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Thermodynamics Relations

  1. Mar 6, 2017 #1
    1. The problem statement, all variables and given/known data
    I need to prove the following equation:
    upload_2017-3-7_0-57-1.png

    2. Relevant equations
    The 4 maxwell relations and their derivations:
    https://en.wikipedia.org/wiki/Maxwell_relations
    3. The attempt at a solution
    I started out with the fundamental equations of
    dU=TdS - PdV
    and as dS=0, and Cv=(dU/dT)v;
    I simplified this to:
    dT= -P(dV/Cv)

    I did a similar procedure, only this time using the definition of enthalpy to get to
    dT = V(dP/Cp)

    But I don't know how to proceed from here. I've tried looking at the relations but i dont know what Im missing or if I'm going about this totally wrong...

    Thanks in Advance
    Cheers
     
  2. jcsd
  3. Mar 7, 2017 #2
    The Maxwell relations are not needed to solve this problem.

    You can solve this problem by working with the following equations:
    $$dS=\left(\frac{\partial S}{\partial P}\right)_VdP+\left(\frac{\partial S}{\partial V}\right)_PdV\tag{1}$$
    $$dS=\left(\frac{\partial S}{\partial T}\right)_PdT+\left(\frac{\partial S}{\partial P}\right)_TdP\tag{2}$$
    $$dS=\left(\frac{\partial S}{\partial T}\right)_VdT+\left(\frac{\partial S}{\partial V}\right)_TdV\tag{3}$$
    $$dT=\left(\frac{\partial T}{\partial V}\right)_PdV+\left(\frac{\partial T}{\partial P}\right)_VdP\tag{4}$$

    Chet
     
    Last edited: Mar 8, 2017
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