In the heat of a midday, a bungee jumper perform a stunt where she leapt off a 1

Question

In the heat of a midday, a bungee jumper perform a stunt where she leapt off a 100 foot crane and her elastomeric bungee cord stretched just far enough allowing her to pick a flower from the ground. In the evening, a cold front came dropping the temperature 25 C. If she repeated her setup with the exact same setup would she:

A. pick the flower just like before

B. undershoot and miss the flower or

C. overshoot and hit the ground

Assume bungee cord was not plastically damaged from the first jump and defend your answer based on the molecular origin of rubber elasticity including thermodynamic properties.

Explanation / Answer

C. overshoot and hit the ground

When the elastomeric bungee cord is assumed to be in a stretched state, heating causes them to contract. Vice versa, cooling can cause expansion.This can be observed with an ordinary rubber band. 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 the Gibbs Free Energy. Rearranging G=HTS, where G is the free energy, H is the enthalpy, and S is the entropy, we get TS=HG. Since stretching is nonspontaneous, as it requires external work, TS must be negative. Since T is always positive (it can never reach absolute zero), the S must be negative, implying that the rubber in its natural state is more entangled (with more microstates) than when it is under tension. Thus, when the tension is removed, the reaction is spontaneous, leading G to be negative. Consequently, the cooling effect must result in a positive H, so S will be positive.

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