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Calculating the change in entropy of an ideal gas under compression

  1. Oct 17, 2014 #1
    1. The problem statement, all variables and given/known data
    Initial
    pressure: 140kPa
    Temperature: 25C or 298K
    Volume: 0.14m^3

    Final
    Pressure:1.4MPa or 1400kPa

    It uses index compression, n=1.25. So PV^1.25 = constant.

    c_p = 1.041kJ/kg.K and c_v = 0.743 kJ/kg.K

    2. Relevant equations
    ¥ = c_p/c_v
    ΔS=c_v*ln(Tf/Ti) + R*ln(Vf/Vi) [i think]
    3. The attempt at a solution
    I found ¥ to be 1.4012
    PV^n = 12 therefore Vf = 0.0222

    140*0.14^1.25=11.989
    1400*Vf^1.25=11.989
    Vf^1.25=11.989/1400
     
  2. jcsd
  3. Oct 17, 2014 #2

    PeterDonis

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    Staff: Mentor

    So far your work looks OK. Where are you stuck?
     
  4. Oct 17, 2014 #3
    hi,

    So where do i use the Vf? I don't I use "ΔS=c_v*ln(Tf/Ti) + R*ln(Vf/Vi) " as part two asks for the final temperature. So part one wants me to find the entropy, but i dont know how to do this.
     
  5. Oct 17, 2014 #4

    PeterDonis

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    2016 Award

    Staff: Mentor

    Are there any other equations that involve the entropy? For example, for the special case (which it seems would apply to your problem) where the gas does not exchange heat with the environment?
     
  6. Oct 17, 2014 #5
    I don't see any problem with solving for the final temperature first and then substituting for the delta S. Alternately, you can solve for the temperature ratio in terms of the volume ratio by combining the polytropic relationship with the ideal gas law:
    ##\Delta lnT-\Delta lnV=\Delta lnP##
    ##n\Delta ln V=-\Delta lnP##

    Solve for ##\Delta lnV## and ##\Delta lnT## in terms of ##\Delta lnP##

    Chet
     
    Last edited: Oct 18, 2014
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