# Homework Help: Coefficient of performance of refrigerator

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1. Apr 28, 2017

### Elias Waranoi

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

What did I do wrong?

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2. Apr 28, 2017

### TSny

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?

3. Apr 29, 2017

### Elias Waranoi

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.