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Old Oct 18th 2018, 04:20 AM   #1
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Compressibility factor behavior

That happens to be my first post, so hi everyone!

I am currently trying to model the fluid mixture behavior and at the same time I am trying to understand it. Right now I struggle with understanding the behavior of the compressibility / compression factor.

I attached two figures I plotted.
First: isotherms in figure Z = f(pressure);
Second: isotherms in figure (Z - 1) / density = f(density).

So the question I have is more visible in the second figure as it is a single point at D = 60 mol / dm^3.

The question is: why do we observe this crossing of isotherms at around 60 mol/dm^3?
How to explain it from the thermodynamics point of view?
I struggle to find the answer.. it is not the critical point (even though for mixtures we should speak about the critical line - it is far from that region).

I attached the first graph because it is more common representation of a standard behavior and one can easily find similar figures for other fluids (with similar crossing point or region).

Another example here: https://media.springernature.com/ori..._Fig1_HTML.gif

Edit: sorry, I posted it in pre-university forum instead of the university one but I don't know how to move it. I would appreciate moving the thread, thanks!
Attached Files
File Type: pdf (Z-1) per D_50_50.pdf (139.8 KB, 10 views)
File Type: pdf Z=f(P_red).pdf (75.5 KB, 8 views)

Last edited by jackt; Oct 19th 2018 at 04:51 AM.
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Old Oct 26th 2018, 07:32 AM   #2
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Location: Brasília, DF - Brazil
Posts: 32
Good question!

First, we have to understand why change from $\displaystyle Z$ to $\displaystyle \frac{Z-1}{D}$.

This change sounds like when we migrate from mass to density, that is, we transform an extensive property whose comparison would be inconclusive, for an (intensive) property in which the comparison would occur in a more natural way.

Example: We do not compare who has a larger mass: 1 kg of water or 10 kg of air. It's rhetorical. We transform these factors into intensive properties that may, in fact, represent a state.

In our case, we're analyzing the difference between the actual and theoretical ($\displaystyle Z=1$) compressibility factor, and we divide by the number of moles in 1 $\displaystyle dm^3$. In theory, now we now know the expected variation for any substance that exhibits this density and temperature.

In the second plot, an interesting phenomenon happens. For the same temperature, the thermodynamic pressure increases as well as density. In case of Helium/Neon when $\displaystyle D\approx 60$, $\displaystyle P\approx 10^1$, which corresponds to the region that Z values ​are very close. If we divide by 60, becomes practically a point in your plot.
Work on:

General thermal systems


Micro-drop fluid mechanics

Last edited by mscfd; Oct 26th 2018 at 03:38 PM.
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Old Oct 31st 2018, 01:25 AM   #3
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Hi mscfd, thanks for your answer. I completely agree with what you said, it is reasonable from the mathematical point of view.

I am still looking for an answer which can be explained through thermodynamics. I would like to explain why do we observe this "interesting phenomenon" which you mentioned.

I'll post an answer if I manage to find anything. Thanks!
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behavior, compressibility, factor

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