Reminds me of that ole cowboy song that Tex Redox used to sing, "Gimme room, room, lots of room, room to roam, room to ride..." Well, I won't actually sing to you.

As the spring corrodes during its futile effort to break the bonds of the box, it will weaken. As it weakens and bends under the corrosive assault of the acid, the spring will eventually snap in two under its own once mighty forces, expending its energy splashing the acid uselessly around inside the box.

The energy must remain within the spring, box, acid boundary. I would think that the metal spring would corrode faster than normal and that the energy would be converted to heat and the temperature fo the acid would rise.

Hydrogen is always generated whenever a metal is attacked by an acid. In a closed system the increasing pressure of the hydrogen will slow down and finally stop the reaction. So it could happen that the spring will not be corroded totally and therefore not collapse. The stored energy of the spring possibly does not contribute to the chemical reaction itself. The chemical reaction is exothermic and the energy released during this reaction is transferred to the walls of the box as heat. From the walls of the box this heat is passed on to the environment. When the temperature of the box and it´s contents decreases also the hydrogen-pressure decreases and the corrosive reaction will proceed and so on and so on until even at ambient temperature the hydrogen pressure is too high for a further reaction of the acid with the spring. Here is the true (practical) problem: if the spring is still intact enough, the pressure from the spring against the walls of the box adds to the hydrogen-pressure against the box and maybe the stability of the box is not high enough to withstand this combined pressure at a certain point: in this case you produced an acid bomb with timer function. The spring puts pressure on both sides against the walls of the box which in return puts a force equal to this pressure against the two ends of the spring. So when the force of the spring (in equivalent to its stored energy) gradually dercreases due to the corrosion also the force from the box against the spring decreases to the same degree which gives mathematically a 0. Force against force = equilibrium until these forces are 0.

Precise, detailed, and humorous. Welcome to the madhouse (and a well-deserved GA vote from me)

Fyz

There are many variables to consider, The question states only a small sturdy box. It does not indicate the type of material from which the box is made. Nor the type of sealing applied to close the box with the spring inside. If the corrosive acid completely fills the box, the corrosive action with the spring will release the energy stored in the spiring and will expand the box, possibly opening it. If the box material is corrosive resistant and strong enough to withstand the pressure built by the corrosive action then the energy will be contained until the box is opened. Then since the spring has been absorbed by the corrosive, it will flow out of the box the pressure is depleted.

The stored energy will be added to the corrosion reaction enthalpy (which can be positive or negative; if the reaction is exothermic, the situation will produce more heat than with an un compressed spring; if endothermic, it will absorb less heat, i.e. get less cool).

This as an approximation...might also change the DG of the stuff.

As the spring will be corroded, energy stored will be released as smaller spring decompression while corrosion is affecting the spring. As the corrosion pattern will be uneven because the crystalline structure of the spring have some imperfections. This decompression will be dampened by viscosity of the acid and will raise the temperature of the acid-box system.

By "the energy originally stored in the spring" I am assuming that we are considering only the potential energy due to the compression of the spring. Clearly there are other energies associated with the spring. There is even some portential energy stored in the "uncompressed" spring due to the residual stresses in the steel. There are also chemical energy potential but I have no clue what they might be. What we are really considering is the differences between the box with acid and spring with the spring either compressed or not compressed. I believe the spring compression potential energy will be converted to heat. Even if the spring releases some of its potential energy to kinetic energy if it breaks, this energy will ultimately be converted to heat. I think an important question is how much heat might be generated. I have a 4.6 gram spring about 7/8 inch long that, when fully compressed to 1/2 inch, requires a compressive force of about 25 pounds. I calculate that if all of the energy of compressing the spring fully (0.52 foot pounds) were used to heat up only the spring, the temperature rise would be 0.55 F. I'm guessing weight of the acid, box, and whatever was used to keep the spring compressed would several times the spring's weight. The box, acid, and spring would be maybe 0.1 F if the spring were compressed and there were no heat loss from the box. If there were heat loss, I don't think we could ever measure the difference.

The problem assumes as given that we have a box capable of containing all reaction products and enough acid of enough strength to dissolve the spring completely despite any change in chemistry, pressure or temperature, so we are not to fuss about those real world alternatives.

The energy of the compressed spring and any energy stored in it's crystaline structure such as the carbon atoms stretching the lattice of the iron speeds the chemical reaction of the acid, and if the chemical reaction of this acid and steel is exothermal (gives off more energy than it absorbs, then that energy will all become additional heat, but if endothermal, some of the energy is stored in the chemical bonds of the resulting compound. The exact chemistry of this acid is not specified; we just know it has an acidic PH. Obviously, it can react at least with the majority iron atoms within the steel, leaving a sediment of any un-reacted carbon and other atoms.

HI everybody,

The stored mechanical energy in the spring will be not transformed in any thing ; it will decrease slowly to zero. Because this enegy is produced by the box walls as a reaction to the force of the spring.The spring is pushing the box walls and the walls are pushing the spring.We can say also that there is a stored energy in the box walls.The total stored mechanical energy is equal to zero. When the spring starts to be corroded its action on the walls will start to decrease and therefore the reaction of the walls which is responsible of the stored mechanical energy in the spring will decrease. When the spring will be completly corroded the stored energy in the spring will have been decreased to zero and not transformed to any thing.The final total mechanical energy will be zero (agreement with conservation of mechanical energy for an isolated system (spring plus box).

The sides of the spring which apply the pressure on the walls will have lesser corrosion as one of their surfaces is not exposed to the acid. This will lead to the centre of the spring to be more prone to acids as the surface area of exposure to acid will be greatest at the center. The weak link at the center therefore will snap first making the spring loose its energy in meachanical form only by hitting the opposite walls once the links snap.

Since E=Mc^2, the box will be slightly heavier eventually?

Well, after years of being a mechanic and driver, I know that rust dissipates compression. In other words, the spring loses ir's "springiness," so to speak.

As to where the energy goes, what energy? If the spring remains compressed while in the box with the liquid, the energy is only potential energy (Again, I refer to physics 101 as taught by Mr. Lariton), and as such does not exist until the spring is allowed to return to it's uncompressed state.

Or did the laws of physics change while I wasn't looking?

Ken Leigh

The name potential is unfortunate, and probably refers to it's longevity compared to real world kinetic energy that, before we got to outer space, was always a short lived phenomenon.

If you exercise with a spring-loaded device, you only get potential exercise, not real exercise! It's all reminiscent of isotonic versus isometric exercises!

No, I think I'm right.

The energy is potential because until it's released, it does not exist. The potential for energy is there, but nothing else.

Ken Leigh

Energy, subtype potential is a kind of real energy. Many people get power and energy mixed up, and I think this contributes to the notion that any energy not associated with flow or motion is somewhat unreal. Entropy was increased to put that energy in the bottle up on that potential shelf, just as it was to put things in motion.

Think of potential more in terms of voltage than liabilkity insurance. If you charge up a capacitor, the voltage, aka potential, rises as the energy is pushed in there. You have to buy the gas to drive your car up the hill, so it is a very real energy that is stored. It won't send the car from that hill to the top of a higher hill, as that is a higher potential. The energy is stored in gravity in place of inertia, but it is still energy, and it is still a stored thing, just a different media. If the media hits you in the head, that is power, not energy, and not a different kind of energy.

If you got shot in the head with a bullet, it is the effect of kinetic energy. If I use a hydraulic press, that applies potential energy, but still a hole in the head is made, so, the energy is no so much different. Potential is a silly old blanket that covers every energy storage but inertia. Leave it in old science, along with melancholy, sanguine, phlegmatic and choler, earth, wind, fire and water.

Re your first paragraph - I can see what I missed now.

Back to the drawing board.

Thanx.

Ken

The principle of "conservation of energy" is based on the premise that it potential energy is a form of energy; you may if you wish say that it is not - but that has nothing to do with conventional physics. (Moreover, I can't see how it can lead to a satisfactory model - unless you rename what is currently called energy so that we can again have a law of conservation.)

Well, there are all sorts of tricks in the land of simple math. You can only have conservation of energy if you have potential energy -- well, of course, since most energy is potential, it might be better to say you can only have conservation of energy if you include kinetic energy, which in the real world is generally always decaying away, so measure quickly and extrapolate back!

It reminds me of imaginary and complex numbers, which have a use where they describe things like energy storage as if it was energy loss (energy bank failure without bailout?), such as resistance in electricity, and when the energy is returned from storage, you have to have a magic additional dimension to explain it, like two dimensional flatlanders explaining rainfall. You get to use old, familiar equations at the cost of complex arithmetic, but it seems far less muddy to me if you model it as storage in the first place!

Terminology should be used as rigorously defined, so the facts are not lost in the mush. Rigor is one of my favorite words. However, potential and kinetic energy terms, while a prominent part of elementary education, are not very useful when you go to engineer things. When you are cold, you are happy for any sort of energy source to produce heat; the ability of an energy source to be converted to motion at 100% efficiency is totally irrelevant. If the sun shines on my house for no additional cost, then a solar array converting it to electricity and then motion in my blender is fine, and the real efficiency is how soon I can pay for the solar array. It's easy to get overly fixated on the moving objects -- an evolved survival trait. Neither kinetic energy, chemical energy or heat can be converted to electricity with 100% efficiency, but you use the best available source you can get, and are glad you get anything back. If you are sitting on a volcano, you are up to your femaroles in hot water, and the conversion efficiency goes by the side until you run low.

So, we did work when we compressed the spring, and that energy was stored in a form not 100% convertable to kinetic. When it dissolves, it must be in there, so whatever portion of that energy that does not contribute to stored chemical energy in the final chemistry will be in there as heat.

The link with (and consequent exclusion of) kinetic energy is merely historic - I'm not fixated on that. The crucial word is "ordered". In principle any ordered form can be converted to any other other ordered form with 100% efficiency - though there are always losses in practice - K.E. to electrical is no different in that respect to any other conversion.

For the case of the spring, there are losses in compression, but the potential energy is defined as that which is in principle convertible to other forms of ordered energy, and therefore to kinetic. As ever, the built-in systematic losses (in this case due to the material of the spring itself) make that impractical - hence the inclusion of "in principle". So far as I know, the solution as described in the challenge is already converting chemical energy to heat, and there is no pathway for the potential energy in the spring to be converted to chemical energy - but I'm prepared to be demonstrated wrong.

But I see you have changed the subject from the Potential Energy as defined in physics to "emotional economics". I'm out of that aspect.

If the acid reaction is endothermal, it sucks up energy from the solution as it makes new chemical bonds. So, the energy might find a new home in chemical, not thermal, territory. An honest evaluation might assume that if 99% of the energy absorbed in the reaction came from the solution, so we would say only 1% of the stored energy in the spring is stored chemically. It is so hard to keep track of every molecule and photon, so we usually assume an equal division.

By compressing the spring, the crystalline structure of the steel get tensioned and acquires a higher chemical potential

hmm. So, mechanical energy stored in a spring is defined at the level of atomic bonds. Could the answer go the whole hog and define that energy in terms of mass? There's a bit of chat about that here, and a whole bunch of places. The question would work even if the metal was not shaped like a conventional spring (eg, just a compressed block of steel). Is this some evil plot by the Chemists of the world ?

"Is this some evil plot by the Chemists of the world?"

White cats, piranhas...?
More likely a plot by the divine chemist, perhaps? Next stop (stop! right there) cold fusion...
Are you paranormal?

Nah, Kris is just uninormal. You have to add Del to get paranormal.