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Thermodynamics - Maxwell Relations

  1. Jun 26, 2015 #1
    1. The problem statement, all variables and given/known data

    nipRMSi.jpg

    2. The attempt at a solution
    I've tried using the relation Cp = T(dS/dT), isolating "T" for T = Cv2(dT/dS) and using the maxwell relations to reduce the derivatives, reaching, T = Cv2/D (dV/dS), but i don't think this is the right way to do solve this problem, i couldn't find a similar example on the chapter either.
     
  2. jcsd
  3. Jun 26, 2015 #2

    TSny

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    ##T## is a state variable that can be thought of as a function of ##v## and ##P##: ##\;T(v,P)##.

    Consider ##dT## which will be something times ##dv## plus something times ##dP##. Can you express the coefficients of ##dv## and ##dP## in terms of ##\alpha## and ##\kappa_T##?
     
  4. Jun 28, 2015 #3
    Ok, so i've tried looking at dT as a function of both P and v and reached dT = (∂T/∂P)v dP + (∂T/∂v)P dv
    And after reducing the derivatives, dT = KT/α dP + 1/vα dv , and using the problem's KT and α.
    dT = 1/D dv + Ev2/D dP
    dT = 1/D dv + EPava2/(PbD) dP
    Tb = Ta + (vb - va)/D + EPava2 Ln(Pb/Pa)/D

    which is close but still different from the answer given on the question and i can't find a reason why, what did i miss?
     
    Last edited: Jun 28, 2015
  5. Jun 28, 2015 #4

    TSny

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    Check the sign of the first term on the right. Otherwise, that looks good.

    Can you express ##\ln(P_b/P_a)## in terms of ##v_a## and ##v_b##?
     
    Last edited: Jun 28, 2015
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