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[Phys-l] Rubber band and thermodynamics



This has finally engaged the PTSOS people with much puzzlement.


Here's one reply to the question:

I am planning on doing activity today in which stretch a rubber band against their lips. It should feel colder when it's allowed to contract again. All the explanations I've found get into polymer chains and the chemistry. I was hoping to demonstrate conservation of energy as the elastic potential energy of the band becomes thermal energy. But as the rubber band contracts shouldn't it be releasing thermal energy as its losing it's elastic potential energy??

Reply:

This demo is really about the second law.
Entropy change requires an energy flow. dS = dQ/T where S is entropy , Q is heat flow, T is temperature. (Heat flow into a system is positive by definition)
So positive increase in entropy requires positive and therefore inward flow of energy.

When the rubber band is stretched the polymers are aligned, when it relaxes they become more randomly oriented.
Randomly oriented molecules have higher entropy than aligned molecules.
So when you relax the rubber band, its entropy increases.

When entropy increases heat must flow into the rubber band.
The heat flows from the outside world, your lips for example. So your lips are cooled as energy flows into the rubber band to increase the entropy.


And Wiki's:

Thermodynamics

Temperature affects the elasticity of a rubber band in an unusual way. Heating causes the rubber band to contract, and cooling causes expansion.[9]
An interesting effect of rubber bands in thermodynamics is that stretching a rubber band will cause it to release heat (press it against your lips), while releasing it after it has been stretched will lead it to absorb heat, causing its surroundings to become cooler. This phenomenon can be explained with Gibb's Free Energy. Rearranging ΔG=ΔH-TΔS, where G is the free energy, H is the enthalpy, and S is the entropy, we get TΔS=ΔH-ΔG. Since stretching is nonspontaneous, as it requires external work, TΔS must be negative. Since T is always positive (it can never reach absolute zero), the ΔS must be negative, implying that the rubber in its natural state is more entangled (fewer microstates) than when it is under tension. Thus, when the tension is removed, the reaction is spontaneous, leading ΔG to be negative. Consequently, the cooling effect must result in a positive ΔG, so ΔS will be positive there.[10][11]
The result is that a rubber band behaves somewhat like an ideal monatomic gas, inasmuch as (to good approximation) elastic polymers do not store any potential energy in stretched chemical bonds or elastic work done in stretching molecules, when work is done upon them. Instead, all work done on the rubber is "released" (not stored) and appears immediately in the polymer as thermal energy. In the same way, all work that the elastic does on the surroundings, results in the disappearance of thermal energy in order to do the work (the elastic band grows cooler, like an expanding gas). This last phenomenon is the critical clue that the ability of a elastomer to do work depends (as with an ideal gas) only on entropy-change considerations, and not on any stored (i.e., potential) energy within the polymer bonds. Instead, the energy to do work comes entirely from thermal energy, and (as in the case of an expanding ideal gas) only the positive entropy change of the polymer allows its internal thermal energy to be converted efficiently (100% in theory) into work.
Rubber band - Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Rubber_band

bc thinks there's a contradiction between the two above, and didn't find a discussion on rubber bands in the phys-l archive or JD's site.
A trivium:
“ My greatest concern was what to call it. I thought of calling it ‘information’, but the word was overly used, so I decided to call it ‘uncertainty’. When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, ‘You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage. ”
—Conversation between Claude Shannon and John von Neumann regarding what name to give to the “measure of uncertainty” or attenuation in phone-line signals [37]
Entropy - Wikipedia, the free encyclopedia

http://en.wikipedia.org/wiki/Entropy




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