# Example Problem with Complete Solution

6F-2 : Determining Whether a Power Cycle is Reversible, Irreversible or Impossible 4 pts
Consider the power cycle described by the diagram, below. Consider each of the following cases and determine whether the power cycle in each case is reversible, irreversible or impossible. a.) QH = 1150 kJ, Wcycle = 988 kJ
b.) QH = 1122 kW, QC = 207 kW
c.) Wcycle = 1660 kJ, QC = 499 kJ
d.) h = 74%

Read : What is the relationship between QC/QH and TC/TH for a reversible cycle?
Read about the Kelvin temperature scale. How does this allow you to determine the maximum theoretical efficiency of a thermodynamic cycle from TC and TH?
Note that the maximum efficiency by definition is associated with a reversible cycle.
Any real cycle always possesses some losses or friction and these irreversibilities reduce h below hmax.
Diagram: The diagram in the problem statement is adequate.
Given: TH 1870 K
TC 345 K
a.) QH 1150 kJ c.) Wcycle 1660 kJ
Wcycle 988 kJ QC 499 kJ
b.) QH 1122 kJ d.) h 74%
QC 207 kJ
Find: Reversible ? Irreversible ? Impossible ?
Assumptions: 1 - The system shown undergoes a power cycle.
Equations / Data / Solve:
To determine if each case is reversible, irreversible, or impossible we need to compare the actual efficiency of the case to the maximum efficiency.  There are 3 possibilities :
If the efficiency of the process equals the maximum efficiency, then the process is reversible.
If the efficiency of the process is less than the maximum efficiency, then the process is irreversible.
If the efficiency of the process is greater than the maximum efficiency, then the process is impossible.
Since the maximum efficiency, by definition, is associated with a 'reversible' cycle, the maximum thermal efficiency for any power cycle operating between thermal resevoirs TH and TC is: Eqn 1
The efficiency for each case is determined by: Eqn 2
Only in part (a) do we know Wcycle and QH but realizing: Eqn 3
or : Eqn 4
Combining Eqns 2 and 4 gives an equation we can use to resolve parts (b) and (c) : Eqn 5
Plug values into Eqn 1 to determine the maximum thermal efficiency : hmax 0.816
a.) Plug values into Eqn 2 to determine h : h 0.859
b.) Plug values into Eqn 5 to determine h : h 0.816
c.) Plug values into Eqn 5 to determine h : h 0.769
d.) Given : h 0.740
Verify: The assumptions made in this problem cannot be verified with the given information.
Answers : Part (a) The process is impossible because the efficiency of the process is greater than the maximum efficiency for any power cycle operating between thermal resevoirs at TH and TC.
Part (b) The process is reversible because the efficiency of the process equals the maximum efficiency for any power cycle operating between thermal resevoirs at TH and TC.
Part (c) The process is irreversible because the efficiency of the process is less than the maximum efficiency for any power cycle operating between thermal resevoirs at TH and TC.
Part (d) The process is irreversible because the efficiency of the process is less than the maximum efficiency for any power cycle operating between thermal resevoirs at TH and TC. 