# Example Problem with Complete Solution

8B-1 : Entropy Generation in a Compressor 2 pts
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 Tsurf in the 2nd Law equation to determine Sgen for only the turbine. Finish this problem by using the sign of Sgen 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
S1 1.42 kJ/kg-K Tsurf 410 K
S2 1.23 kJ/kg-K WS 128 kW
Find: Sgen ??? kW/K
Is this compressor internally reversible, internally irreversible or impossible?
Assumptions: 1 - The compressor operates at steady-state.
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 steady-state 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 THT = Tsurr, 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 Tsurf and Tsurr.
We were given the values of all the variables on the right-hand side of Eqn 1, so we can immediately evaluate (Sgen)comp.
(Sgen)comp -0.01205 kJ/kg-K
If the (Sgen)comp is  ... negative, the compressor is impossible
... zero, the compressor is reversible
... positive, the compressor is irreversible
This compressor is impossible because Δ(Sgen)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(Sgen)comp < 0. 