Let's look at a typical gas compressor used for large scale processes and not go into the details of the piece of equipment.
For the most part, the known data for such a calculation are pump efficiency, inlet conditions (T,P,flow) and the desired compression pressure. To find the unknown, outlet temperature, the laws of thermodynamics must be applied with more or less the following assumptions:
-the gas is a real fluid
-adiabatic and reversible process.
For this system the energy and entropy balances are, dH = W(input) and dS = 0.
To do a calculation by hand would require an E.o.S. and departure functions for enthalpy and entropy. Or a nice computer program that will facilitate the process.
The calculations could be simplified even more with different assumptions (i.e. ideal gas), but where do you draw the line, as to modeling a real piece of process equipment?
Assuming adiabatic makes the energy balance easier to work with because it allows you to avoid the second law of thermodynamics. but leaving Q out implies the energy that would have been meant for Q (and transferred to the surroundings) is now stuck in the system and adding heat to the flowing medium. This "added" heat increases the outlet temperature of the gas to a higher degree than would have Q existed.
Realistically, the gas would increase in temperature with increase in pressure, but the increase in temperature would not be huge, as seen with adiabatic assumptions.
Every system will have it's own list of assumptions, but how good are certain assumptions for modeling a process flow (Adiabatic, steady-state, reversible, etc..)?
Process Flow Assumptions
