2 replies to this topic

[tophat22]

The question reads:

In a large refrigeration plant it is necessary to compress a fluid, which we will assume to an ideal gas with constant heat capacity, from a low pressure P1 to a much higher pressure P2.

a. If the compression is done in a single compressor that operates reversible and adiabatically, obtain an expression for the work needed for the compression in terms of mass flow rate, P1, P2, and the initial temperature, T1.

b. If the compression is to be done in two stages, first compressing the gas from P1 to P*, then cooling the gas at constant pressure down to the compressor inlet temperature T1, and then compressing the gas to P2, develop an expression for the work needed for the compression. What should the value of the intermediate pressure be to accomplish the compression with minimum work?


Any help would be appreciated!

[fallah]

The intermediate pressure to accomplish the compression with minimum total work is the geometric mean of the initial and final values.
P1=Initial pressure
P2=Final pressure
P=Intermediate pressure
P=(P1*P2)^1/2
It means that, the pressure ratio in both stages is the same and equal to (P2/P1)^1/2,provided that the gases being cooled to initial temperature in the intercooler.

[Art Montemayor]

Tophat:

What you are asking is found in just about every thermodynamics text book I have in my library. It is analytically expounded in thermo and the derivation of the power requirements (which you are citing) equation is detailed step-by-step. The subject of how to determine the pressure distribution in multistage compressors is another subject and few thermo texts will discuss that one. As fallah has indicated, the basic assumption to multistage compression is that the work is evenly divided between stages. The equation that fallah cites is the one for 2-stage compression.

What is the reason for your query? Have you not covered this subject in thermo class? Here I have to assume that you are taking a thermo course. Please give us ALL the facts if you want us to help you with anything you don't understand. You can pretty well give up on having us on the Forum do your homework assignments, so I won't go into that one. But if you need help on any specific point, tell us what you have, why you are having problems with it, and any specific questions.