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Homework Help: Archived Adiabatic expansion in a steady flow question

  1. Sep 17, 2010 #1
    I an working on a problem in the text "Mechanics and Thermodynamics of Propulsion" 2e. The problem states a perfect gas with molecular weight M=20 and a specific heat ratio of Y=1.2 expands adiabatically in steady flow from a pressure of 6MPa, a temperature of 3000K, and a velocity of 200 m/s to a final pressure of 0.101 MPa. If the final temperature is 1800K and the final velocity is negligible, what is the work done

    I know that adiabatic means no heat in or out of the system so dq=0
    Y=cp/cv and cp=cv+R
    dq=de+dw

    My attempt:
    First i find R=8314.3/20=415.715
    then i find cv by cv=R/(Y-1) cv=2078.58
    thus dw= (-de) where de=cv(T2-T1)
    my answer for the work done is 2494.29 kJ/kg however the books answer is 3013 Kj/kj

    what am i doing wrong?
    thanks for your help
     
  2. jcsd
  3. Sep 19, 2016 #2
    dw = m*[(e2-e1)+(p2/rho2 - p1/rho1)+(v2^2 / 2 - v1^2 / 2)]
    so, v2 = 0 , p/rho = RT(p=rho*R*T)
    and Cp=Cv+R finally dw = CP(T2-T1) - v1^2 / 2

    you do not think V1 ok?
     
  4. Sep 19, 2016 #3
    This looks correct to me. Nice job of applying the open system version of the 1st law.
     
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