How does thermal expansion affect the energy of elastic materials?

[abcd8989]

I am puzzled with the energy conversion (actually I think I am easily get stuck with PE, KE and work done) when an elastic matter is being stretched or relaxed.

First of all, regarding the elastic hysteresis of a rubber, in the Force-extension graph, the area when the rubber is loaded is larger than that when unloaded. My interpretation is as follows. Please inspect whether I have any wrong or seemingly wrong concepts and kindly correct them.

While the rubber is being loaded, we do work on the rubber, by applying equal but opposite forces at the two end of the rubber, minor part of which is converted to the KE of the molecules as a result of work done against friction between molecular chains, as well as sound energy, major part of which is converted to the PE gained by the molecules as a result of the increased in separation of their mean positions. However, when it is being unloaded, the stored PE is converted to the KE of the molecules and sound energy. We do work to extend the rubber, which is lost to the surroundings. However, the rubber relaxes using its already stored PE, The difference in area is equal to the heat lost to the surroundings?

Secondly, regarding a matter which obeys Hooke's Law when being stretched (before the elastic limit), is there any gain in KE of the molecules of the matter? Or there is simply gain in strain energy? As the loading straight line in the force extension graph superpose with the unloading straight line, it seems that there is no heat lost to the surroundings.

Moreover, I don't understand the explanation for thermalexpansion using a simple PE-molecular separaion curve. The main idea is as follows: At absolute zero, the molecules have no KE and thus the molucules' PE is U_o, which is the lowest value. At a higher temperature, the molucules have some energy, which is above the minimum value U_o". The mean position of molecules is greater than the equilibrium position. When the temperature further increase, the mean position further increase non-symmetrically. As far as I know, it is the KE of the molucules. However, why does the increase in KE lead to an increase in PE? Is it because the mean separation of the molecules increases, so that the work done required to bring the molecules from infinity to a certain point decreases?

Much obliged for patient reading!

 

[Mapes]

I am puzzled with the energy conversion (actually I think I am easily get stuck with PE, KE and work done) when an elastic matter is being stretched or relaxed.

First of all, regarding the elastic hysteresis of a rubber, in the Force-extension graph, the area when the rubber is loaded is larger than that when unloaded. My interpretation is as follows. Please inspect whether I have any wrong or seemingly wrong concepts and kindly correct them.

While the rubber is being loaded, we do work on the rubber, by applying equal but opposite forces at the two end of the rubber, minor part of which is converted to the KE of the molecules as a result of work done against friction between molecular chains, as well as sound energy, major part of which is converted to the PE gained by the molecules as a result of the increased in separation of their mean positions. However, when it is being unloaded, the stored PE is converted to the KE of the molecules and sound energy. We do work to extend the rubber, which is lost to the surroundings. However, the rubber relaxes using its already stored PE, The difference in area is equal to the heat lost to the surroundings?

Secondly, regarding a matter which obeys Hooke's Law when being stretched (before the elastic limit), is there any gain in KE of the molecules of the matter? Or there is simply gain in strain energy? As the loading straight line in the force extension graph superpose with the unloading straight line, it seems that there is no heat lost to the surroundings.

Moreover, I don't understand the explanation for thermalexpansion using a simple PE-molecular separaion curve. The main idea is as follows: At absolute zero, the molecules have no KE and thus the molucules' PE is U_o, which is the lowest value. At a higher temperature, the molucules have some energy, which is above the minimum value U_o". The mean position of molecules is greater than the equilibrium position. When the temperature further increase, the mean position further increase non-symmetrically. As far as I know, it is the KE of the molucules. However, why does the increase in KE lead to an increase in PE? Is it because the mean separation of the molecules increases, so that the work done required to bring the molecules from infinity to a certain point decreases?

Much obliged for patient reading!

Your first two descriptions look fine.

On the thermal expansion issue: as you describe, the energy vs. separation curve of bonded atoms is not symmetric, though it is approximately parabolic for small deviations around the equilibrium point. (This is why elastic solids have the same stiffness in tension and in compression.)

I'm not sure what you mean when you say "it is the KE of the molecules." Also, no work is necessary to bring the atoms to the equilibrium point; they are attracted there spontaneously. But other than that, your description looks fine and is in agreement with the general understanding of atomic spacing.