Why do solids maintain their individual identity when placed together?

[russ_watters]

I am not convinced that the pressure we are measuring in my container is weight.

I think the main problem here is that you are bouncing around between many different scenarios, then mixing and matching answers that may or may not apply to each.

If you want to discuss a closed container on or near earth, then it will have two sources of pressure:
1. The momentum of the molecules.
2. The weight of the molecules.

Depending on the specifics of the scenario - which you haven't specified and keep changing - one may be much more relevant than the other.

Try this: pick one scenario, make it very specific, and mathematically identify the sources of pressure.

 

[Dale]

On return to earth, we now have a pressure gradient. But this is what I said earlier - the effect of gravity is to increase density at lower levels, which introduces a pressure gradient. But that's not weight, at least it isn't what I understand by the term 'weight'.

You seem to have this backwards. Gravity introduces a pressure gradient as a primary effect. The density changes only as a consequence of the material response to the pressure. Many materials are incompressible and their density changes very little if at all in response to the pressure gradient. But there is a pressure gradient in any static material whether is compressible or not. That pressure gradient is equal to the weight density of the material.

 

[A.T.]

You seem to have this backwards. Gravity introduces a pressure gradient as a primary effect.

Or maybe the whole cause-effect thinking is pointless here?

 

[Graeme M]

sophiecentaur, thank you for your comments throughout this thread. The paragraph in your earlier post regarding sources of pressure has helped me crack this. As I said earlier, I have limited science education and I think I use terms that have a specific meaning to you which they don't have to me, so there is perhaps some level of missed communication.

That said, in tussling with this overnight, I came up with a way to explain the whole thing that makes sense and answers all my objections (well most of them anyway). I will try to form this model into a succinct model to share with you, but I need to craft my words carefully.

What helped most were these words:
"Yes you can create pressure by using a container but that does not imply that its the only way of creating pressure. The alternative way of creating gas pressure is by attracting each and every molecule to a central point (gravity). In both cases, the molecules are constrained into a finite region. The constraining influence is just different."

I had been worrying over why a container of gas on the Earth's surface would have the same pressure in space without the 'weight' of the atmosphere. What you have made clear to me is that the pressure is 'set' on Earth's surface by the fact that the parcel of air in my container has a particular density of molecules at a particular temperature. This remains in my container no matter where it is - the container walls act to constrain my molecules and the conditions in the container then remain the same. Hence the pressure is the same. The weight of the atmosphere led to the pressure in the first place, but the walls of my container act to preserve it.

DaleSpam, I cannot quite follow your comment, i think it's that terminology thing again. You seem to mean something different by density to what I understand that to mean.

All, I will return later with my mental model that explains this to my satisfaction while incorporating the learning you have given me. I'll be most interested in your opinions.

 

[Graeme M]

Oops, one more thing. Sophiecentaur, what I mean by 'weight' is indeed central to this. In your last post you make the point that we could measure the weight of the atmosphere with a special sealed scale. But we already have such a thing and it's called a barometer. I would argue that your sealed scale would read the same whether I placed it up down or sideways in my loungeroom, because it is measuring air pressure. The weight of the atmosphere gives rise to the pressure, but the pressure is not the weight. Or so it seems to me. And I have an idea to explain why it works that way, I just have to come up with a way to put that into words.

 

[anorlunda]

Two clean surfaces of the same metal could stick together very easily

Put a steel bolt through a hole in an aluminum sailboat mast, come back 30 years later and they will be welded together. That happens even if the surfaces were dirty or greased. Only anti-galling compound will prevent it.

It also happens in devices like windlasses that use both aluminum and steel parts.

 

[sophiecentaur]

Put a steel bolt through a hole in an aluminum sailboat mast, come back 30 years later and they will be welded together. That happens even if the surfaces were dirty or greased. Only anti-galling compound will prevent it.

It also happens in devices like windlasses that use both aluminum and steel parts.

HAHA. Don't talk to me about metals and boats!
On the subject of sticking metals together, I also remembered the Cold Welding of chain links. Get them red hot (but no where near melting) and bash the ends together and you have a join that is approved of by the British Admiralty no less!

 

[sophiecentaur]

Oops, one more thing. Sophiecentaur, what I mean by 'weight' is indeed central to this. In your last post you make the point that we could measure the weight of the atmosphere with a special sealed scale. But we already have such a thing and it's called a barometer. I would argue that your sealed scale would read the same whether I placed it up down or sideways in my loungeroom, because it is measuring air pressure. The weight of the atmosphere gives rise to the pressure, but the pressure is not the weight. Or so it seems to me. And I have an idea to explain why it works that way, I just have to come up with a way to put that into words.

You are right. The two are not synonymous - just strongly connected, usually. Of course Pressure is not Force - that's dimensionally wrong. But it is true to say that the Weight of a 1m² column of the whole atmosphere is also the pressure measured on a Barometer.

With your sealed box in your front room, there would, of course, be a finite difference in pressure from top to bottom. This could be related to the weight of a 1m² column of air, from its floor to its ceiling. You cannot get away from the effect of gravity inside a box.

 

[Dale]

what I mean by 'weight' is indeed central to this. ... The weight of the atmosphere gives rise to the pressure, but the pressure is not the weight.

Weight has a well defined meaning in physics, it is the force of gravity on an object. Please, do not invent your own terms, stick with the standard meaning of standard terms.

I don't think that anyone is saying that the weight is the pressure. Weight is a force, so it is a vector quantity, pressure is not. Also, as mentioned above the units are different. Weight is measured in Newtons, pressure is measured in Newtons/meter^2. The weight density is a vector measured in Newtons/meter^3, and the gradient of pressure is also a vector measured in Newtons/meter^3. In a stationary fluid, the pressure gradient and weight density are equal, so pressure and weight are distinct, but very closely related.

 

[Graeme M]

My apologies DaleSpam, but as i said, I have no great science background so I do not necessarily know either the correct terms, or the meaning of the terms. As far as pressure being weight, when I have read up on what atmospheric pressure is, I typically read that it is the weight of the atmosphere.

So, having only a limited science background, I am trying to make sense of why the pressure of the atmosphere is the same as the weight. Or why the pressure is caused by the weight. or... I dunno, something about how weight and pressure and atmosphere and so on relate.

You guys all get it and it seems to be quite obvious, but it hasn't been to me, so far.

Anyways, I think I have put it all together in my mind and I wanted to share my mental model with you. If it is largely on the money, then great. If not, welll... back to the drawing board. But at least, I think I now know why a solid is solid, and why the weight of the atmosphere gives rise to pressure.

I will post my 'model' up over the next few posts. As I say, if I am wildly off the mark I shan't dig any further, I am happy with some basic improvements in my understanding and I've really enjoyed thinking it through and reading up on it.

 

[Graeme M]

In response to all of the discussion so far, I hereby present my mental model of what's going on for critique.

I must again note that my terminology in what follows may be quite amiss. And conceptually, what I describe is probably inherent in everything that's already been said and I just didn't 'see' what is obvious to you all. Or I am still completely at sea!

However, this mental model explains everything for me, so I am hoping it is the right way to look at things. I apologise if I am just stating things that are obvious, or being sloppy in how I describe these concepts. Or if my explanation just goes on at length about nothing much at all, I can't quite figure out how to condense it down.

The model explains all my problems in the original air pressure thread of 2011, my difficulty in understanding the birds in a truck problem, and now my current question re solids, weight, and atmospheric pressure.

First, weight. By weight I mean the idea of weight as something that can be measured. I think this can be referred to as a Newtonian quality of weight. I last used the idea of Operational Weight and Gravitational Weight in the birds in a truck thread and I'd like to reintroduce those terms here. By these terms, I mean simply that all objects of mass in a gravitational field will have weight, potentially. That is, an object in free fall in a gravity field will have no weight relative to itself, but will have a force resulting from its mass times its acceleration. Relative to the object, I cannot measure this force but I can calculate it. I think this is equivalent to the F=MA equation?

I call this unmeasurable weight Gravitational Weight or GW.

But we can measure weight in some circumstances. Measuring weight is simply measuring the extent to which our falling object is prevented from being accelerated by gravity. If an object is prevented from falling, there must be an agency which does the preventing. This agency comprises a surface against which our falling object bears.

The force expressed against that surface can be measured, it is what I refer to as Operational Weight, or OW.

All objects have a GW that is unchanging at all times in a gravitational field (although of course that GW will change depending on the strength of the field such as when on a different planet - that is, if the A part in MA changes). However, each object can have a different OW in the same field, depending on what our preventing surface is doing. If my object is a 1kg ball and it is resting on the ground, it has an OW of 1 kg. if it is falling from my roof, I cannot place a scale under it and weigh it, so its OW is zero, or close to it. If I had a board on which the ball rests, and I allow the board to accelerate down at half the value of local gravitational acceleration, I think this means my ball's OW, relative to the board, is .5 kg.

So, that is weight. I think... <grin>

 

[Graeme M]

My problem with air presure is why it has no obvious OW. It has a pressure, but is that the same thing? I don't think so, as an OW is measurable downwards only (or more exactly, only relative to the direction of movement induced by the gravitational force). If I place a solid such as my 1kg steel ball on a scale, my scale reads its OW as 1kg. If I place my scale on the side of my ball, it measures nothing. And if I place it on top, I am measuring the weight of my scale.

But with the atmosphere, my scale will register nothing in any orientation. This is, as is well known, because the air everywhere has the same pressure so there is the same force pushing up under the scale as down. If I create a measuring device that reacts to the atmospheric pressure, I think it is totally ignorant of its orientation - that is, it will measure the same pressure regardless of which way its measuring surface faces. Atmospheric pressure is the same in all directions at any given level of the atmosphere.

However, the air has weight - it must as it has mass and there is gravity. In this thread it has become clear to me that the effect of gravity on a gas is to increase, on average, the number of molecules at each level. Disregarding effects of temperature, gravity creates a pressure gradient and that is expressed as an increase in measured pressure at each level as we come closer to the source of the gravity (I know that's not technically correct, I think I mean closer to the centre of mass between the two things).

Now, this must also happen in a solid. If I have a large column of some material, as sophiecentaur noted earlier, the force of gravity is expressed throughout that column and the pressure builds internally and can even deform the column at its lower extremity.

However, that internal pressure, and the internal deformation, is not weight in the OW sense. The column will weigh the same regardless.

This is where I had an idea about what we are seeing happen. It seems to me that for OW to be expressed, we need a bounded object. That is, our object has to have a boundary which is able to be acted upon by another boundary. In the case of the solid, say my 1kg ball, it has a surface and that surface can rest upon another surface - that prevents the ball accelerating and the force is expressed on the second surface as OW. Internally of course the force is being propagated throughout the structure via the atomic/molecular bonds.

Now, I *think* this means that inside a solid, we have an internal pressure resulting from gravity that is largely the same as the internal pressure in a volume of gas. In other words, internally we see pressure at every 'level' in the solid, and taken over its whole form there is a pressure gradient. Hence a tall column of material will have a lower internal 'pressure' at the top than at the bottom. If I could measure that pressure, I'd find that at the top of the column it is less than at the bottom, but that at any level it would be the same to the top, side or bottom of my layer, or slice.

Cumulatively, the pressure builds as we come down the column closer to the centre of mass between our two objects. At the very bottom, it could have enough force to deform the object.

Again though, this is not the weight of the object, rather it is the internal pressure. The weight, or operational weight at least, cannot be measured directly from the prssure, that can only be done outside the boundary of the object. I would imagine though that the relationships are such that we could calculate the weight from the various properties including the pressure at the very lowest layer.

Now, this leads me to assume that if my object were in free fall, ie accelerated by a local gravitational field, it has GW but no OW, and hence no pressure gradient internally. That is, the deformation sophiecentaur describes in my stationary column on the Earth's surface, does not occur. This I think is broadly analogous to the notion that my container of gas, in space, loses its pressure gradient and becomes homogenous throughout.

So that makes sense to me. What of the weight of my atmosphere?

 

[Graeme M]

Well, I think I can explain this by the fact there is no lower boundary. The atmosphere is constrained above by gravity. It is constrained to the side by the fact it is a of a spherical shape - there is no 'side' as such and hence it is not able to expand overall - that is, it can vary over its total shape, but it can never have a greater volume sideways. And it is constrained in the downwards direction by the ground. We cannot measure OW because the lower boundary is the solid earth, We cannot get beneath the boundary to be able to weigh the atmosphere.

Or put another way, if we consider the total atmosphere to be a 'thing' in the way that our 1 kg ball is a thing, we are INSIDE the thing. It is operationally impossible to weigh the thing from inside, although we can infer the weight from the properties we observe. We can go up and down in our atmosphere and measure its pressure, but we cannot directly weigh it.

However, we can bind any solid, liquid or gas. If we place a solid inside a container that is an absolutely skin tight fit, the weight of the new arrangement is that of the solid plus the container. The same applies to a liquid or solid. If we constrain a gas in a container, we create a boundary for it. A sealed container full of gas will weigh more than the same container without a gas. And if we pump more gas in, it will weigh more. Inside the container the effect is an increase in pressure as we add gas. Outside, we have no idea of the pressure, but we can measure the weight.

So, pressure can be used to derive a weight, but pressure is not weight. It is the internal manifestation of gravity, while weight is the external manifestation.

This explains my problem with the container in space, and it explains the birds in a truck thing. If I have a sealed box full of air and a 1 kg block attached to the ceiling, the total system will weight X. If I allow the block to fall, I am predicting that the block will have no OW relative to itself, but the total system will still weigh X. So birds in flight inside a truck are 'held' aloft by the air and the total weight does not change. However, if the truck had no back to it and it were open to the rest of the atmosphere? I predict the truck would be lighter while they are in flight.

So, how does that all sound? Have I largely 'got' it?

 

[Dale]

I have no great science background so I do not necessarily know either the correct terms, or the meaning of the terms

That is fine. This site is primarily educational. But the point is to learn the correct meaning of the terms, not invent your own meanings.

 

[Dale]

I call this unmeasurable weight Gravitational Weight or GW.

The correct term is just "weight". Weight is simply the gravitational force acting on an object.

The force expressed against that surface can be measured, it is what I refer to as Operational Weight, or OW.

The usual term for this is "apparent weight".

http://en.wikipedia.org/wiki/Apparent_weight

 

[Dale]

In this thread it has become clear to me that the effect of gravity on a gas is to increase, on average, the number of molecules at each level.

This is true for a compressible fluid (gas) but not for an incompressible fluid (liquid).

Disregarding effects of temperature, gravity creates a pressure gradient and that is expressed as an increase in measured pressure at each level as we come closer to the source of the gravity

Yes, as I said above the pressure gradient is equal to the weight density. Although pressure does not have a direction, a pressure gradient does.

Now, this must also happen in a solid. If I have a large column of some material, as sophiecentaur noted earlier, the force of gravity is expressed throughout that column and the pressure builds internally and can even deform the column at its lower extremity.

Things are a little more complicated in a solid since you can also have shear stress on the sides. However, in the absence of shear stresses then yes, there is a vertical pressure gradient equal to the weight density, just like in a fluid.

This is all assuming that the fluid or solid is stationary.

 

[Graeme M]

Wow... things get so complicated so fast. DaleSpam, did you read the Talk section of that article on "Apparent Weight"? I did, quickly, and there seems some controversy over that article. It all refers back to the Wiki article on Weight at http://en.wikipedia.org/wiki/Weight wherein they do talk of gravitational and operational definitions for weight. I recall now that this is where I got those terms when I used them in (I think) the thread about birds in a truck. Now I will have to find the time to reread that and see if my understanding of weight accords with that or if I've mistaken what they say there!

 

[Dale]

did you read the Talk section of that article on "Apparent Weight"? I did, quickly, and there seems some controversy over that article

There is nothing at all informative about the fact that controversy exists. There is still some controversy about whether the Earth is flat or round.

 

[Graeme M]

DaleSpam, could you clarify an earlier comment? I thought I'd more or less worked this question out, at a very elementary level of course, but one of your comments leaves me thinking I am still completely missing something.

You said "But it is true to say that the Weight of a 1m2 column of the whole atmosphere is also the pressure measured on a Barometer."

This still comes back to my difficulty in understanding why the pressure on the barometer is also the weight. I suggested above the idea that the pressure is measurable but the weight is not, directly. However, there is a related matter regarding pressure and weight that isn't clear to me.

Again, using a very tall box containing a gas as a thought experiment, if I measure the pressure in my box there is a pressure gradient arising from the gravity effect. I think I follow that. But I am not sure how the pressure is directly derived from the weight. If my gas was cooled to a very low temperature, wouldn't the pressure similarly reduce? And equally if heated the pressure would increase? But my box containing the gas would still weigh the same in all cases wouldn't it? Disregarding the small weight gain due to expansion/contraction which from what I have read would be much much smaller than the variation in pressure.

 

[Dale]

You said "But it is true to say that the Weight of a 1m2 column of the whole atmosphere is also the pressure measured on a Barometer."

I did not say that. Sophiecentaur said that. I would say it slightly differently. I would say that "the magnitude of the weight of a 1 m^2 column of stationary atmosphere, measured in Newtons, is numerically the same as the barometric pressure at the bottom of the column, measured in pascals." Weight is a vector measured in Newtons, and pressure is not a vector and it is measured in pascals. Sophiecentaur's comment gets to the heart of the matter, but is a little imprecise.

Again, using a very tall box containing a gas as a thought experiment, if I measure the pressure in my box there is a pressure gradient arising from the gravity effect. I think I follow that. But I am not sure how the pressure is directly derived from the weight.

As I have said before, the weight density is equal to the pressure gradient in a stationary fluid. Weight is not equal to pressure, they have different units and are different types of quantities, but weight density is equal to pressure gradient, those both have the same units and are the same type of quantity. Mathematically this is expressed by $\vec{\rho}=\nabla P$ where $\vec{\rho}$ is the weight density and $P$ is the pressure.

For the usual case where $\vec{\rho}=(0,0,\rho_z)$ this can also be written as $\rho_z=dP/dz$. Applying that to a vertical box gives $W=A(P(b)-P(a))$ where $W$ is the vertical component of the weight of the box, $A$ is the area of the box, $P(b)$ is the pressure at the bottom of the box, and $P(a)$ is the pressure at the top of the box. In words, this says that the weight of the gas in a box is equal to the area of the box times the difference in the pressure at the top and bottom of the box.

If my gas was cooled to a very low temperature, wouldn't the pressure similarly reduce? And equally if heated the pressure would increase? But my box containing the gas would still weigh the same in all cases wouldn't it?

Yes, and $P(b)-P(a)$ would therefore be the same in all cases. When you heat it up both $P(a)$ and $P(b)$ will increase such that their difference does not change. Similarly for cooling it.

 

[Graeme M]

Ahhh... I see, my problem is not understanding the meaning of 'weight' in context. I am hung up on the idea of weight being a measurable quantity as in a thing on a scale, which is your 'apparent weight'. But you are talking of weight as the force over the whole fluid arising from gravity. I'm not sure I explained that correctly but its right there in your equation
W=A(P(b)−P(a)).

I think I can adapt my earlier mental model to that sort of idea.

Now I get it, as much as I can get it.

Thanks to all, sorry I took so long to understand this one. Never having learned this stuff at school means I didn't have the hooks to hang this off...

 

[Dale]

I am glad I could help.

 

[Graeme M]

Aaaargh! I must be as dumb as a fence post. DaleSpam, thanks to your last post I grasped the difference in concepts of weight and how that applies in this context. But on rethinking it...

In words, this says that the weight of the gas in a box is equal to the area of the box times the difference in the pressure at the top and bottom of the box.

That sentence makes sense as did your equation and gave me the right feel for how it works, but I am still baffled about how a single barometer reading is equivalent to the weight. You are saying that we need pressure at top and bottom to be able to derive the factor for our calculation. That is two barometric readings, surely? You can't come up with a pressure gradient from one reading at the bottom of the column can you?

Or does it follow that in the case of the atmosphere, the value at the top of the column is just zero? Still, for any other box of gas, say one 5000 feet in height, both A and B have non-zero values, so in those cases the lower barometric reading would not equal weight?

Or maybe I am still not getting 'weight'? Or 'pressure gradient'. Or 'weight density'.

Sigh... Back to school for me!

 

[Dale]

That is correct. You need two barometric readings in general. You can only get away with a single reading if for some reason you know what the other one is. For example, you know that the pressure at the top of the atmosphere is 0

 

[K1NS]

Why is a solid so solid? Because a solid is NOT SOLID! Normal matter (excluding special cases like neutron stars or black holes), even very dense materials like a block of metal, are actually mostly empty space. Subatomic particles, relative to their size, are farther apart than stars in the sky. Look up in the sky at night. You see mostly black, right? That's because stars and other objects are very far apart relative to their size. The same is true of that block of solid metal.

But the block of metal LOOKS solid because the wavelength of visible light is longer than the distance between particles, so the light reflects off the matter and it looks solid and smooth. It FEELS solid because if you try to push your hand through the block of metal, powerful forces repel your hand, and the block of metal feels solid when in fact it is mostly empty space.

Imagine for a moment you are a neutrino, tiny particles that fly around the universe and pass right through "solid" matter. This very moment, billions of neutrinos are passing through you, and me, and the "solid" core of the earth. Neutrinos are not susceptible to the forces that most matter is,, and the blissfully pass right through the empty space that is solid matter, ignoring the particles they come close to but never collide with. When you imagine the universe as a neutrino "sees" it, it becomes a very different place, and we see that we are actually all a part of the same immense field of particles and forces. There is no line between us. There is no surface to "solid" matter. The center of the earth, as dense as it is, is hardly different from intergalactic space.

When a spiritual mystic says that reality is illusion, he may be right, eh?

 

[Graeme M]

I guess that was partly my original question K1NS. Given a 'solid' object is composed of atoms/molecules, what forces actually bind it together in a form that has a certain integrity to it. Regardless of how it looks at the sub-atomic level, at our level solid objects are solid, they have boundaries, and they have properties that can be quantified. At our scale, solid objects certainly DO differ from intergalactic space. I for one am glad of that otherwise I shouldn't be writing this. I was simply wondering why things ARE like that, which led to an interesting (to me) discussion about gasses and weight in which I gained an understanding I didn't have before!

But I take your point, it is intriguing to visualise the universe as nothing but a field of particles and forces.

 

[jerromyjon]

When a spiritual mystic says that reality is illusion, he may be right, eh?

Reality is merely an illusion, albeit a very persistent one.- [URL='http://www.brainyquote.com/quotes/authors/a/Albert_einstein.html']Albert Einstein

 

[jerromyjon]

But I take your point, it is intriguing to visualize the universe as nothing but a field of particles and forces.

Or one step further, just electromagnetic radiation and its attraction.

 

[Albert Newton]

well...when taking about the properties of Liquids and Solids...we have to consider their structure and the types of bondings between the Molecules...
In Liquids.., if we take water., the molecules are connected through weak hydrogen bonds and also they don't have a definite Lattice Structure and the Molecules are free to Break bonds and move around due to weak Hydrogen bonds ...
While in Solids.., ..they have a Rigid Lattice Structure and are held Strongly by neighboring atoms and need some amount of Energy to break those Bonds which in case of metals / some other Solids is very High ...

also remember that when you are talking about merging of two portions or whatever .., its all about the Bonds between the consecutive Molecules...if the Molecules are mobile and can break their bonds easily..,.then they merge easily.. :)

 

[jerromyjon]

...If they have similar atomic structure or they conform to each other.