When a rubber band is stretched it heats up, but how can this be explained (from the microscopic view) in the case of an adiabatic expansion (meaning that the entropy remains constant). Further more how would we perform such an expansion because typically stretching a rubber band would straighten its molecules and decrease entropy?
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answered here: http://physics.stackexchange.com/questions/54738/rubber-band-stretched-produces-heat-and-when-released-absorbs-heat-why – gregsan Nov 17 '15 at 16:09
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@gregsan this question talks about it in the general case, the answer given is relies on the fact that there is an increase in entropy. My question is in the case when we hold entropy constant. And hence this does not really answer my question. – Quantum spaghettification Nov 17 '15 at 16:26
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Your disconnect is in thinking that stretching the rubber band occurs adiabatically - as noted both below, and in @gregsan's answer, that does not occur. The act of stretching changes the entropy of the configuration. – Jon Custer Nov 17 '15 at 17:42
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@JonCuster I know I never said it was adiabatic, but I want to theoretically force it to be adiabatic. – Quantum spaghettification Nov 17 '15 at 17:45
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1So, given the linked answer by @gregsan, and the answers below, how, exactly, do you expect to force the expansion to be adiabatic - you simply can't. Theoretically calculating something that won't happen, even in theory, does not make sense. – Jon Custer Nov 17 '15 at 17:47
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@Joseph: you can't 'theoretically force it to be adiabatic'. Reality is what it is. – Gert Nov 17 '15 at 17:47
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@JonCuster we can force an expansion of a gas to be adiabatic by putting it into a thermally insulated container. We could surround the elastic can by a thermally insulated 'shell' and then do work on it. In this case no heat will be transferred to or from the surroundings and the process will be adiabatic. – Quantum spaghettification Nov 17 '15 at 17:54
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The point is that a polymer is not an ideal gas. The polymer has internal degrees of freedom such that the entropy can change. Keeping it at constant temperature does not guarantee constant entropy. It does not work that way. – Jon Custer Nov 17 '15 at 18:02
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@JonCuster I nether said constant temperature, I said thermally insulated meaning no heat transfer, such that $dQ=0$ and therefore $dS=0$. – Quantum spaghettification Nov 17 '15 at 18:10
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1dQ=0 to the outside world does not mean dS = 0 internally. – Jon Custer Nov 17 '15 at 18:21
2 Answers
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The answer lies in changes in Gibbs Free Energy:
$$\Delta G= \Delta H -T \Delta S,$$
where $G$ is Gibbs Free Energy, $H$ is Enthalpy, $S$ is Entropy and $T$ absolute temperature.
When we stretch the rubber band it heats up due to viscous friction of the molecules sliding over each other as we stretch the object. It as nothing to do with with adiabatic expansion because there in no expansion: rubber is an incompressible material (it deforms on stretching but $\Delta V \approx 0$).
Now we know the stretched rubber wants to snap back, so why is this? We know that this spontaneous phenomenon of snapping back means that:
$$\Delta G<0$$
We also know that on snapping back, $\Delta H<0$, so that doesn't really help.
The reason that $\Delta G<0$ is caused by an Entropy change $\Delta S$, so that for snapping back:
$$T\Delta S>\Delta H,$$
and thus for snapping back:
$$\Delta G=\Delta H-T\Delta S<0$$
This increase of Entropy when going from the stretched to the unstretched state is also easily explained from a structural molecular point of view. Rubber is made up of cross-linked macro-molecules that have a larger number of molecular conformations (micro states) when relaxed as opposed to when stretched. This translates into higher Entropy content in the relaxed state.
Gert
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OK, sorry for the confusion, only now maybe I really understand your question. The answer is probably as simple as this: when you stretch the band, the molecules of the rubber band actually move (or fluctuate) faster. Why they move faster? You can think of a string, one end is fixed to the wall, the other is at your hand. In the middle of the string you have a mass. The mass is moving with some kinetic energy. When you stretch the string, although the space seems to be narrow for the mass to move, its kinetic energy increases because of your action of pulling the string. (This is again a mechanical adiabatic process as I wrote.) The (kinetic) energy, and therefore the temperature increase. The entropy is logarithm of the phase volume (space x momentum), and can be shown to be actually constant, however.
cnguyen
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Hi, sorry I should have made I clearer in my question, I am looking a for a microscopic description of why the temperature increases (i.e. in terms of the rubber molecules) – Quantum spaghettification Nov 17 '15 at 15:08
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Well, I find that I probably made a rather lengthy argument just to convince your intuition. Maybe it is not necessary and you may find it natural after sometime. You can have a look at the gregsan's link for a more concrete answer. – cnguyen Nov 17 '15 at 16:23
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I'm sorry but this is a confused answer that mixes up concepts, 'intuitions' and more, yet fails to answer the question concisely. – Gert Nov 17 '15 at 17:43
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@Gert: I actually agree :-) I answered differently when the question was posed a bit not clearly and just adapted it after that; this caused myself confused about the question. I do not know how to delete the whole thing, actually. – cnguyen Nov 17 '15 at 17:46
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@Rumpel: there should be a button that allows you to delete your entire answer. I've done it with some of mine on occasion. – Gert Nov 17 '15 at 17:51
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OK, actually perhaps now I understand what he is asking and revert the answer. Hope that helps :-) – cnguyen Nov 17 '15 at 18:12