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Homework Help: Entropy Difference of an Unknown Gas (not an ideal gas)

  1. Dec 17, 2015 #1
    1. The problem statement, all variables and given/known data
    Temperature, pressure and volume measurements performed on 1 kg of a simple compressible substance in three stable equilibrium states yield the following results.

    State 1 (T1=400 C , V1= 0,10 m3, P1=3 MPa)
    State 2 (T1=400 C , V1= 0,08 m3, P1=3,5 MPa)
    State 3 (T1=500 C , V1= 0,10 m3, P1=3,5 MPa)

    Estimate the difference in entropy S2-S1

    2. Relevant equations
    We don't know the gas. So I can't assume this is an ideal gas and I can't go to thermodynamics tables. I don't know the relevant equation.

    3. The attempt at a solution
    First, I didn't get why the question identifies state 3. I think we can completely ignore state 3 because the question is entropy difference between state 2 and state 1.

    This is clearly a compression process, (volume decreases, pressure increases) but temperature stays still. But when a gas is compressed, its pressure and temperature rises. So there must be heat transfer going on.

    Entropy change = Sgen + Q/T
    But we don't know the entropy generation so we can't go from here.

    I assume I need a relation related with volume and pressure that yields entropy but in constant temperature. Is there a relation like that?
  2. jcsd
  3. Dec 17, 2015 #2
    Yes. There is a relation for the partial derivative of entropy with respect to pressure at constant temperature in terms of the P-V-T properties of a gas.
    Have you studied that yet? Are you learning about the Maxwell equations in your course yet? The derivation starts off with dG=-SdT+VdP.
  4. Dec 17, 2015 #3
    Yes we are learning maxwell equations in fact. That derivation must be dG=-SdT+VdP+∑μidNi from my notebook.

    The relation you have mentioned is probably -(∂S/∂P)T=(∂V/∂T)P and with that equation my solution would include state 3. But how could i go with this equation I'm not clear. Although I'm very doubtful, can I think the above equation as -(ΔS/ΔP)between state 1-2=(ΔV/ΔT)between state 2-3? Otherwise I don't know what to do.
  5. Dec 17, 2015 #4
    Yes, that's what you do. They said "estimate" the entropy change, so using finite differences is OK.
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