Calculate DS_{universe} for the power cycle shown below. Is this cycle reversible, irreversible or impossible? 









Read : 
The key to this
problem is that the sign of ΔS_{univ} 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 ΔS_{univ}. 










Diagram: 
See the problem
statement. 







Q_{H} 
700 
kJ 
Given: 
T_{H} 
450 
K 



Q_{C} 
350 
kJ 

T_{C} 
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 ΔS_{univ} from: 






Eqn 1 











Because the cycle begins and ends
in the same state, S_{init} = S_{final} and ΔS_{cycle} = 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 ΔS_{hot} and ΔS_{cold} using the following
simplifications of the
definition of entropy. 












Eqn 2 


Eqn 3 











ΔS_{hot} 
1.556 
kJ/K 


ΔS_{cold} 
1.250 
kJ/K 












Now, we can plug
values back into Eqn 1 to
complete this problem. 
















ΔS_{univ} 
0.306 
kJ/K 












If the ΔS_{univ} is … 
... negative, the cycle is impossible 






... zero, the cycle is reversible 






... positive, the cycle is irreversible 













This cycle is impossible because ΔS_{univ} < 0. 










Verify: 
The assumptions made
in the solution of this problem cannot be verified with the given
information. 










Answers : 
This cycle is impossible because ΔS_{univ} < 0. 














