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4F-2 : Efficiency of a Power Cycle
2 pts
The net work of a power cycle is 8 x 106 Btu and the heat transfer to the cold reservoir, QC, is 12 x 106 Btu. What is the thermal efficiency of the cycle ?   Figure 1.
Read : This one is a straightforward application of the definition of the the 1st Law and the efficiency of a power cycle.
Given: Wcycle =
8.0E+06
 Btu
QC =
1.2E+07
 Btu
Find: ηcycle
???
Assumption: - The cycle only exchanges heat with the two thermal reservoirs.
Equations: 1st Law applied to the heat engine: Equation. Eqn 1
Definition of efficiency : Equation. Eqn 2
Degree of freedom analysis: 2 eqns in 2 unk
Solve equations: Solve Eqn 1 for QH : Equation. Eqn 3
     
QH =
2.0E+07
 Btu
Next, plug numbers into Eqn 2 : ηcycle
0.400
Verify assumption: The only assumption cannot be verified.
Answer questions: ηcycle
40%