Entropic Force - Heat Transfer Mechanism

[mgkii]

Is anyone able to explain something to do with entropic force at a level I might be able to understand please! Ok... you need to know what level I'm at?
Formal Maths & Physics at high school (I'm 50, so distant past :-)
Informal Maths & Physics - lifelong interest. Consume a lot of youtube channels like 3Blue1Brown, PBS Spacetime, Mathlogger, Science Asylum, Numberphile (and would recommend them all!). I've read Edward Frenkel's book on Langlands Program and wished I could better understand the math rather than just the concepts (well - must of them!)
Summary - reasonable on concepts and breadth of knowledge... veeeery shallow on the math.

Sorry for the rambling start - onto my question.

I've been watching videos on / reading material on Entropic force and there's one aspect that I can't get my head around, which is tying to understand the *mechanism* by which (for example) heat is caused to flow out/in of rubber band is it stretched and relaxed?

The bits I think get
- There's no difference in internal energy between a polymer that has been stretched into a straight chain, or one that's in a curled state.
- There's a big difference in entropy - there's only 1 configuration for a straight polymer a very large number of possible configurations for a curled one
- Energy is put into the system when you stretch a rubber band (and released when it is relaxed).
- I even get that it is completely logical from a 2nd law POV for the stretched rubber band to heat up as you reduce the entropy of the band
- I'm almost certain that friction doesn't come into this - it seems plausible for the stretching argument, but as soon as you consider the relaxing band then you'd have to have some kind of "anti-friction" to cause the cooling.

QUESTION (finally)
If I have a rubber band in a stretched state at temperature X and suddenly release the tension allowing it to shrink back to it's normal state, the temperature of that band will reduce - quite noticeably. The internal energy of the polymer chains that make up that band remains unchanged (or so all the material tells me).
1. What is the mechanism by which energy from the surrounding area is drawn into the band, causing whatever is touching the band to cool?
2. Where is that energy stored if it's not in the internal energy of the individual polymer chains

Thank you for you patience whilst I got to my question!

Best Regards
Matt

 

[mjc123]

There's an important point you omitted. "There's no difference in internal energy between a polymer that has been stretched into a straight chain, or one that's in a curled state" - at the same temperature. If you stretch or relax the band slowly, so that it remains in thermal equilibrium with the surroundings, it will stay at the same temperature, and ΔU = 0. Since dS = dQ/T, the heat gained or lost in changing the entropy will be gained from or lost to the surroundings. Now if you release a stretched band suddenly, so there isn't time for it to equilibrate with the surroundings, as its entropy increases it must gain the heat from its own internal energy, so the temperature drops.

 

[mgkii]

Thanks for the quick reply - I'd definitely missed that point. I'm still not understanding what physical process causes the temperature change when the stretch or release of the band is done at speed? What is the physical process involved that results in energy being "expelled" as the band gets smaller?

 

[Lord Jestocost]

If I have a rubber band in a stretched state at temperature X and suddenly release the tension allowing it to shrink back to it's normal state, the temperature of that band will reduce - quite noticeably. The internal energy of the polymer chains that make up that band remains unchanged (or so all the material tells me).

Stretching of a rubber band (ordering) restricts the available microstates for its internal degrees of freedom, so that its thermal energy – under adiabatic conditions – has to be redistributed among a lesser number of degrees of freedom. Reversely, when a rubber band is allowed to relax.

Richard Feynman, The Feynman Lectures on Physics, Volume I, Chapter 44 „The Laws of Thermodynamics“:

"The internal machinery of rubber that causes these effects is quite complicated. We will describe it from a molecular point of view to some extent, although our main purpose in this chapter is to understand the relationship of these effects independently of the molecular model. Nevertheless, we can show from the molecular model that the effects are closely related. One way to understand the behavior of rubber is to recognize that this substance consists of an enormous tangle of long chains of molecules, a kind of “molecular spaghetti,” with one extra complication: between the chains there are cross-links—like spaghetti that is sometimes welded together where it crosses another piece of spaghetti—a grand tangle. When we pull out such a tangle, some of the chains tend to line up along the direction of the pull. At the same time, the chains are in thermal motion, so they hit each other continually. It follows that such a chain, if stretched, would not by itself remain stretched, because it would be hit from the sides by the other chains and other molecules, and would tend to kink up again. So the real reason why a rubber band tends to contract is this: when one pulls it out, the chains are lengthwise, and the thermal agitations of the molecules on the sides of the chains tend to kink the chains up, and make them shorten. One can then appreciate that if the chains are held stretched and the temperature is increased, so that the vigor of the bombardment on the sides of the chains is also increased, the chains tend to pull in, and they are able to pull a stronger weight when heated. If, after being stretched for a time, a rubber band is allowed to relax, each chain becomes soft, and the molecules striking it lose energy as they pound into the relaxing chain. So the temperature falls."

http://www.feynmanlectures.caltech.edu/I_44.html

 

[mgkii]

I think I'm getting close to understanding :-) As always Feynman had such a great way of explaining.

So I am I right in concluding that entropic force isn't something that's separate to the other classical forces I (mostly) understand, but the way in which those forces work together and balance out because not to do so would violate the 2nd law? (not suggesting this is "causal" - just that this is how things work).

 

[Lord Jestocost]

Entropic forces have their causes in the thermal movement of particles under external constraints. Have a look at https://johncarlosbaez.wordpress.com/2012/02/01/entropic-forces/