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Quick thermodynamics question

  1. Feb 4, 2010 #1
    I need to show that adiabatic stretching of a rubber band causes an increase in temperature.

    I've managed to reduce the 1st Law of Thermodynamics to dU=kLdL.

    k,L and dL are all positive so dU is positive - the total internal energy increases.

    But does this immediately imply that the temperature also increases?

    Any help would be appreciated.
    Thanks.
     
  2. jcsd
  3. Feb 4, 2010 #2
    (I've basically done:
    dU = dQ + dW
    dQ = TdS and dW=-PdV+fdL
    => dU = TdS-PdV+fdl
    Assume constant volume => dV=0
    f=kL
    => dU = TdS+fdl
    S is constant in an adiabatic process so dS=0
    => dU = kLdL)
     
  4. Feb 4, 2010 #3

    Mapes

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    I'd start with [itex](\partial T/\partial L)_S[/itex] and start applying differential identities, Maxwell relations, etc., to get it in terms of derivatives whose sign you know.

    For example, are [itex](\partial S/\partial T)_L[/itex], [itex](\partial L/\partial T)_F[/itex], [itex](\partial L/\partial F)_T[/itex] positive or negative for an elastomer?
     
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