Quick thermodynamics question

  • Thread starter ryanwilk
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  • #1
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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.
 

Answers and Replies

  • #2
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(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)
 
  • #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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