1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted