Physics thought experiment / contest

[MooreBonds]

Clever ideas, but you'd have to subtract out the potential to kinetic energy of the atmosphere or water you're using, as that is external to the sphere.

(The general intent is to extract energy from the sphere somehow, not extract energy from the environment using the sphere.)

But doesn't this fly in the face of your initial post, where you say:

In your lab, you have enough personnel, materials, finances, time, knowledge, etc. to build or obtain any currently existing energy extraction device known to humankind. No science fiction, though. Lasers are OK, faster-than-light travel is not.

Any energy you add to the object will be subtracted from your energy output total. So, for example, if you lifted it up onto a tower and used its newly obtained potential energy to produce energy output, that doesn't count.

So you can expend any amount of energy to "build or obtain any energy extraction device" (like a nuclear reactor)...but you can't simply place it under a waterfall with a small plastic pool

 

[imoldernu]

build the theory around tardigrades

 

[MarieIG]

But doesn't this fly in the face of your initial post, where you say:




So you can expend any amount of energy to "build or obtain any energy extraction device" (like a nuclear reactor)...but you can't simply place it under a waterfall with a small plastic pool

Um, I was wondering if you could drop it on the floor.

 

[SecondCor521]

But doesn't this fly in the face of your initial post, where you say:

I don't see the conflict, but if you can point it out to me I can try to clarify.

So you can expend any amount of energy to "build or obtain any energy extraction device" (like a nuclear reactor)...but you can't simply place it under a waterfall with a small plastic pool

Yes, exactly so. The goal is not to make this an economically feasible or energy-rational thought experiment. It is to see how to extract the most energy out of a simple-but-not-completely-so object with unlimited access to other tools and equipment.

Sorry if this isn't fun for you, it was an interesting thought experiment to me and I was curious what others here would say.

And I'm not trying to play "Hey, folks, try to guess the rules" - I just know from prior experience that I sometimes don't expound my thoughts clearly in an initial post, so all I can do is try to write my initial post as clearly as I can and then clear up any additional questions subsequent to that.

 

[GrayHare]

But the sphere is 'filled' with nothing - a perfect vacuum!
-ERD50

Exactly, hence opening the sphere's value will allow something to be placed inside it. OTOH whatever one places inside the sphere is adding to its mass/energy, and thus per the rules it needs to be subtracted back out of the final energy calculation.

 

[NW-Bound]

... The two reasons for specifying a mole of stuff was to (a) quantify and limit the size of the sphere, and (b) try to induce creativity in terms of trade offs - maybe a larger molecule has more chemical energy (is that the right term) but produces a sphere of a smaller diameter...

But the above is in conflict with the original problem statement:

(Let us stipulate/ignore, although it is probably not true, that the construction of the object above is of sufficient strength to maintain its shape indefinitely given the pressure differential between the inside of the object and your lab.)

A mole of material is not that much. If made of tungsten, it weighs 184 grams (6.5 oz), and of uranium 238 grams (8.4 oz).

Let's call the object a ball rather than a sphere, because the object is hollow.

If I want to make use of the vacuum, then I would want that ball as large as possible. The volume of the sphere is limited by the strength of the material, because the larger the sphere the thinner its wall, with the weight of the ball being fixed.

Theoretically, a perfectly spherical ball can be quite large before getting collapsed under the atmospheric pressure, but there are practical engineering limits. I am not qualified to even make a guess as to how large one can make such a ball.

 

[SecondCor521]

But the above is in conflict with the original problem statement:





A mole of material is not that much. If made of tungsten, it weighs 184 grams (6.5 oz), and of uranium 238 grams (8.4 oz).

Let's call the object a ball rather than a sphere, because the object is hollow.

If I want to make use of the vacuum, then I would want that ball as large as possible. The volume of the sphere is limited by the strength of the material, because the larger the sphere the thinner its wall, with the weight of the ball being fixed.

Theoretically, a perfectly spherical ball can be quite large before getting collapsed under the atmospheric pressure, but there are practical engineering limits. I am not qualified to even make a guess as to how large one can make such a ball.

Again, I'm not sure of the conflict; perhaps I am still communicating poorly. You're right that the size of a sphere (or ball) constructed of one mole of any given molecule would be limited in practice. What I was trying to get at in the part of my quote that you bolded was that it couldn't be an arbitrarily large sphere/ball - say, 200 miles in diameter. If the size of the object were not constrained, it would seem easy to decree it to be of arbitrarily large size, which would provide an arbitrarily large amount of energy, and make the contest/optimization/engineering problem moot.

You're also right about a mole not being that much. 184 grams of tungsten, though, for example, would at least seem to make a sphere the size of a softball or even larger, if it only has to sustain a vacuum against one Earth atmosphere.

 

[mountainsoft]

I never took physics or chemistry in school, so I'm basically an idiot with this stuff.

My first thought was to fill the sphere with water (open valve, gravity fed), let it heat up in sunlight and release the pressure as steam to turn a generator of some kind. Probably violates the terms of the question, but what do I know.

I also thought about some kind of solar generating sphere, maybe made of silicon near the equator to extract the most solar energy. Something like this: What is Sphelar® - Technology - Sphelar Power Corporation

Off to detention I go...

 

[ERD50]

Again, I'm not sure of the conflict; perhaps I am still communicating poorly. You're right that the size of a sphere (or ball) constructed of one mole of any given molecule would be limited in practice. What I was trying to get at in the part of my quote that you bolded was that it couldn't be an arbitrarily large sphere/ball - say, 200 miles in diameter. If the size of the object were not constrained, it would seem easy to decree it to be of arbitrarily large size, which would provide an arbitrarily large amount of energy, and make the contest/optimization/engineering problem moot.

You're also right about a mole not being that much. 184 grams of tungsten, though, for example, would at least seem to make a sphere the size of a softball or even larger, if it only has to sustain a vacuum against one Earth atmosphere.

But this appears to be in conflict with your OP:

(Let us stipulate/ignore, although it is probably not true, that the construction of the object above is of sufficient strength to maintain its shape indefinitely given the pressure differential between the inside of the object and your lab.)

If we are ignoring strength, then what I assumed was that the material could be just one molecule thick. So the size would be determined by the maximum spacing of the molecules which would still allow a bond between them. I don't know how to determine that for various materials, would have something to do with their (covalent?) bonds, I think. Outside my area of knowledge, not even sure how to look it up.

So, does the sphere need to be able to withstand an atmosphere, or not?

-ERD50

 

[NW-Bound]

Let's put aside the problem of not knowing how large a ball we can make that, when evacuated, will stand up to the atmospheric pressure trying to collapse it.

Given that ball, we can extract some work when we allow the ball to be refilled when it is connected to the ambient air. The airflow into the ball can drive a turbine, or a piston engine, for example.

What is the theoretical limit of the energy that can be extracted?

Now, imagine that if instead of refilling an evacuated ball, we have a huge syringe with a perfectly sealed plunger or piston. Starting with the piston at the top of the syringe, we draw the piston out such that we create a vacuum space inside the cylinder, and this vacuum space has the same volume as our evacuated ball.

The energy that is required to draw the piston out to create the evacuated space is simply P*V, where P is the atmospheric pressure, and V is the volume of the created vacuum space. When we allow the piston to be pushed back to the top of the cylinder, the work that we can recover is the same P*V. Note that the force exerted by the ambient air on the piston stays constant during the piston travel, whether we draw it in or out.

The work recovered by refilling the ball is more complicated to compute, because the gas allowed into the ball raises the internal pressure during the process. An amount of air released into the ball early on will create more work than the same amount of air near the end, because the differential pressure becomes less and less.

I am trying to formulate an answer using the perfect gas law equation. It may turn out that the energy is the same as that we can get with a closed-off cylinder/piston of the same chamber volume. Else, we gain or lose something, and that would bother me.

 

[SecondCor521]

But this appears to be in conflict with your OP:

If we are ignoring strength, then what I assumed was that the material could be just one molecule thick. So the size would be determined by the maximum spacing of the molecules which would still allow a bond between them. I don't know how to determine that for various materials, would have something to do with their (covalent?) bonds, I think. Outside my area of knowledge, not even sure how to look it up.

So, does the sphere need to be able to withstand an atmosphere, or not?

-ERD50

Ah, now I see what you're asking about.

The way I would try to answer your question is "Yes, but I don't know how to calculate or even know intuitively whether a sphere constructed of a molecule and thickness of your choosing would actually withstand an atmosphere, feel free to snow me with your answer."

I *think* a tungsten sphere of, say, 1 cm thickness would work. I think a plutonium sphere of 1 molecule thickness would not. But I don't know for sure in either case. If you told me you worked out the math and a 1 molecule thick sphere of carbon nanotubes would work, then I'd be surprised but I'd trust you on it.

HTH.

 

[ERD50]

Ah, now I see what you're asking about.

The way I would try to answer your question is "Yes, but I don't know how to calculate or even know intuitively whether a sphere constructed of a molecule and thickness of your choosing would actually withstand an atmosphere, feel free to snow me with your answer."

I *think* a tungsten sphere of, say, 1 cm thickness would work. I think a plutonium sphere of 1 molecule thickness would not. But I don't know for sure in either case. If you told me you worked out the math and a 1 molecule thick sphere of carbon nanotubes would work, then I'd be surprised but I'd trust you on it.

HTH.

No, this isn't making sense.

It is up to you to set the conditions. Earlier, you said: "Let us stipulate/ignore, although it is probably not true, that the construction of the object above is of sufficient strength to maintain its shape indefinitely given the pressure differential between the inside of the object and your lab.)"

I take that to mean to ignore reality for this exercise, and assume the sphere can withstand the pressure regardless of its construction. But now you say you want us to figure out if it can withstand the pressure? Which is it?

And what is 'work'? How much safety factor? Dynamic or static loads, temperatures, etc?

This is too open ended to be meaningful or fun.

Suggestion - knock the problem down to one thing at a time. For example:

I have a 100 Liter strong walled (assume no flexing of the walls) container filled with dry Nitrogen gas, pressurized to 1 bar, at 20C. It has a standard Schrader valve. How much energy could you extract from this sphere in a 20C environment? How would you do it? (hint - consider that a decompressing gas will absorb heat).

-ERD50

 

[SecondCor521]

No, this isn't making sense.

It is up to you to set the conditions. Earlier, you said: "Let us stipulate/ignore, although it is probably not true, that the construction of the object above is of sufficient strength to maintain its shape indefinitely given the pressure differential between the inside of the object and your lab.)"

I take that to mean to ignore reality for this exercise, and assume the sphere can withstand the pressure regardless of its construction. But now you say you want us to figure out if it can withstand the pressure? Which is it?

And what is 'work'? How much safety factor? Dynamic or static loads, temperatures, etc?

This is too open ended to be meaningful or fun.

Suggestion - knock the problem down to one thing at a time. For example:

I have a 100 Liter strong walled (assume no flexing of the walls) container filled with dry Nitrogen gas, pressurized to 1 bar, at 20C. It has a standard Schrader valve. How much energy could you extract from this sphere in a 20C environment? How would you do it? (hint - consider that a decompressing gas will absorb heat).

-ERD50

Bummer. I think you're one of the smartest people on this board, and I would be interested in your thoughts and ideas.

I did not say I wanted you to figure out if it can withstand the pressure. I wrote "feel free to snow me with your answer". This means you have the option of worrying about whether or not your sphere will work, and you have the option of doing the math/physics/whatever correctly or incorrectly.

"Work" in this case would mean that it would maintain it's shape against the pressure differential indefinitely while sitting on the lab floor. If you need extra strength for whatever energy extraction method you are considering, then that would need to be included.

Since it's a thought experiment, I don't know how to address safety factors. Is there an engineering standard for those?

STP if you wish, so 0 degrees Celsius.

And it's a thought experiment, not a problem. I was hoping more for creative solutions and ideas and tradeoffs, and less exact calculations and math.

HTH.

 

[CardsFan]

And it's a thought experiment, not a problem. I was hoping more for creative solutions and ideas and tradeoffs, and less exact calculations and math.

HTH.

You do know there is a higher than average concentration of engineers here.

Numbers is what we do

 

[ERD50]

You do know there is a higher than average concentration of engineers here.

Numbers is what we do

Yes, sorry, but I'm just lost. Is this a physics question, or what... science fiction?

I really don't understand what is being asked by the OP.

This means you have the option of worrying about whether or not your sphere will work,

But that's like the old "how long is a string?" question. There must be constraints and requirements, or it isn't a 'problem' to be solved.

I was hoping more for creative solutions and ideas and tradeoffs,

Creativity exists within constraints. Think of Picasso's 'Blue Period", he was constrained by a monochrome choice and produced wondrous art. Or a pen and ink drawing, or solo acoustic guitar. Constraints are what make the challenge.

Without constraints, it's too much like the "100% renewable energy" fans - just dream it and it will happen!

Sorry, maybe I'm just not a match for whatever it is you are looking for. I'd like to play, if I could only figure out what game is being played.

-ERD50

 

[SecondCor521]

Thanks for trying! I've refunded your entry fee ;-)

 

[ERD50]

Thanks for trying! I've refunded your entry fee ;-)

That's OK. You did get me thinking about moles (the chemical/physical type) and how molecules would be distributed in a single thickness plane. But I'll need to research that more to get a better feel for it.


-ERD50