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Homework Help: Thermodynamics Problem - Adiabatic Reversible Process...

  1. Sep 30, 2015 #1
    The problem statement, all variables and given/known data
    A specific type of ideal gas has a specific heat capacity at constant pressure (cp=cv+R) that is a function of temperature T, such that cp=0.5+876T, where cp has units of J/kg/K and T has units of K. The gas, which is initially at T1 = 294 K and P1 = 1x105 Pa, undergoes a reversible adiabatic process such that its final temperature is T2 = 778 K. Calculate the pressure of the gas (in Pa) in this final state. Assume the following ideal gas constant: R = 287 J/kg/K. Recall that ds = cpdT/T – RdP/P.

    Relevant equations
    Reversible Adiabatic process:
    Entropy is 0 because this is adiabatic and reversible.
    Constituitive relation for entropy of such a process is:
    S2 - S1 = ∫12dS = 0
    dS = cp(dT/T) - R(dP/P) = 0

    Integrating I got:
    T1T2(0.5 + 876T).(dT/T) - 287∫P1P2(dP/P)
    876(778 - 294) + (0.5) ln (778/294) = 287ln(P2 / 100,000Pa)
    Getting 1488.810788 = lnP2

    But e1488.810788 is undefinable? I am confused? Did I integrate this wrong?
  2. jcsd
  3. Sep 30, 2015 #2
    That 876 looks very, very, very suspicious. Are you sure it's not 0.0876 or 0.00876 or, more likely, 0.000876? There's definitely something wrong here.

    Your methodology and arithmetic are correct, however.

  4. Oct 1, 2015 #3
    876 is part of "a +bt", the linear relationship between temperature and Cp, it's 0.5 + 876T
  5. Oct 1, 2015 #4
    What I'm saying is that there is something wrong with that value. It can't be correct.
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