Example Problem with Complete Solution

7C-1 : Entropy Change of the Universe for a Cycle 3 pts
Calculate DSuniverse for the power cycle shown below. Is this cycle reversible, irreversible or impossible?
     
     
 
Read : The key to this problem is that the sign of ΔSuniv determines whether a process is impossible, reversible or irreversible. Use the definition of entropy to evaluate ΔS for each reservoir and for the cycle and add them up to get ΔSuniv.
Diagram: See the problem statement.
QH 700 kJ
Given: TH 450 K QC -350 kJ
TC 280 K
Find: Is this cycle reversible, irreversible or impossible?
Assumptions: 1 - The cycle only exchanges heat with the hot and cold reservoirs shown.
Equations / Data / Solve:
In this problem, the universe consists of the cycle, the hot reservoir and the cold reservoir. We can calculate ΔSuniv from:
Eqn 1
Because the cycle begins and ends in the same state, Sinit = Sfinal and ΔScycle = 0.
By definition, the temperatures of the thermal reservoirs remain constant and there are no irreversibilities within the reservoirs because no process takes place in either reservoir. As a result, it is relatively simple to calculate ΔShot and ΔScold using the following simplifications of the definition of entropy.
Eqn 2
Eqn 3
ΔShot -1.556 kJ/K ΔScold 1.250 kJ/K
Now, we can plug values back into Eqn 1 to complete this problem.
ΔSuniv -0.306 kJ/K
If the ΔSuniv is ... negative, the cycle is impossible
... zero, the cycle is reversible
... positive, the cycle is irreversible
This cycle is impossible because ΔSuniv < 0.
Verify: The assumptions made in the solution of this problem cannot be verified with the given information.
Answers : This cycle is impossible because ΔSuniv < 0.