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Coefficient of performance of refrigerator

  1. Apr 28, 2017 #1
    1. The problem statement, all variables and given/known data
    The pV-diagram in Fig. P20.51 (See attached file) shows the cycle for a refrigerator operating on 0.850 mol of H2. Assume that the gas can be treated as ideal. Process ab is isothermal. Find the coefficient of performance of this refrigerator.

    2. Relevant equations
    K = QC/|QH - QC|
    pV = nRT
    Cp = Cv + R
    Isothermal expansion: Q = W = ∫p dV = nRT*ln(V2/V1)
    Constant volume: Q = nCvΔT
    Constant pressure: Q = nCpΔT
    3. The attempt at a solution
    QC = Qa-b + Qb-c = nRTa * ln(Vb/Va) + nCv(Tc - Tb) = paVa * ln(Vb/Va) + VbCv(pc - paVa/Vb)

    QH = Qc-a = n(Cv + R)(Ta - Tc) = pc(Cv + R)(Va - Vc)/R

    My answer K = QC/|QH - QC| = 0.462
    Correct answer K = 6.23

    What did I do wrong?
     

    Attached Files:

  2. jcsd
  3. Apr 28, 2017 #2

    TSny

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    Homework Helper
    Gold Member

    Did you leave out R somewhere in the last term on the right side?

    Does this give a postive or negative value for QH? In the formula K = QC/|QH - QC|, is QH considered as positive or negative?
     
  4. Apr 29, 2017 #3
    QC = paVa * ln(Vb/Va) + VbCv(pc - paVa/Vb)/R

    QH is heat the leaves the working substance so it should be negative. Apparently K = |QC|/( |QH| - |QC| ), thanks for the help I got the correct answer now.
     
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