Example Problem with Complete Solution

4F-2 : Efficiency of a Power Cycle 2 pts
A power cycle produces 2.4 x 108 Btu and rejects 7.1 x 108 Btu of heat to the surroundings. Calculate the thermal efficiency of the cycle.
Read : This one is a straightforward application of the definition of the the 1st Law and the efficiency of a power cycle.
Diagram :
Given: Wcycle 2.4E+08 Btu QC 7.1E+08 Btu
Find: hcycle ???
Assumption: 1 - The cycle only exchanges heat with the two thermal reservoirs.
Equations / Data / Solve:
1st Law applied to the heat engine:
Eqn 1
Definition of thermal efficiency :
Eqn 2
Degree of freedom analysis: 2 eqns in 2 unknowns: QH and h.
Solve Eqn 1 for QH :
Eqn 3
QH 9.5E+08 Btu
Next, plug numbers into Eqn 2 : h 0.2526
Verify: The only assumption cannot be verified.
Answers : h 25.3 %