Rubber bands and thermodynamics

In summary, polymers such as rubber are made up of long molecules that are tangled in a high entropy configuration. A simplified model of a rubber band can be represented by a chain of N links, each with two possible states. The total length of the rubber band, L, is the net displacement of the links. By using the thermodynamic identity, the tension force, F, can be expressed as a partial derivative of the entropy. From this expression, the tension can be calculated using the variables L, T, N, and l. The thermodynamic identity for this system is dU=TdS+fdl, where f can be solved for by f=dU/dl - TdS/dl.
  • #1
jason177
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Homework Statement



Polymers, like rubber, are made of very long molecules, usually tangled up in a configuration that has lots of entropy. As a very crude model of a rubber band, consider a chain of N links, each of length l. Imagine that each link has only two possible states, pointing either left or right. The total length L of the rubber band is the net displacement from the beginning of the first ling to the end of the last link.

Using the thermodynamic identity,express the tension force F in terms of a partial derivative of the entropy. From this expression compute the tension in terms of L,T,N, and l.

Homework Equations


I'm pretty sure the thermodynamic identity for this system is

dU=TdS+fdl

so then solving for f gets

f=dU/dl - TdS/dl

The Attempt at a Solution


so I found an equation for dS/dl but I have no idea how to get dU/dl in terms of L,T,N, and l.
 
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  • #2
Never mind, I got it
 

1. How do rubber bands stretch and contract?

Rubber bands are made from long chains of polymers, which are molecules composed of repeating units. When the rubber band is stretched, the polymer chains are pulled apart, causing them to align and store potential energy. When the tension is released, the polymer chains return to their original state, releasing the stored energy and causing the rubber band to contract.

2. Can rubber bands break due to thermodynamic processes?

Yes, rubber bands can break due to thermodynamic processes such as thermal expansion and contraction. When a rubber band is exposed to high temperatures, the molecules in the polymer chains vibrate more vigorously, causing the band to expand. This expansion can put stress on the band and potentially cause it to break. Similarly, when a rubber band is exposed to low temperatures, the molecules in the polymer chains slow down, causing the band to contract and potentially break.

3. What is the relationship between rubber bands and entropy?

Entropy is a measure of disorder or randomness in a system. When a rubber band is stretched, the polymer chains become more ordered and aligned, decreasing the entropy of the system. When the rubber band is allowed to contract, the polymer chains become less ordered and the entropy of the system increases. Therefore, the stretching and contracting of rubber bands can be seen as examples of entropy changes in a system.

4. How does the elasticity of rubber bands relate to thermodynamics?

The elasticity of rubber bands is a result of the thermodynamic properties of the material. When a rubber band is stretched, it stores potential energy in the form of stretched polymer chains. This potential energy is released when the band is allowed to return to its original state, causing the band to contract. This process is governed by thermodynamic principles such as the conservation of energy and the second law of thermodynamics.

5. Can rubber bands be used to demonstrate basic thermodynamic concepts?

Yes, rubber bands can be used as a simple and accessible tool to demonstrate basic thermodynamic concepts such as entropy, energy transfer, and phase changes. For example, stretching and contracting a rubber band can illustrate the concepts of entropy and energy storage and release. Additionally, exposing a rubber band to different temperatures can demonstrate thermal expansion and contraction.

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