Confused about Mercury Barometers

[rtareen]

TL;DR

A mercury barometer is used to measure the pressure of the atmosphere, we determine the pressure by observing the height of the mercury in a tube.

The figure shows two mercury barometers.
1. My first question is why specifically does it have mercury? Is the mercury a gas or a liquid? Why can we not just use water? Does the pressure of the liquid have to be less than that of the atmosphere for this to work?
2. The book says for a given atmospheric pressure, the height h does not depend on the cross sectional area of the vertical tube. But doesn't the height also depend on the volume of mercury? If you have less mercury its volume will fill out less of the tube and h will be smaller.
3. How do you actually get this to work? Do you fill the tube completely then invert it into the dish? What if it overflows? Is the tube supposed to float on the mercury below it?

 

[ZapperZ]

Summary:: A mercury barometer is used to measure the pressure of the atmosphere, we determine the pressure by observing the height of the mercury in a tube.

View attachment 266618

The figure shows two mercury barometers.
1. My first question is why specifically does it have mercury? Is the mercury a gas or a liquid? Why can we not just use water? Does the pressure of the liquid have to be less than that of the atmosphere for this to work?

It can be ANY liquid that doesn't sublimate that easily. However, Hg is a dense liquid, and thus, you won't need that high of a column. To do this for water, you will need at least 33.9 feet or more than 10,000 mm, instead of 760 mm of Hg. So think of the practicality of such a device.

2. The book says for a given atmospheric pressure, the height h does not depend on the cross sectional area of the vertical tube. But doesn't the height also depend on the volume of mercury? If you have less mercury its volume will fill out less of the tube and h will be smaller.

But that is the point of this topic, i.e. to correct your idea on this. I don't know what book you are using, but most General Physics text will have a derivation on why it doesn't depend on the cross-sectionial area of the tube.

3. How do you actually get this to work? Do you fill the tube completely then invert it into the dish?

That's one say of doing it.

What if it overflows? Is the tube supposed to float on the mercury below it?

Use a bigger pan/bucket/etc. You don't do such things without having a ballpark calculation on what is needed. The tube is held by a support.

Zz.

 

[phyzguy]

1. My first question is why specifically does it have mercury? Is the mercury a gas or a liquid? Why can we not just use water? Does the pressure of the liquid have to be less than that of the atmosphere for this to work?

You can use water. If you do it with water, the height of the column of water will be about 30 feet, so your barometer is very tall. You use mercury because it is very dense and the height of the column is less.

2. The book says for a given atmospheric pressure, the height h does not depend on the cross sectional area of the vertical tube. But doesn't the height also depend on the volume of mercury? If you have less mercury its volume will fill out less of the tube and h will be smaller.

No, the height will be the same regardless of the area of the tube. You need to have enough volume of mercury to fill the tube and some of the dish.

3. How do you actually get this to work? Do you fill the tube completely then invert it into the dish? What if it overflows? Is the tube supposed to float on the mercury below it?

Yes, you fill the tube completely then invert it into the dish. You have to make sure the dish has enough volume to handle the overflow. You have to support the tube somehow, it doesn't float.

 

[snorkack]

It can be ANY liquid that doesn't sublimate that easily.

Liquids by definition do not sublimate, solids do.

However, Hg is a dense liquid, and thus, you won't need that high of a column. To do this for water, you will need at least 33.9 feet or more than 10,000 mm, instead of 760 mm of Hg. So think of the practicality of such a device.

And since the vapour pressure of water at freezing point is still 5 mm Hg, you´d get the air pressure seem to be 755 mm Hg, not 760 mm Hg. Even less in warmer water.
The vapour pressure of mercury at 20 Celsius is of course not zero - but it is about 1,3 μm of Hg.
I cannot recall any really stable room temperature liquids with density between about 6 (alloys of Ga - Ga itself freezes at +30) and 13,5 (alloys of Hg)

 

[Ibix]

Why can we not just use water?

I saw this done at school, with a large rubbish bin full of water and a bright coloured dye and a long tube dangled off the roof.

If you have less mercury its volume will fill out less of the tube and h will be smaller.

A wider tube means you need more mercury to fill it, and hence a bigger reservoir. But as long as you don't empty the reservoir the height of the column will be the same.

 

[brainpushups]

The book says for a given atmospheric pressure, the height h does not depend on the cross sectional area of the vertical tube. But doesn't the height also depend on the volume of mercury? If you have less mercury its volume will fill out less of the tube and h will be smaller.

There's nothing more convincing than experimental evidence. When I teach this subject I start with a demonstration using "Pascal's apparatus" which shows that the force exerted by a column of liquid with a given base area depends only on the height and not the volume (and thus not the weight) of the liquid - a nonintuitive phenomena.

This is an image from Pascal's treatise. The top image illustrates the idea of the apparatus. No matter the vessel, it takes the same amount of weight to hold the plug (figure V.) as long as the heights are equal. In vessel III the weight of the liquid could be 100 lbs and in vessel V it might only weigh 1 lbs, but both will require (say) 10 lbs to balance the plug. I couldn't find a video of someone demonstrating the apparatus. Next time I use it I'll have to make one.

My first question is why specifically does it have mercury? Is the mercury a gas or a liquid? Why can we not just use water? Does the pressure of the liquid have to be less than that of the atmosphere for this to work?

Others have answered this, and I can't upload the video, but here's as screenshot from a video I took of using water for a barometer. I used a bucket of water and a vinyl tube. I sucked the water through the tube so that the tube was completely filled and used a rubber stopper to seal one end. Then I went to the local fire department and they let me go up on their ladder truck until the water would not rise any further (about 30 ft as others have mentioned). Interestingly, you can see bubbles from the water boiling due to vacuum pressure of the "void" at the top of the tube. The video is much more impressive for that aspect of the demonstration. The second photo shows what I assume is gas that has not had the chance to dissolve back into the water, but others can correct me if I'm wrong.

 

[sophiecentaur]

Is the tube supposed to float on the mercury below it?

The tube has to be supported. The weight of the glass is irrelevant to this - it's only thick enough to be strong enough but the column of mercury inside it would instantly sink into the reservoir if it were not supported. The reservoir has to have the capacity to contain all the mercury or it would be all over the floor if the tube were broken by mistake. As the air pressure varies, mercury flows into and out of the reservoir so that level changes, as well as the level at the top of the column. Hence, the ruler / scale has to be adjusted to bring Zero against the level at the bottom and that avoids a significant measurement error.

I must say, I've always desired one. At School, there was a demonstration with a tube and a supply of mercury. Not allowed these days, for H and S reasons (brain damage). I remember, as a 'trusty' being allowed by the Physics master to run the used mercury through a 'mercury cleaner' filter, before it was returned to the bottle. It may explain my mental inadequacies but I never thought to sue the school.

 

[sophiecentaur]

If you have less mercury its volume will fill out less of the tube and h will be smaller.

Just pointing out that there will be no void above the mercury unless the tube is high enough (assuming, of course, that the tube was full in the first place - but that goes without saying).

 

[Frodo]

The manner in which barometers are taught is very misleading.

The important level is the base of the tube where the pressure from the mercury in the entire tube (h + d) must be balanced by the pressure from the atmosphere plus the pressure from the depth d of mercury in the bowl. If they are not the same, mercury will be forced into or out of the tube.

The pressure at depth d is given by:

atmospheric pressure + pressure of depth d of fluid in bowl = pressure of height h of mercury + pressure of depth d of mercury + pressure above mercury in tube (usually 0 or very small).

If the fluid in the tube is the same as the fluid in the bowl then the two d terms cancel each other.

If the fluid in the bowl is different from the fluid in the tube, they don't cancel.

A difficult question to answer is what happens if I add a couple of inches of water above the mercury in the bowl.

First, at what level does the mercury now stand? That is easy to calculate when you have the "proper" description here.

Now I slowly and gently raise the tube until the mouth is exactly at the level of the mercury-water. What happens?

What happens if I raise the tube until the mouth comes right out of the mercury and is located in the body of the water?

 

[sophiecentaur]

The important level is the base of the tube where the pressure from the mercury in the entire tube (h + d) must be balanced by the pressure from the atmosphere plus the pressure from the depth d of mercury in the bowl. If they are not the same, mercury will be forced into or out of the tube.

That is very misleading and stresses the wrong thing. The pressure is the same at any level. What is really relevant is that the Air pressure is equal to the pressure at the part of the mercury column that's on the same level as the air / mercury surface.

What could be the point in adding that depth d and then subtracting it (?) on the other side of an equation to get h? A practical barometer has to indicate h, one way or another so messing about with d?

 

[Frodo]

The school explanation only works because the fluid in the bowl and the fluid in the tube are the same. If the fluids are different the school explanation does not work. As so often happens, the school example is a special, simplified case.

The important point at which to equate the pressure is the bottom of the tube. That is the place the mercury flows in or out of the tube if the tube_mouth_pressure due to the mercury in the tube is not equal to the pressure in the bowl at the tube mouth. You can now cope with fluids of different densities.

You say " The pressure is the same at any level". The pressure increases the deeper you go into the bowl and is a function of the density of the fluid - it is definitely not "the same at any level".

Try using the school explanation to calculate the height of the mercury column, previously 760mm, if 100mm of water, density 1g/cc is floated on the mercury. You will find you are effectively calculating the pressure at the tube mouth.

Try answering my questions about raising the tube.

 

[ZapperZ]

The school explanation only works because the fluid in the bowl and the fluid in the tube are the same. If the fluids are different the school explanation does not work. As so often happens, the school example is a special, simplified case.

So why are you complicating the issue? Having two different liquids is not what the OP is asking for, nor is it within the scope of the problem.

I can give you plenty of 2-or-more-liquids-of-different-densities in many different types of problems. These are the ones I give to my students for their homework and exam questions. Doesn't mean that they belong in this thread!

Zz.

 

[Frodo]

Because the post is entitled "Confused about Mercury Barometers". I am attempting to remove confusion.

 

[ZapperZ]

Because the post is entitled "Confused about Mercury Barometers". I am attempting to remove confusion.

... and you read the title without bothering to read the context?

You attempted to show what you know regardless of what the OP is asking for. It is specific to a particular situation.

This isn't about you. It is about the person who asked the question.

Zz.

 

[sophiecentaur]

You say " The pressure is the same at any level".

OK - bad choice of words. Try "The pressure is the same at every point at a particular level". I assume that makes sense now.

I didn't say "at every level", btw.

 

[epenguin]

Probably those answering have an advantage rtareen doesn't seem to have. Time ago, many decades in my case, we saw the thing demonstrated at school with real tubes etc. by a teacher. I don't say we did it ourselves because even then it was realized mercury was nasty stuff impossible to clean up if it disappeared in woodwork and everywhere, so it wasn't put in our Irresponsible hands. Some of the answers to rtareen's questions would have been answered or wouldn't have come up if he had had the benefit of such lessons and teachers.

If you haven't had such lesson, as well as textbook diagrams which may, as we see, not quite do it, you should be able to find online demonstrations nearly as good, maybe even better.

 

[Frodo]

These are the ones I give to my students for their homework and exam questions.

Thank you for that point as you have explained the precise reason for my post.

In general, teachers teach special, simplified cases. The majority of students think they understand it but they understand the special case and not the general principle. Then, when the exam comes, the teacher gives a more complicated case which cannot be handled by the simple case they taught and which many students are completely unable to answer. It makes the teacher feel good (a wonderful Freudian slip caused me initially to type that as god) but the student understandably feels very frustrated.

I was trying to give the student the correct general principle - look at the pressure at the tube mouth - which gives a complete understanding and which allows those more difficult examples a student is likely to be asked in an exam to be analysed.

epenguin: I completely agree - I don't think the poster has the advantage we had.

As an aside, we did the experiment at school and all played around pushing our fingers deep into the mercury feeling how peculiar it felt. I shudder to think what would happen were that done today. As we were at an altitude of 5,000 feet the barometer stood at 660mm and water boiled at 95C giving us a real appreciation that the text in textbooks often didn't allow for local variations.

Actually teaching that "water boils at 100C" is an excellent example of a simplified case which ignores the general principle. The correct principle is "water boils when its temperature rises to the level at which its vapour pressure equals the external pressure". This gives a deep understanding of what boiling is.

 

[Frodo]

There's nothing more convincing than experimental evidence ...
... I went to the local fire department and they let me go up on their ladder truck until the water would not rise any further (about 30 ft as others have mentioned).

Wonderful!

 

[ZapperZ]

Thank you for that point as you have explained the precise reason for my post.

In general, teachers teach special, simplified cases. The majority of students think they understand it but they understand the special case and not the general principle. Then, when the exam comes, the teacher gives a more complicated case which cannot be handled by the simple case they taught and which many students are completely unable to answer. It makes the teacher feel good (a wonderful Freudian slip caused me initially to type that as god) but the student understandably feels very frustrated.

Sorry, but I explain and show examples of all cases, not just simplified cases. So my example is not a point in your favor.

And oh, here's a shocker for you. Practically everything you were taught in a General Physics class is "special case".

Your encounter with bad teaching should not be your guiding principle of steamrolling into a thread on this forum and disregarding the exactly question and situation that was asked.

Zz.

 

[Frodo]

There's nothing more convincing than experimental evidence ...
... I went to the local fire department and they let me go up on their ladder truck until the water would not rise any further (about 30 ft as others have mentioned).

While painting the garage door I thought of a possible addition to your lovely experiment.

Ask the students to calculate how much the water in one foot of the tube weighs. And how much the water in 32 feet of the tube weighs.

Attach a spring balance to the top of the tube and record its readings as you ascend up the ladder and when you are at the top with a vacuum above the water level. You could ask them beforehand what they expect those readings to be.

The balance will show only the weight of the tube, not the weight of the tube and the water in it. It leads to a discussion of how does the water get into the tube and what is supporting the water.

 

[hutchphd]

This is wrong:

The balance will show only the weight of the tube, not the weight of the tube and the water in it

The unbalanced atmospheric pressure at the top of the sealed tube will provide a force equal to the weight of the water column..

 

[Frodo]

This is wrong:
The unbalanced atmospheric pressure at the top of the sealed tube will provide a force equal to the weight of the water column..

Good catch!

It's so easy to make mistakes without drawing the diagram, especially if you are painting the garage door at the time.

 

[jbriggs444]

The unbalanced atmospheric pressure at the top of the sealed tube will provide a force equal to the weight of the water column..

This general principle continues to hold even if one tries to get creative by having a tube with a variable diameter, a flare at the top, loops or various other manipulations.

 

[brainpushups]

The unbalanced atmospheric pressure at the top of the sealed tube will provide a force equal to the weight of the water column..

Yes, and I can verify that the weight I had to support with my hand was certainly greater than the weight of the tube itself!

 

[snorkack]

The tube has to be supported. The weight of the glass is irrelevant to this - it's only thick enough to be strong enough but the column of mercury inside it would instantly sink into the reservoir if it were not supported.

It is not theoretically irrelevant. In principle, you could have the emerged part of the tube AND the column of mercury in it supported by the buoyancy of the glass submerged under the mercury surface. In practice, you´d need a large volume of buoyant glass on the lower end AND it would have to be afloat stable against falling over.

 

[sophiecentaur]

Glass does float on mercury, indeed. I remember going up to the top of a lighthouse (I was about ten yrs old) and being told that that enormous Fresnel lens and shutter system actually floated in an anular trough of mercury. Pretty good as a bearing and it didn’t need a lot of mercury in a well fitting trough. Self leveling too.

 

[snorkack]

Glass does float on mercury, indeed. I remember going up to the top of a lighthouse (I was about ten yrs old) and being told that that enormous Fresnel lens and shutter system actually floated in an anular trough of mercury. Pretty good as a bearing and it didn’t need a lot of mercury in a well fitting trough. Self leveling too.

And that Fresnel lens was floating stable, not toppling over?
You might have had a small bored hole inside the lens, forming a barometre...

 

[sophiecentaur]

And that Fresnel lens was floating stable, not toppling over?

It was the lens of an operational lighthouse with a stable set of light beams. The diameter of the cylinder was greater than its height and, no doubt, it had some ballast around the bottom. It was constantly rotating through the day to avoid problems with the Sun's image being focussed and distorting. Worked by clockwork in the old days so an efficient bearing was needed.
But I digress . . .