Question

How much of elastic energy is stored as entropy?

Answer 1

There are two cases of elastic stretching: springs and rubber.

When you streach a spring or a piece of rubber both absorb some energy as Entropy (S) and some as plain energy (U)

Fi=T∂S∂qi−∂U∂qiFi=T∂S∂qi−∂U∂qi

"The force of a rubber band or stretched spring has an entropic part (the first term) and an energetic part (the second term). The entropic part is proportional to temperature, so it gets bigger when it’s hot. The energetic part doesn’t change....

Energetic forces are familiar from classical statics: for example, a rock pushes down on the table because its energy would decrease if it could go down. Entropic forces enter the game when we generalize to thermal statics, as we’re doing now. But when we set T = 0, these entropic forces go away and we’re back to classical statics!"

Is there a difference between rubber and metal springs from a thermodynamic analysis of the ratio between energetic and en-tropic energy storage? if so, what is the difference

Answer 2

In the rubber you have entangled polymer chains that in the unstressed state can be viewed as a random walk. Stretching the material starts aligning the chains, which reduces their entropy. This is also the reason why rubber has a negative coefficient of expansion. Steel springs do not exhibit a similar physical phenomena (although one could argue for creep or fatigue mechanisms I guess). So, yes, there are substantial differences in the entropic factors.