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Thermodynamics of a rubber band

  1. Dec 23, 2011 #1
    1. The problem statement, all variables and given/known data
    For a stretched rubber band, it is observed experimentally that the tension f is proportional tot he temperature T if the length L is held constant. Prove that:

    (a) the internal Energy U is a function of temperature;

    (b) adiabatic stretching of the band results in an increase in temperature;

    (c) the band will contract if warmed while kept under constant tension.

    2. Relevant equations



    3. The attempt at a solution

    Start with the fundamental equation for a thermoelastic system

    du = T ds - f dl.

    Then I am stuck as to how to continue from here.

    I have tried tp then take the total differential of U:

    [tex] du = \frac{\partial U}{\partial S}_Lds +\frac{\partial U}{\partial L}_SdL [/tex]

    but that doesn't seem to help. I think I need to use a maxwell relation but I unable to figure out a suitable relationship to do the firs part. Any help will be greatly appreciated.
     
  2. jcsd
  3. Dec 24, 2011 #2

    rude man

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    Homework Helper
    Gold Member

    (a)
    Start with your equation du = T ds - f dl.
    What is dl here? Therefore, what is dW?
    OK, so then can you rewrite the first law in terms of U and Q, where dQ = Cl*dt?

    (b)
    First law again! dQ = 0, so how is U affected when W is added to the system?
    And what did part (a) say?

    (c)
    Go back to you 1st equation, now df = 0. How is W, and therefore l, affected?
     
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