It is easily veiied that a rubber band heats up when it is stretched adiabatically. Given this fact, determine whether a rubber band will contract or expand when it is cooled at constant tension

contrasting and expanding at constant tension is called Entropy change.

Explanation:

Entropy change (stretching and contracting at constant T):

Heat is produced in the rubber band as it is stretched. If we stretch slowly in air at room temperaure, we have a reversible, isothermal process with q< 0 (heat is lost to the surroundings). Then ∆Sstretch = qrev/T <0 in the stretching process. Since entropy is a state function, ∆Scontract = qrev/T >0 for the reverse process of slowly allowing the rubber band to contract. The rubber band has lower entropy, (is more orderd) when stretched. Under tension, the molecules in a rubber band line up and the arrangement becomes much more ordered, lowering the entropy. The criterion for spontaneity for an isolated system is ∆Ssys >0. Suppose the system is the rubber band and the air in a large room. Therefore, if a constraint keeping the rubber band stretched is removed, it will spontaneously contract, with ∆Ssys, contract >0

Rubber band will expand when it is cooled at constant tension.

Explanation:

Rubber band is different from other materials. It is made of long chain molecules. These long chain molecules are called polymers. Temperature has surprizing effect on rubber band. When these long chains are heated they vibrate and shortened. That's why rubber band contracts.

On the other hand, when these long chains are cooled they get relax cuasing the rubber band expansion.

From above explanation, it can be observed that rubber band behaviour is opposite to most of other materials becuase they expand when they are heated and contracts when they get cool.  

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