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

• 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.