Physics thought experiment / contest

[SecondCor521]

Disclaimer: I'm not really any good at physics. I think I got a C on the subject in college.

Imaginary Scenario:

You are a scientist / engineer. You have a lab on the equator of the Earth, at sea level, at one atmosphere, standard temperature and pressure.

You are given an object and a task.

The object is a perfect, hollow sphere. The sphere is manufactured (by someone else) of one mole of any molecule of your choosing. It contains a perfect vacuum. On it's otherwise featureless surface, there is, integrated into the sphere, a single valve of any industrial standard of your choosing.

(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.)

The task is for you to extract as much energy from this object as possible.

There is no time limit.

Before you start, the object will be placed on the floor in your lab long enough to acclimate, so it will neither be hotter nor colder than your lab.

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.

Of what molecule do you choose to have the object made?

What methods and energy extraction devices do you use?

How much energy can you generate?

What kind of valve do you use?

If it matters, at what longitude do you locate your lab?

 

[njhowie]

Simply put a match to it, burn it, and don't waste any more energy thinking about it.

Minimal energy expended, light/heat generated.

Call it a day.

 

[Spock]

Plutonium-239

 

[atmsmshr]

The engineer in me rises to the bait..........

Since limit is 1 mole, this is in the realm of nanoparticles.

Fullerene would be the molecule (carbon nano tube is the structure).

Fuel would be hydrogen, which is a cheat since it combusts with oxygen in the air - but hey it works. Also makes the structure stronger.

Nano valve of carbon.

Light it up with a flame.

How much energy? Much less than from burning a mosquito's fart.

Equator - and no I am not showing my work for this choice.

 

[atmsmshr]

Plutonium-239

My go to answer was fission. However, the size limit would exclude critical mass calculations.

A close second is a particle accelerator. Maybe, but the efficiency is extraordinarily low.

My last thought was fusion - we are not quite there yet.

 

[ckelly78z]

By being on the equator, i'm only concerned with which direction the toilet flushes (clockwise/counter clockwise). I don't even want to think about the individual particles that are involved, but would appreciate a vacuum in that scenario.

I would prefer a low energy transaction, and not have to strain.

 

[GrayHare]

Since there is no time limit, wait for the given object's matter to naturally decay into energy. The energy derived is per E=mc^2.

 

[Ready-4-ER-at-14]

If any item were sent to the sun the energy there would release energy as fission occurred.
I assume if it were sent to a black hole fusion would happen.
My memory of the magnitude of energy released is that fusion gives the most energy.

The kicker is if you intended this thought process to be usable energy and what time limit.

If the big bang happens repeatedly no need to send to a black hole as it will come to the lab floor.

As to which element or compound to use seems the bigger the better as more bonds to break and more to squish. Not sure which compound that is but some organic compound with radioactive side chains is fun to comtemplate… so will ask for c1000-p239x1000-O(x)-H.

 

[Dalmore]

Material: Carbon

Method: a molecular paddle wheel connected to a generator. I would fill the vacuum with anti-Nitrogen, the last particle allowed in would be a Nitrogen molecule. Significant electricity would be produced filling the vacuum, the Nitrogen molecule will react with the the anti-nitrogen, creating heat, causing the carbon sphere to react with O2 in the atmosphere, allowing more Nitrogen in to react with the remaining anti-nitrogen.

Energy produced: Bunches?

The longitude of the lab would be 180 degrees opposite of where I am.

 

[The Cosmic Avenger]

Plutonium-239

I believe using a radioactive element is the only sensible answer. Any other answer would either rely on the pressure equalization when the valve was opened to generate power, which would be very limited compared to even the best potential alpha decay, IIRC, or having the sphere be made of something combustible and burning it, which I think would do better than the vacuum but not as well as radioactivity. Anything else would require putting energy into the system, which would be subtracted from your output, and if you could get more mechanical energy out of this system than you put into into it, you would have a perpetual motion machine!

 

[stepford]

Ordinarily I'd assume fusion would produce more energy than fission, but I think the key here is the requirement of using 1 mole of material. There's a LOT more material in 1 mole of Pu239 than a mole of H, He or any other light element. When a single atom of Pu 239 fissions it releases about 200 MeV of energy. Alternatively when a couple of Hydrogen atoms fuse to Helium they release about 27 MeV. For a given amount of mass fusion wins, but for a given number of atoms, as in the problem given by the OP, fission wins handily.


So make my magic sphere out of Plutonium please.

 

[GrayHare]

In any direct matter to energy conversion, the most massive particles will yield the most energy, so if a choice is permitted at no cost the object should be made of a mole of the most massive transuranic element, which at the moment is Oganesson.

 

[Exrook]

Material: Francium


Since one mole of francium would weigh 223 grams, and francium is currently valued at approx. $1 billion per gram, simply sell the sphere and buy as much energy as desired.

 

[CardsFan]

Material: Francium


Since one mole of francium would weigh 223 grams, and francium is currently valued at approx. $1 billion per gram, simply sell the sphere and buy as much energy as desired.

Winner!!!

 

[SecondCor521]

The kicker is if you intended this thought process to be usable energy and what time limit.

No usable energy requirement. Pretend that it's just for bragging rights among your fellow scientists and engineers.

As stated in the OP, no time limits.

Interesting and excellent responses so far. Thank you.

 

[MooreBonds]

I would go for something utilizing the natural thermal incline in the atmosphere. Build it out of graphene, which (in theory) should be the lightest material. The vacuum inside the sphere should make it buoyant enough to rise up. Tie the sphere to the valve, such that as the sphere gets blown about in the wind, it tugs on a cord that generates electricity by means of a magnet set-up.

Or, use a setup that I one day envisioned based on a toilet flapper that was malfunctioning: place your lab at the base of a waterfall. Have some of the water fall into a tank that contains this magic sphere. This is a large tank/pool, such that there are some baffles to reduce turbulence of the entering water, so the only real motion of water in the tank by this sphere is essentially zero.

Connected to the sphere's valve is a flat cover. This flat cover is covering a hole in the bottom of the tank that the water is discharging out of.

Step 1. The very light density of the sphere is buoyant enough that it wants to rise up. As it rises up, it pulls with it the the flat cover that is covering the tank discharge hole.
Step 2. When the cover is lifted up, the water starts rushing out the hole in the tank bottom.
Step 3. As it does so, the rushing water pulls down on the large flat cover, and pulls the sphere/cover back down to cover the hole.
Step 4. When the sphere/cover get pulled down far enough, at some point the upward buoyancy force of the very low density sphere again exceeds the force of the water pushing down on the flat cover, and the sphere/cover again rises up (repeating Step 1).

One point I didn't mention was that connected to the sphere/cover is a rod/flywheel/some mechanism that is tied to a magnet around a coil. As the sphere/cover move up and down, it's moving the magnet to induce an electric current.

With a sufficiently large natural water supply, a sufficiently large tank, and enough time, you might be able to create more electricity from this than from consuming a sphere made from nuclear fissionable material.

 

[bada bing]

Since you specified mole of molecules rather than atoms, I would go with a polymer of some sort with a high molecular weight. I would specify 1/2 of matter and 1/2 of the antimatter of the polymer. Depending on how much mass it was, I wouldn't want to be anywhere near it though, maybe not on the same continent. You can't get any better than perfect, total conversion of the mass to energy, E=mc2. Seems like I remember from class that 3 ounces of mass = 10 megatons of TNT energy equivalent, or some such useless factoid. You could easily specify a polymer that weighed 100lbs per mole (or any number really). Enough to blow up the world.

 

[Oz investor]

since i had a reputation at high school for being LAZY ( ' the laziest bastard i have ever seen ' , if i remember the maths teacher's statement correctly )

the inner contents would be hydrogen , the sphere ( of light weight attached to the floor via a piezo system to generate a mild electrical charge .. for as long as there is an atmosphere on earth .

more efficient is to forget about the sphere entirely and put piezo device under any available table leg and have an electrical charge as long as the Earth has a gravational field , better still is use an upper floor in the building where extra vibrations will add to the yield

 

[NW-Bound]

Responders so far ignore the following attributes of the object that they are given.

The object is a perfect, hollow sphere. The sphere is manufactured (by someone else) of one mole of any molecule of your choosing. It contains a perfect vacuum. On it's otherwise featureless surface, there is, integrated into the sphere, a single valve of any industrial standard of your choosing.

 

[SecondCor521]

Since you specified mole of molecules rather than atoms, I would go with a polymer of some sort with a high molecular weight. I would specify 1/2 of matter and 1/2 of the antimatter of the polymer. Depending on how much mass it was, I wouldn't want to be anywhere near it though, maybe not on the same continent. You can't get any better than perfect, total conversion of the mass to energy, E=mc2. Seems like I remember from class that 3 ounces of mass = 10 megatons of TNT energy equivalent, or some such useless factoid. You could easily specify a polymer that weighed 100lbs per mole (or any number really). Enough to blow up the world.

As the poster above implies, this would violate the intent of the rules. The intent was that the sphere was of a single, uniform molecule (all titanium, all carbon, all steel, whatever). The above construction is of two different molecules.

 

[SecondCor521]

I would go for something utilizing the natural thermal incline in the atmosphere. Build it out of graphene, which (in theory) should be the lightest material. The vacuum inside the sphere should make it buoyant enough to rise up. Tie the sphere to the valve, such that as the sphere gets blown about in the wind, it tugs on a cord that generates electricity by means of a magnet set-up.

Or, use a setup that I one day envisioned based on a toilet flapper that was malfunctioning: place your lab at the base of a waterfall. Have some of the water fall into a tank that contains this magic sphere. This is a large tank/pool, such that there are some baffles to reduce turbulence of the entering water, so the only real motion of water in the tank by this sphere is essentially zero.

Connected to the sphere's valve is a flat cover. This flat cover is covering a hole in the bottom of the tank that the water is discharging out of.

Step 1. The very light density of the sphere is buoyant enough that it wants to rise up. As it rises up, it pulls with it the the flat cover that is covering the tank discharge hole.
Step 2. When the cover is lifted up, the water starts rushing out the hole in the tank bottom.
Step 3. As it does so, the rushing water pulls down on the large flat cover, and pulls the sphere/cover back down to cover the hole.
Step 4. When the sphere/cover get pulled down far enough, at some point the upward buoyancy force of the very low density sphere again exceeds the force of the water pushing down on the flat cover, and the sphere/cover again rises up (repeating Step 1).

One point I didn't mention was that connected to the sphere/cover is a rod/flywheel/some mechanism that is tied to a magnet around a coil. As the sphere/cover move up and down, it's moving the magnet to induce an electric current.

With a sufficiently large natural water supply, a sufficiently large tank, and enough time, you might be able to create more electricity from this than from consuming a sphere made from nuclear fissionable material.

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.)

 

[ERD50]

Responders so far ignore the following attributes of the object that they are given.

I was also confused by this. Is the objective to extract energy from the material that forms this sphere? But then why a sphere, why a perfect vacuum and why a valve? Why not just specify "one mole of any molecule of your choosing"?

I took it to mean extracting energy by the pressure difference (hence the valve), which would just be an atmospheric pressure difference. It doesn't matter if there is a perfect vacuum inside or simply one atmosphere above STP (Standard Temperature/Pressure), which would be ~ 14.7 PSI gauge pressure. And we need to know the volume.

Or was that to distract from the one mole condition?

Can you clarify? And BTW, the first step for an engineer/scientist is to have a clear understanding of the conditions, the limits, and the goals, before any attempt at a solution is made!

edit/add: Perhaps the "one mole" is to be used to choose a molecule that will form the largest sphere of a one molecule thickness, therefore providing the largest volume of one atmosphere pressure delta? I'm not sure how that works, I'd need to research it.

-ERD50

 

[SecondCor521]

I was also confused by this. Is the objective to extract energy from the material that forms this sphere? But then why a sphere, why a perfect vacuum and why a valve? Why not just specify "one mole of any molecule of your choosing"?

I took it to mean extracting energy by the pressure difference (hence the valve), which would just be an atmospheric pressure difference. It doesn't matter if there is a perfect vacuum inside or simply one atmosphere above STP (Standard Temperature/Pressure), which would be ~ 14.7 PSI gauge pressure. And we need to know the volume.

Or was that to distract from the one mole condition?

Can you clarify? And BTW, the first step for an engineer/scientist is to have a clear understanding of the conditions, the limits, and the goals, before any attempt at a solution is made!

edit/add: Perhaps the "one mole" is to be used to choose a molecule that will form the largest sphere of a one molecule thickness, therefore providing the largest volume of one atmosphere pressure delta? I'm not sure how that works, I'd need to research it.

-ERD50

I think I really had two thoughts:

1. I wondered what creative ways people would come up with to extract energy from such a setup, and what ways are actually out there.

2. I wondered which of those creative ways would be the best.

The reason for the vacuum and valve was to provide a more complex (and to me more interesting) problem with more options.

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.

I haven't seen any solutions offered that utilized both the pressure differential and the material of the sphere itself in either sequence or combination of any type, which surprised me. That's sort of what I was hoping for and tried *not* to exclude from the solution space by anything that I wrote in the OP but somehow failed at that.

HTH.

 

[GrayHare]

Assuming compressed material from a neutron star or black hole is not permitted, I suppose one could fill the Oganesson sphere with more Oganesson.

 

[ERD50]

I think I really had two thoughts:

1. I wondered what creative ways people would come up with to extract energy from such a setup, and what ways are actually out there.

2. I wondered which of those creative ways would be the best.

The reason for the vacuum and valve was to provide a more complex (and to me more interesting) problem with more options.

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.

I haven't seen any solutions offered that utilized both the pressure differential and the material of the sphere itself in either sequence or combination of any type, which surprised me. That's sort of what I was hoping for and tried *not* to exclude from the solution space by anything that I wrote in the OP but somehow failed at that.

HTH.

OK, so a combination does make it more interesting. But that takes it beyond my knowledge level, but I might get motivated/interested enough to do some research and see if I can come up with an attempt at an answer. And maybe the material energy is so great as to make the pressure difference so slight as to not matter? But I don't know what I don't know.

Assuming compressed material from a neutron star or black hole is not permitted, I suppose one could fill the Oganesson sphere with more Oganesson.

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


And in case you don't get enough responses here, you could try at:

https://www.physicsforums.com/


-ERD50