Inverted Mercury Rod: Will Gas Pressure Change?

[phymatter]

if i take a thin glass rod sealed at one end fill some gas at 1 atm in it and then add 760mm mercury and invert the rod then will the mercury not fall?

also will the pressure of the gas change?

i do not see any reason for this to happen! :(

Thanks in advance!

 

[porcupine6789]

Somebody correct me if I'm wrong but 1atm is 760mm of Hg. So when you invert the tube the pressure exerted by the air and Hg is the same so therefore the Hg will not fall. And I don't think the pressure of the air would change.

 

[K^2]

There is no gas in the rod itself. (Well, there are some mercury vapors, but their pressure is nearly zero.)

 

[Andy Resnick]

if i take a thin glass rod sealed at one end fill some gas at 1 atm in it and then add 760mm mercury and invert the rod then will the mercury not fall?

also will the pressure of the gas change?

I'm a little confused by this thought experiment- you have a tube full of gas at 1 atm, and then somehow add Hg to the tube- unless you are letting the gas out, the gas pressure will increase as the available volume decreases.

So instead, say you have a tube mostly full of Hg, with some gas at 1 atm in the 'headspace' of the tube. Inverting the tube will then mean the gas (assuming the Hg doesn't flow down the sidewalls- Hg doesn't wet glass, so this is a reasonable assumption) has to support the weight of the Hg, meaning it will compress, and the pressure will increase by mg/A, where m is the mass of the Hg and A the cross-sectional area of the tube. Whether or not a Hg vapor bubble will nucleate at the top of the tube will depend on the column height of the Hg- if it's greater than 760 mm, then a vapor bubble should nucleate.

Or do you mean something lese?

 

[phymatter]

I'm a little confused by this thought experiment- you have a tube full of gas at 1 atm, and then somehow add Hg to the tube- unless you are letting the gas out, the gas pressure will increase as the available volume decreases.

So instead, say you have a tube mostly full of Hg, with some gas at 1 atm in the 'headspace' of the tube. Inverting the tube will then mean the gas (assuming the Hg doesn't flow down the sidewalls- Hg doesn't wet glass, so this is a reasonable assumption) has to support the weight of the Hg, meaning it will compress, and the pressure will increase by mg/A, where m is the mass of the Hg and A the cross-sectional area of the tube. Whether or not a Hg vapor bubble will nucleate at the top of the tube will depend on the column height of the Hg- if it's greater than 760 mm, then a vapor bubble should nucleate.

Or do you mean something lese?

Thanks Andy , you got the right thing !
also i think that the mercury will fall down if Hg is more than 760mm Hg , pl conform..

 

[cragar]

And is the reason the air doesn't want to rise up because of mercury's high surface tension?

 

[sophiecentaur]

If all the mercury stays above the gas and if the 'upper' end is open, the pressure on the gas will be 2Ats (no? - Ambient pressure plus 760mm Hg on top of it) so its volume will go down to about 1/2.

 

[cragar]

makes sense sophiecentaur , this setup makes me think of a Sprengel pump where they used falling mercury in a tube to push out air in a container.

 

[Andy Resnick]

Thanks Andy , you got the right thing !
also i think that the mercury will fall down if Hg is more than 760mm Hg , pl conform..

And is the reason the air doesn't want to rise up because of mercury's high surface tension?

If all the mercury stays above the gas and if the 'upper' end is open, the pressure on the gas will be 2Ats (no? - Ambient pressure plus 760mm Hg on top of it) so its volume will go down to about 1/2.

I'm not sure I understand all the questions, but here goes:

Phymatter- unless the Hg can flow around the bubble, the bubble will act as a spring supporting the weight of the Hg, regardless of the mass of the Hg. The nucleation of a vapor bubble at the top of the column *does* depend on the column height, and will occur once the column height is greater than 760 mm (YMMV).

Cragar- If I understand your question, the answer is sort of 'not really'. Specifically, it's because Hg does not wet glass- the glass would rather be in contact with air than Hg. If your column were of sufficient diameter, or if your column were made of say, copper, the Hg would flow down and dislodge the air bubble.

Sophiecentaur- I understood the column to be sealed, and I don't know what you mean 't' to represent. The gauge pressure on the compressed gas is given simply by the weight of the Hg divided by the cross-sectional area: mg/A. The mass of the Hg is the area times the column height 'h' times the density 'd' , so mg/A = h*d*g. This compresses the gas (and drives some of the air into solution with the Hg).

This is an odd thought experiment- I would be cautious about extrapolating too much.

 

[sophiecentaur]

Sorry - sloppy speak. I meant Atmospheres.
There isn't any need to talk about areas, surely, as it's uniform section and, anyway, it's fluid pressure we're dealing with??

 

[Andy Resnick]

Sorry - sloppy speak. I meant Atmospheres.
There isn't any need to talk about areas, surely, as it's uniform section and, anyway, it's fluid pressure we're dealing with??

Pressure = force/area. And, as you can see above, the area cancels out.

 

[sophiecentaur]

Natch. So why were people introducing it, I wonder?