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1st & 2nd Laws for SS, SISO Systems

Now, let's compare a real, adiabatic process such as a pump, compressor, turbine, or a nozzle to a comparable isentropic process.

2nd Law
(Entropy Balance):

For SS, SISO Systems:

1st Law :

2nd Law
(Entropy Balance) :

Processes for which we use isentropic efficiency are designed to have insignificant heat transfer, so we will assume our processes are adiabatic.
In this course, we will usually consider processes for which ΔEK ≈ 0 and ΔEP ≈ 0 because changes in the fluid velocity and elevation from the inlet to the outlet of the process are negligible. This is not always true !
If you know inlet and outlet elevations, velocities and/or pipe diameters, you should include changes in kinetic and potential energies in your analysis.

When ΔEK ≈ 0 and ΔEP ≈ 0 and the process is adiabatic:

1st Law:

Lesson
8C Blog

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Lesson 8C: page 2 of 21

The processes we are interested in usually have one inlet stream and one outlet stream. They are SISO processes.
Pumps, turbines, compressors and nozzles all fall into this category.
As usual, we are going to limit our analysis to processes that are operating at steady state.
We can write 1st Law and 2nd Law equations for this type of process, as shown here.
We are lucky here because we can often neglect changes in potential and kinetic energies.
These devices are generally not very tall, so changes in potential energy are almost ALWAYS negligible.
Changes in kinetic energy are occasionally important. If you know the inlet and outlet velocities, then you should include ΔEkinetic. Otherwise, you can probably neglect it.
When the process is adiabatic and changes in potential and kinetic energies are negligible, the 1st and 2nd Laws can be simplified a great deal, as shown here.
Now, let’s apply these equations to a real turbine and to an isentropic turbine in order to determine the isentropic efficiency of the real turbine.

1st & 2nd Laws for SS, SISO Systems

Ch 8, Lesson C, Page 2 - 1st & 2nd Laws for SS, SISO Systems