Consider the compressor shown below. 





Determine the entropy
generation rate within the compressor in kW/K. Is this compressor internally
reversible, internally
irreversible or impossible? 


Read : 
This is a
straightforward application of the 2nd Law in the form of an entropy balance on an open system. Use T_{surf} in the 2nd Law equation to determine S_{gen} for only the turbine. Finish this problem by using the sign of S_{gen} to determine whether the compressor is impossible, internally reversible or internally rreversible. 










Diagram: 
See the problem
statement. 










Given: 
m 
0.41 
kg/s 



Q 
27 
kW 

S_{1} 
1.42 
kJ/kgK 



T_{surf} 
410 
K 

S_{2} 
1.23 
kJ/kgK 



W_{S} 
128 
kW 










Find: 
S_{gen} 
??? 
kW/K 

















Is this compressor internally reversible, internally irreversible or impossible? 










Assumptions: 
1  
The compressor operates at steadystate. 


2  
Kinetic and potential energy changes
are negligible. 


3  
Shaft
work and flow work are the only forms of work that cross the system boundary. 


4  
Heat loss
from the compressor
occurs at a constant
and uniform temperature
of 410 K. 










Equations
/ Data / Solve: 


















We can determine the entropy generation from an entropy balance on the compressor. 











The entropy balance equation for a SISO process operating at steadystate that exchanges heat only with the surroundings is: 







Eqn 1 











Because we are
interested only in the entropy generation inside the turbine, the temperature at which heat transfer occurs is the surface temperature of the turbine, 410 K.
If we used T_{HT} = T_{surr}, we would obtain the total entropy generation for the process. This would include both the entropy generated inside
the turbine and the entropy
generated due to the irreversible nature of heat transfer through a finite temperature difference, that is between T_{surf} and T_{surr}. 











We were given the
values of all the variables
on the righthand side of Eqn 1, so we can immediately evaluate (S_{gen})_{comp}. 







(S_{gen})_{comp} 
0.01205 
kJ/kgK 











If the (S_{gen})_{comp} is … 
... negative, the compressor is impossible 






... zero, the compressor is reversible 






... positive, the compressor is irreversible 













This compressor is impossible because Δ(S_{gen})_{comp} < 0. 










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










Answers : 
This compressor
is impossible because
Δ(S_{gen})_{comp} < 0. 













