1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
  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
    => dU = TdS+fdl
    S is constant in an adiabatic process so dS=0
    => dU = kLdL)
  4. Feb 4, 2010 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook