bonds. It simply isn’t possible that all these bonds will break simultaneously. A bunch of them will break early in the experiment, more will break during the middle, and some will break near the end. And one of them will be last. At some point in time, long before the very last chemical bond breaks, the spring will be almost completely dissolved (but not quite), just a bare wisp of a thread of what’s left of the spring. And the bonds break one by one, there has to be a point in time where breaking one more bond will cause the spring to lose its integrity and what’s left of it will go BOING and release that potential energy.
Hypothetically, in a game of Jenga, if you could remove all the blocks of wood simultaneously then the tower would never fall, but that’s simply not possible.
As others have pointed out, the energy is distributed throughout the spring as well. I’m sure you were only pointing out that the OPs scenario is impossible, but I want to illustrate the point of the energy being released with practically every dissolved atom by making the OPs scenario slightly less impossible.
Picture two springs identical in shape, except one is made from thinner/narrower material than the other. The thinner one will be easier to wind, so will have less energy stored. Dissolving part of the heavier spring uniformly turns it into the narrower one. So either you now have a spring that is wound the same as an identical spring, but it stores more energy, or the energy was lost gradually along the way. And of course the latter is what happens.
I think Nefario started the discussion with the “sproinggg” as a set up for his thought experiment. This part is easy to visualize and understand.
Next he proposes numerous microscopic “sproinggs” as each atom is removed from the spring. Beowulff sais the same thing upthread. Naita is making the same point, I think.
Should be, although it will only be a small amount (imagine the amount of heat from friction if, say, you allowed the decompressing spring to push a rod between your fingers - a one-time deal and they might get a little warm)
The tension within the metal means that as particles dissolve away, they will do so a little more energetically than otherwise they might (i.e. they sort of ‘ping’ off into the liquid, rather than floating away serenely).
The change will be miniscule. You need a lot of kinetic energy to create any meaningful change in temperature. The water at the bottom of a waterfall should be warmer than it was at the top, since all its potential energy has been released. In practice, you’d need a microscopically precise thermometer to measure the difference, though.
Ignore the acid, and assume we put the spring in a bath of plain water. Now use the spring as a stir-rod and swirl the water just a teeny bit.
We used the molecules of spring to impart kinetic energy into the molecules of water. The water is now hotter than it was. How much hotter? A couple of nano-Kelvins.
Your acid dissolving a wound spring does exactly the same thing, just with smaller-scale individual motions rather than one big macro-scale motion.
Another issue to consider is that if you start with a spring at rest and then wind it you’ll find that will be hotter at the end of winding than it was when you began. The act of injecting strain (i.e. potential energy) into the metal will heat it.
So you’ve got to decide if you want the starting point of your measurements to be the pre-wound temp of the spring + pre-immersed bath temp, or the post-wound temp of the spring + pre-immersed bath temp. Or the post-wound, then cooled to ambient, spring temp + pre-immersed bath temp.
All in all you’re seeking the weight of angels on pinheads. They’re 100% real, but they’re tiny.
Also dissolving metals in acids is an exothermic process, although I don’t know enough to say if any particular combination of spring metal and acid wouldn’t swamp the energy released from the wound spring.
By my calculation it’s 2 mK per meter height. I think it’s safe to say not much energy is carried away by sound or spray. I suppose “microscopically precise” is still accurate if the product of the upper limit of microscopic precision, m[sub]p[/sub] and the height h, of the waterfall in meters is more than that. I.e. this has to hold: 2 < h*m[sub]p[/sub]
The evaporation of atomized water drops imparts tremendous cooling to the air around significant waterfalls. Since the warmest droplets evaporate, the ones left behind are on average the cooler ones. We also ought to get some conductive cooling back into the surviving water.
For sure this effect is negligible in short falls. But it would expand more or less exponentially in tall falls. If we could engineer a 10 mile high waterfall we might well have zero liquid water hitting the bottom; it would all evaporate on the way down.
