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Is Cp/Cv applicable to steam to calculate?

Thursday, June 23, 2016   By: P I [1983] 3 Stars
I recently have talked with a steam expert and he has given me a rough analysis of the power consumption to compress steam from low pressure to higher level. What is stunning to me is that he used Cp/Cv to calculate the power necessary. But, I just want to know how Cp/Cv can be applicable for steam as its just vapour, not gas.
A fluid can be vapour when its below its critical temperature and critical pressure. Above that its gas because it cant be liquefied by applying pressure. For steam, critical temperature is 375C and critical pressure 220 bars. Then how the Cp/Cv formula can be applicable to steam to calculate power to compress it?

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Friday, June 24, 2016   By: Ross [390] 5 Stars
I cannot comment on the applicability of specific heats too much to your application, what I can say is Cv is for constant volume and Cp is for constant pressure. They are usable in water and steam work, but they are not found steam tables except for a few. Cp is applied with liquids such as water or solids.

When they are used in this form Cp/Cv then it is equal to k or ratio of specific heats. Of course we think of these when applying them to air or ideal gases.

But, I just do not see the steam reciprocating compressor as a constant volume process or constant pressure process. Sure we can force the applicability. So, since the reciprocating steam compressor has pistons, stroke, compression, area - such that there is an ever changing volume and pressure - as well as strokes per minute, then the pLAN formula seems most fitting.


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Saturday, June 25, 2016   By: P I [1983] 3 Stars
Problem is, I have talked with a steam expert and he calculated the power consumption during steam compression by using that formula. Cp/Cv is used in gas compression formula and related calculations. But, there are differences in gas and vapour. Any gaseous fluid is vapour when its temperature is below the critical temperature and gas when its above that level. For water/steam, the critical temperature is 375C.

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Sunday, June 26, 2016   By: [50] 4 Stars
Mr. P.I.:

I hope not to be misleading, and I am not sure of the process you plan to follow, but the compression of steam you mention looks very much like the compression of other fluids, like ammonia exiting evaporators in refrigerating plants... In those cases, the compression follows a certain politropic, and if an adiabatic process is envisaged, even as a first aproach, then the politropic exponent will become k or Cp/Cv,as Mr Ross already commented.

In some problems related with steam, a certain value for this ratio is used, such as 1,33 being taken in nozzles estimation instead of the 1,4 when air is the working fluid perhaps that is why the expert you mention used this ratio, Cp/Cv. Both values will vary slightly with pressure and temperature, and I believe are difficult to obtain, as far as I know.

Claudio Molanes

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Thursday, June 30, 2016   By: P I [1983] 3 Stars
Actually, the expert to whom I have discussed the problem considered steam to be just like an ideal gas during compression and that makes power consumption too high. Thats the root of all problems here.

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Thursday, June 30, 2016   By: [50] 4 Stars
Thanks for your reply In fact, considering steam as an ideal gas may not give wrong results after all, as first approach it is usually the way. As the conditions of steam go further and further away from the saturation line in the chart as it si being compressed, the more the superheated steam approaches the ideal gas conditions. When this happens, then the enthalpy will be exactly Cp times the temperature, and the internal energy Cv times the temperature, and this condition is readily seen from the corresponding lines in the Mollier chart, or the T-s charts.

Compressing gases or vapours is usually expensive in terms of energy, and that is why, if possible, cooling is performed trying to compress near the isothermal line and as far as possible from the adiabatic,to save energy consumed by the driving engine. In the case of rotary compressors, this can only be done by intercoolers when compressing in several stages, in reciprocating compressors water-cooling of the cylinders certainly helps as well.

If cooling is done, actually the evolution line on a T-s chart will give a compression which tends to follow the saturation line, bending leftwards from the vertical, isoentropic line, so strictly, what we would be compressing will not tend much to behave as an ideal gas, so you are right, but I believe the results of the power estimations will not differ too much from the real thing.

Claudio Molanes

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Saturday, July 02, 2016   By: P I [1983] 3 Stars
In that case, kindly tell me one thing. What will happen if we compress steam with water together. As for example. we have some water and steam only inside a cylinder with thick non-conducting walls. The cylinder has a movable piston fitted to an end. In short, no heat can enter or leave the system.
Now, if we compress stem and water together with the piston, do the compression will follow the saturation graph?

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Wednesday, July 12, 2017   By: Kent mayhew [2161] 0 Stars
The reason that isobaric Cp heat capacity is greater than isometric Cv is that isobaric involves expansion. Remember our atmosphere has mass, so in order for a system to expand it must displace that mass. And this requires work. So Cp requires work plus the energy to heat the gas , while Cv only requires the energy to heat.

So for all gases and/or steam the work required to expand a given volume is the same that being the work required to displace our atmosphere by a given volume.

Hence the ideal gas constant R - used in physics not by engineers is really nothing more than a representation of the work required to displace our atmosphere by a mole of gas molecules. Note the work required to displace our atmosphere is lost work - it can never be recovered

I discuss the above in my paper on kinetic theory in Progress in physics July 2017
paper: A new perspective in kinetic theory and heat capacity link

also visit my website

hope this bring clarity to a traditionally muddled subject matter

cheers kent mayhew


Click on picture for full size view or to view PDF!

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superheated steam ideal gas
By: [50]

Mr. Pradeep:

Steam behaves well as an ideal gas if not too close to the saturation line if you place yourself on a Mollier chart, when the temperature and enthalpy lines coincide and are straight, horizontal lines, then it behaves as ideal, and this you can easily see on the chart.

I would rely though most on the steam values given by the chart or steam tables, because they are confident independently of the region , e.g. they stand both for ideal and real gas, but the ideal gas equation ....   Read All
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