# Theoretical Torricelli Vacuum Test: Impurity Impact on Pressure

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• hubajs

#### hubajs

TL;DR Summary
In the case of theoretical Torricelli vacuum test, when no impurities left in the vacuum: Is the vacuum 0Pa for 1m height (with 760mm of Hg) or 10m height of the test column?
Does the real vacuum pressure/underpressure depends only on the amount of impurities?

In the case of theoretical Torricelli vacuum test, when no purities left in the vacuum:
Is the vacuum 0Pa at 1m height (with 760mm of Hg) and also the same at 10m height (also with 760mm of Hg) of the test column?
Theoreticaly is the vacuum (0 Pa) the same at 1m and at 1km of the test column height?

see the immage.

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Summary: In the case of theoretical Torricelli vacuum test, when no impurities left in the vacuum: Is the vacuum 0Pa for 1m height (with 760mm of Hg) or 10m height of the test column?

So theoreticaly is also 0 Pa at 1 km of the test column height?
. . . . . and how would you propose to get a column 1km high? (Hint, perhaps on Jupiter?)

This is not a question about how to engineer a structure (thats why I use the word "theoreticaly").
But OK, let's modify: "So theoreticaly is also 0Pa at 10m of the test column height?"

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Ah I understood your "Jupiter" comment now! Thank you, I clarify:

By the column height I mean the "H1" and "H2" in the new image here below.
I am interested by "H1" and "H2" difference impact to the vacuum "p1" and "p3" difference.

Theoretical question: When pressure p1=101,1325Pa. Is also the p3=101,1325Pa?

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sophiecentaur
@hubajs
But not your second ( When pressure p1=101,1325Pa is not a vacuum )

for a first order evaluation,
Knowing that P(h) = ρ g h , would you be able to give your own answer for the difference, if there is a difference, in pressure between the two heights of the "vacuum" column.

@256bits
my bad, p1=101,325kPa is copy paste error. The question was meant to be this:
Theoretical question: When pressure p1=0Pa. Is also the p3=0Pa?

Assumption:
1) reality: vacuum presure "p" can be within an order 0Pa < p < 3.325Pa (for -98Pa underpressure from 101,325kPa)
2) theory: vacuum mass density for theoretical 0Pa is ρ=0kg/m3

Evaluation of my example with P(h) = ρ g h :
mercury part: height doesn't change => pressure difference is 0Pa.
vacuum part: theoreticly there is ρ = 0 kg/m3
vacuum part: realistic, in case of impurities in the vacuum ρ > 0 kg/m3 => Δp > 0 and some pressure difference may occure, but this will be within this range: 0 < p3 < p1 < approx 3.325Pa (for -98kPa underpressure from 101,325kPa)

Conclusion:
theoretical case 1: no impurities in the vacuum 0Pa
=> no matter how small or high is the "h" (1cm or 100m).
=> p1 = p3 = 0Pa will still be the same for all heights cases

This is the goal of my original question. Is my conclusion correct?
I don't believe my conclusion, that's why I ask here.

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256bits
I think we should ask someone who actually does work with vacuum and how they do deal with height of the container in their calculations. At some small height the pressure difference becomes insignificant from top to bottom.

If the height of the container is small and the vacuum high ( I would think that the mean free path would be a more predominant criteria of consideration ) the pressure difference due to gravity should not matter.

If the height is great, than we could run into problems.
Such as.
Suppose your tube, or column is so high that it extends several miles upwards so that we could consider the top end above the atmosphere. ( In that case we could consider the pressure to be that of space ). If we place our pump at the top, could we achieve a better vacuum further down the column.
In fact, if the column has been filled with air, the pressure differential would be exactly that of the surrounding atmosphere.
Of course that is a extravagant example, but it does exhibit that the placement of the measuring instrument of the vacuum, whether at the top or the bottom can give different readings.

We should wait and see what the people who do work with vacuums have to say, and if they ever do run into something of the sort with tall columns.

Summary: In the case of theoretical Torricelli vacuum test, when no impurities left in the vacuum: Is the vacuum 0Pa for 1m height (with 760mm of Hg) or 10m height of the test column?

I don't understand your question- the 'empty space' is actually not a perfect vacuum due to vapor pressure of the fluid. Are you asking how the density of that vapor varies in height due to gravity?

Lord Jestocost
OK, lets, see. I am the most interested by theoretical explanation where I assume p1 = p3 = 0Pa for all heights which is quite weired to me.
Please everyone, let's stay within Newton's world, no quantum physics. :-)

the 'empty space' is actually not a perfect vacuum due to vapor pressure of the fluid.
I need theoretical advice on Torricellian vacuum pressure and tube length relation to vacuum pressure (see the new image here).
What happen when I use 10000mm long tube? Will the h2=8240mm?
Is the Torricellian vacuum pressure p = 0 Pa for 1000 mm long tube?
Is the Torricellian vacuum pressure p = 0 Pa for 10000 mm long tube? Also?

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Not a vacuum user nor expert in nothing! Just amused by the theoretical question, irrespective of practicalities.

Would the nature of the "impurity" be important?
If contaminant were liquid would the decrease in pressure be limited to svp.
I guess material adsorbed on the tube surface would similarly mitigate the PV decrease in pressure by providing a reserve which produces more gas as the pressure falls.
I suppose some solids might have significant vp. Though I can think of only one very unlikely candidate for which I've found data, I wonder about greases and adhesives.
As for the 100m or longer tube, would the vp of the mercury limit the lowest pressure to around ##10^{-4}## Pa?

what is "svp" and "PV"?

What happen when I use 10000mm long tube? Will the h2=8240mm?

Yes!
The length and cross-sectional area of the tube have no effect on the height of the fluid column of a Torricelli barometer. The pressure at the top of the fluid column is always equivalent to the vapor pressure of the liquid at the ambient temperature.

Nature of the "impurity" will not be important.

I just need to know the theory limit of vacuum pressure I have to take into account in my calculations.
I prefer to stay within the theory frame and not enter to the real world for now.

My further application lowest pressure I wish to reach should be between 0.1 Pa and 1.0 Pa.

Yes!
The length and cross-sectional area of the tube have no effect on the height of the fluid column of a Torricelli barometer. The pressure at the top of the fluid column is always equivalent to the vapor pressure of the liquid at the ambient temperature.

Thank you!

In case I am on the good way:
What is the magnitude of usual real pressure that can be acquired during the Torricelli test with mercury when we use nice clean tube and a clean mercury?
10 Pa
1.0 Pa
0.1 Pa
0.01 Pa
0.001 Pa
less ?

Note: Something is here, but not figured out usual Torriceli vacuum pressure: Orders_of_magnitude_(pressure)

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. . . And the mercury will keep evaporating to fill any low pressure space at the same vapor pressure. (An idea worth bearing in mind.)
Extremely high vacuum has to be maintained by sweeping odd molecules away (from internal surfaces etc.) as they turn up.

Thank you for answers, I have one last question for finalizing my reflection.
Note: Mercury evaporation will take some time and vacuum presure degrades within minutes or hours (so I ignore).

Please, the folowing question is for my better vacuum understanding.
I really appreciate your time you spent with my topic:

When I mutliply the height "h" or "diameter" from initial size 10 times (ie: every 5 seconds), according the volume change, the pressure of ideal gas will change according:

P2 = P1/(V2/V1)
- Isothermal process
Is it?

Then changing the "empty space" by "height" OR "diameter" size, following changes (from initial 0.174Pa) will be reached by volume difference.

height change
 d (m) S (m2) h (m) V (m3) p (Pa) 0,01 0,0000785 0,01 0,000000785 0,174 0,01 0,0000785 0,1 0,00000785 0,0174 0,01 0,0000785 1 0,0000785 0,00174 0,01 0,0000785 10 0,000785 0,000174

tube diameter change
 d (m) S (m2) h (m) V (m3) p (Pa) 0,01 0,0000785 1 0,0000785 0,174 0,1 0,00785 1 0,00785 0,00174 1 0,785 1 0,785 0,0000174 10 78,5 1 78,5 0,000000174

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