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Commentator

Join Date: Dec 2008
Location: Philippines
Posts: 73

Compressors, Cylinders and Specific Heat Capacity

12/23/2008 12:49 AM

My question is about the external work of compression and the legendary cylinder's "specific heat capacity"

Here is a question in case someone here understands thermodynamics, especially the thought experiment I will call the "legendary cylinder".

I'm trying to understand how the legendary "frictionless leakproof cylinder" translates over to things that happen in a real air compressor. The legendary cylinder is used to explain specific heat capacity of air. At constant volume, with the piston locked in place, the one pound of air inside is heated and it takes 0.1689 BTUs to heat it one degree F. Unlock the piston so the heated pound of air can expand, and an additional 0.0686 BTUs is needed to heat the air one degree. The maximum is with pressure held constant inside since pressure outside (the atmosphere) is also constant.

The spec. ht. cap. at constant volume or Cv is 0.1689, at constant pressure or Cp it's 0.2375, and the difference is 0.0686. Cv is the internal energy and is used to describe isothermal compression when the net temperature change during compression is zero. Cp/Cv is the air index n or 1.406 maximum, which is used to describe adiabatic compression, the opposite of isothermal in which all compression heat is retained in the system. The difference is the gas constant R, for example in ft-lbs the 0.0686 translates to about 53.2 ft-lbs of work per pound of air per deg. F.

The meaning of the difference between the specific heat capacities at constant volume and constant pressure is clear in the legendary cylinder. The extra heat is needed to resist the external pressure of the atmosphere on the back side of the piston since expansion is taking place against this constant back pressure. But the legendary cylinder is not a compressor. I am trying to answer the question, What exactly does this number do in a real compressor? It must be nothing to do with the piston in the compressor pushing aside atmosphere, because then it would have to apply in compressors that never see any atmosphere like closed cycle or booster compressors. So the analogy doesn't transfer over to real compressors.

When the number does come into play in compressor equations is the non-isothermal processes where compressing air takes more work because while you are compressing it, heat is generated which results in the air trying to expand due to the heat buildup, in addition to the pressure being generated by the change in volume. Therefore I think that the expansion and extra work required as revealed by the legendary cylinder must refer to the work of resisting heat in non-isothermal compression. But the textbooks don't come out and say this for some reason. They just call this gas constant "external work" and no good explanation for this terminology is forthcoming.

Except that apparently it is in reference to what the legendary cylinder has to do, push aside atmosphere. I don't see how this relates to real compressors. To complicate things, thermodynamics includes terminology like "the machine is driven by external work done on it by another machine" or "the machine does external work on a separate device". This use of the term "external work" seems completely unrelated.

So in short I am trying to clear up some terminology issues before I can really know what the compressed air textbook is saying. Thanks.

Luther

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Join Date: Jan 2006
Location: Tamworth, UK.
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#1

Re: Compressors, Cylinders and Specific Heat Capacity

12/24/2008 4:48 AM

Hello Lutherman

Cant stop now to answer - I am away for Xmas - but I am interested to hear other answers when I get back.

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