# Ark falls off edge of earth

According to the cartoonist Wiley, there were two Arks, and the one that carried the dinosaurs accidentally fell off the edge of the earth.

Well, you’d really have to gullible to believe that.

In other words, maybe it’ll catch on among Ham’s supporters.

Glen Davidson

Hmm..Wiley put the dinosaurs on Ark I and us on Ark II. I wonder if that’s a subtle reference to Adams’ “B” Ark.

This comment has been moved to The Bathroom Wall.

Maybe there was a whole flotilla of arks. One of them landed in Australia to drop of the kangaroos, etc.

Hey, if ‘Elohim’ can mean one god, then ‘ark’ can mean lots of boats. Words mean whatever we need them to to defend our fairy tale holy scripture.

Hey, if ‘Elohim’ can mean one god, then ‘ark’ can mean lots of boats.

We should call it “arkim”

And now for something completely different - A real physics question about deep water.

(yes, yes, I know it’s crazy, but I want to talk about science for a change. Call me a rebel.)

The other day I was watching a documentary about diving in the Mariana trench.

Obviously, the big challenge is water pressure. At the bottom of the trench the pressure is 15,000 PSI.

When structures fail, they fail catastrophically. The water rushing into the void liberates an enormous amount of energy.

This is a source of danger for submersibles. A small external camera housing can fail with the energy equivalent of a hand grenade, threatening the vehicle.

My question is, where does the energy come from?

Imagine I build a submarine from a magic material, crystal blue unobtanium. This material is very strong and of negligible weight, and my submarine is a cube with a volume of one cubic meter.

Now I take this to the bottom of the ocean.

I can understand that I have an enormous amount of potential energy at play. My submarine displaces - essentially lifts - a column of water one meter square by 11,000 meters tall.

This water weighs about 11,000,000 kg.

Lifting eleven thousand metric tons is a lot of work, and that has to come from somewhere.

I can see where the work comes from if my submarine is light.

If my submarine had negligible weight it would take 1000 kg of force to push it under the water. It would take 1000 kg exerted over a distance of 11,000m to push it to the bottom of the sea.

That’s a lot of energy exerted, and the amount of potential energy now available makes sense. Pushing a void to the bottom of the sea is the exact inverse of lifting a weight up in the air.

But real submarines aren’t light. They are quite heavy, almost exactly as heavy as the water they displace.

Imagine I now take my theoretical sub and install a 1000 kg slab of depleted ruby red unobtanium, an extremely dense material of negligible volume.

My sub still represents a 1 cubic meter hole in the water.

But now it is neutrally buoyant. I can move it up or down in the water with almost no effort.

Again, I take it to the bottom of the ocean, this time by taping a paperclip to the side and letting it sink of its own accord.

As far as I can tell, with the cube sitting on the bottom, the void inside the cube represents the same amount of potential energy as it did before.

The water column got equally displaced, and if the hull fails, the energy liberated by the falling water will be the same, and it will be enormous.

But where did the energy come from?

I exerted no energy to push the cube down to the bottom of the sea, and the actual height of the ocean doesn’t change one angstrom, whether the cube was just below the surface or down at the bottom.

I have apparently done no work, but I have somehow stored potential energy.

This one has me stumped.

stevaroni said:

And now for something completely different - A real physics question about deep water.

(yes, yes, I know it’s crazy, but I want to talk about science for a change. Call me a rebel.)

The other day I was watching a documentary about diving in the Mariana trench.

Obviously, the big challenge is water pressure. At the bottom of the trench the pressure is 15,000 PSI.

When structures fail, they fail catastrophically. The water rushing into the void liberates an enormous amount of energy.

This is a source of danger for submersibles. A small external camera housing can fail with the energy equivalent of a hand grenade, threatening the vehicle.

My question is, where does the energy come from?

Imagine I build a submarine from a magic material, crystal blue unobtanium. This material is very strong and of negligible weight, and my submarine is a cube with a volume of one cubic meter.

Now I take this to the bottom of the ocean.

I can understand that I have an enormous amount of potential energy at play. My submarine displaces - essentially lifts - a column of water one meter square by 11,000 meters tall.

This water weighs about 11,000,000 kg.

Lifting eleven thousand metric tons is a lot of work, and that has to come from somewhere.

I can see where the work comes from if my submarine is light.

If my submarine had negligible weight it would take 1000 kg of force to push it under the water. It would take 1000 kg exerted over a distance of 11,000m to push it to the bottom of the sea.

That’s a lot of energy exerted, and the amount of potential energy now available makes sense. Pushing a void to the bottom of the sea is the exact inverse of lifting a weight up in the air.

But real submarines aren’t light. They are quite heavy, almost exactly as heavy as the water they displace.

Imagine I now take my theoretical sub and install a 1000 kg slab of depleted ruby red unobtanium, an extremely dense material of negligible volume.

My sub still represents a 1 cubic meter hole in the water.

But now it is neutrally buoyant. I can move it up or down in the water with almost no effort.

Again, I take it to the bottom of the ocean, this time by taping a paperclip to the side and letting it sink of its own accord.

As far as I can tell, with the cube sitting on the bottom, the void inside the cube represents the same amount of potential energy as it did before.

The water column got equally displaced, and if the hull fails, the energy liberated by the falling water will be the same, and it will be enormous.

But where did the energy come from?

OK.

You have a cube one inch on a side sitting on the sea floor at the bottom of the Mariana Trench. Assume that the sea floor is flat, so that gravity is acting perpendicular to the top face of the cube. If the pressure is 15,000PSI there is 15,000 pounds of matter sitting on the cube. Now think what happens if the cube collapses vertically. Effectively that 15,000 pounds of matter sitting on the cube drops one inch. That is a lot of potential energy.

Your neutral bouyancy example ignores the fact that as your cube drops, it loses potential energy, and the displaced water that was below and is now above has gained energy.

What an excellent thought question for a physics class!

Kevin B said:

Effectively that 15,000 pounds of matter sitting on the cube drops one inch. That is a lot of potential energy.

Your neutral buoyancy example ignores the fact that as your cube drops, it loses potential energy, and the displaced water that was below and is now above has gained energy.

Kevin;

I think I wasn’t clear with my question.

I can see where, when the cube collapses, the matter above would drop into the void, and that’s the source of enormous potential energy.

The point that i still don’t understand is what work did I do to create (or store, or potentialize) that potential energy to begin with.

In your example, there’s 15,000 in/lb(f) of potential energy available, which liberates when the cube collapses.

Where did it come from?

If the 1” cube was a simple void, you would have had to apply a large force over a large distance to drive it down to the bottom of the ocean. Work = F*D. Ergo, stored energy.

But if the 1” cube was heavy enough to be neutral (say there was a scrap of depleted uranium in there), then you need apply no force to push it to the ocean floor.

F*D is reduced to 0*D which is reduced to 0. Ergo no work.

But still, stored energy.

stevaroni said:

And now for something completely different - A real physics question about deep water.

(yes, yes, I know it’s crazy, but I want to talk about science for a change. Call me a rebel.)

The other day I was watching a documentary about diving in the Mariana trench.

Obviously, the big challenge is water pressure. At the bottom of the trench the pressure is 15,000 PSI.

When structures fail, they fail catastrophically. The water rushing into the void liberates an enormous amount of energy.

This is a source of danger for submersibles. A small external camera housing can fail with the energy equivalent of a hand grenade, threatening the vehicle.

My question is, where does the energy come from?

Imagine I build a submarine from a magic material, crystal blue unobtanium. This material is very strong and of negligible weight, and my submarine is a cube with a volume of one cubic meter.

Now I take this to the bottom of the ocean.

I can understand that I have an enormous amount of potential energy at play. My submarine displaces - essentially lifts - a column of water one meter square by 11,000 meters tall.

This water weighs about 11,000,000 kg.

Lifting eleven thousand metric tons is a lot of work, and that has to come from somewhere.

I can see where the work comes from if my submarine is light.

If my submarine had negligible weight it would take 1000 kg of force to push it under the water. It would take 1000 kg exerted over a distance of 11,000m to push it to the bottom of the sea.

That’s a lot of energy exerted, and the amount of potential energy now available makes sense. Pushing a void to the bottom of the sea is the exact inverse of lifting a weight up in the air.

But real submarines aren’t light. They are quite heavy, almost exactly as heavy as the water they displace.

Imagine I now take my theoretical sub and install a 1000 kg slab of depleted ruby red unobtanium, an extremely dense material of negligible volume.

My sub still represents a 1 cubic meter hole in the water.

But now it is neutrally buoyant. I can move it up or down in the water with almost no effort.

Again, I take it to the bottom of the ocean, this time by taping a paperclip to the side and letting it sink of its own accord.

As far as I can tell, with the cube sitting on the bottom, the void inside the cube represents the same amount of potential energy as it did before.

The water column got equally displaced, and if the hull fails, the energy liberated by the falling water will be the same, and it will be enormous.

But where did the energy come from?

I exerted no energy to push the cube down to the bottom of the sea, and the actual height of the ocean doesn’t change one angstrom, whether the cube was just below the surface or down at the bottom.

I have apparently done no work, but I have somehow stored potential energy.

This one has me stumped.

I know this the answer is Yoda

Marilyn said: I know this the answer is Yoda

Mess with the unobtanium, you must not.

Go backwards in time, you will.

IANA physicist, but let me hazard a guess.

If you fell 11,000 meters, think of the energy that would be liberated on your landing! Better yet, eliminate air resistance, so you never reach a terminal velocity (someone with better math skills than I can calculate how fast you’d be falling).

Where did the energy come from? Isn’t it gravity? I guess you could say that you stored up that potential energy in your climb to 11,000 meters.

But in the ocean example, you don’t have to climb – you’re already on top. By creating a vessel with a specific gravity greater than seawater, you are merely giving gravity the ‘opportunity’ to do its work.

The vessel is drawn down, and at the moment of implosion, gravity is ‘freed’ to smash down that 11,000 meter column of water.

The energy is the same thing that’s sticking us to the surface of the Earth, only in your example you’ve provided a way for it to build up a big potential, then release it all at once. Sort of like stretching a rubber band until you get a nasty snap.

When you switch from moving a massless cube to the bottom of the ocean to moving a neutrally buoyant cube across the same span, you’ve replaced whatever external force you were using to overcome buoyancy force with the force of gravity. The same amount of work was done on the cube and on the surrounding water, you’ve just switched where it came from.

Also, the potential energy isn’t in the cube, it’s in the water column above the cube. That potential energy is a state function, and doesn’t depend on how the column ended up with the cube at the bottom.

stevaroni said:

Kevin;

I think I wasn’t clear with my question.

I can see where, when the cube collapses, the matter above would drop into the void, and that’s the source of enormous potential energy.

The point that i still don’t understand is what work did I do to create (or store, or potentialize) that potential energy to begin with.

In your example, there’s 15,000 in/lb(f) of potential energy available, which liberates when the cube collapses.

Where did it come from?

The work done in compressing a volume under pressure is different from the work done in getting the vessel down to the bottom of the ocean.

If the vessel is neutrally buoyant, the amount of work done by gravity on the vessel is exactly cancelled by the work done by the displaced water. In other words the gravitational work done in transporting the vessel to the bottom of the ocean is stored by the displaced water; each successive volume of water, being equal to the volume (and weight, if the vessel is neutrally buoyant) of the vessel is lifted up as the vessel descends through it.

On the other hand, the potential energy stored in the volume of the vessel due to the pressure (either on the inside or the outside) is just the pressure multiplied by the volume. That energy doesn’t appear as kinetic energy unless the vessel ruptures. If the pressure is on the outside and the vessel ruptures catastrophically, the adiabatic compression of the air inside the vessel will cause the temperature to become very high almost instantly; completely incinerating everything inside.

As an old submariner, I have some direct experience with this. We experience increases in temperature when the pressure rises inside the submarine and decreases when the pressure decreases. One of the many training exercises submariners go through is escape training in which we enter an escape chamber that is pressurized to the sea pressure outside. This allows us to open an outer hatch and do a buoyant ascent in the ocean outside. Time is crucial. So we must pressurize as quickly as possible; and in the process the temperature rises until it feels like a sauna inside the escape chamber. Conversely, when the pressure is decreased, it becomes freezing cold in the chamber.

One of my former shipmates was on the USS Scorpion when she sank. It was later discovered that a hydrogen explosion from the storage batteries (nuclear subs still have emergency back-up batteries) started the sequence that lead to the sinking. That explosion was so disruptive that the crew couldn’t get control of the boat in order to get to the surface. She imploded on the way to the bottom, and the sounds of successive implosions of various compartments could be heard on the sonar arrays stationed around the Atlantic.

The first implosion probably incinerated everything inside.

I think that as the submarine descends, its gravitational potential energy is transferred to the water it displaces upward, which therefore now has more gravitational potential energy than it had before.

(This is a deep subject.)

Henry

Henry J said:

(This is a deep subject.)

Henry

Not only that; but if one isn’t careful, one ends up all wet.

Sounds like it’s gravity all the way down.

Sounds like it’s gravity all the way down.

So you believe in gravity? It’s only a theory. Question Gravity

Just Bob said:

Sounds like it’s gravity all the way down.

So was the Flood really the tsunami caused by the turtles imploding?

stevaroni said:

Kevin B said:

Effectively that 15,000 pounds of matter sitting on the cube drops one inch. That is a lot of potential energy.

Your neutral buoyancy example ignores the fact that as your cube drops, it loses potential energy, and the displaced water that was below and is now above has gained energy.

Kevin;

I think I wasn’t clear with my question.

I can see where, when the cube collapses, the matter above would drop into the void, and that’s the source of enormous potential energy.

The point that i still don’t understand is what work did I do to create (or store, or potentialize) that potential energy to begin with.

In your example, there’s 15,000 in/lb(f) of potential energy available, which liberates when the cube collapses.

Where did it come from?

If the 1” cube was a simple void, you would have had to apply a large force over a large distance to drive it down to the bottom of the ocean. Work = F*D. Ergo, stored energy.

But if the 1” cube was heavy enough to be neutral (say there was a scrap of depleted uranium in there), then you need apply no force to push it to the ocean floor.

F*D is reduced to 0*D which is reduced to 0. Ergo no work.

But still, stored energy.

The energy comes from letting your 1000 kg slab of depleted ruby red unobtanium plummet to the seabed, As an extremely dense material of negligible volume, you will have to restore its potential energy without the benefit of its crystal blue unobtanium floatation device before you can repeat your experiment.

Mike Elzinga said: On the other hand, the potential energy stored in the volume of the vessel due to the pressure (either on the inside or the outside) is just the pressure multiplied by the volume.

I think you are wrong there Mike. It’s forty years since I used Boyle’s law, but I remember a square law in there somewhere. Surely if PV is constant, halving the volume and doubling the pressure requires the input of a considerable amount of work.

Mike Elzinga said: If the pressure is on the outside and the vessel ruptures catastrophically, the adiabatic compression of the air inside the vessel will cause the temperature to become very high almost instantly; completely incinerating everything inside.

Nobody’s mentioned yet that the concept of adiabatic heating causes f�hn / foehn winds and causes fuel to ignite in a diesel engine and causes the bottom of your bicycle tire hand pump to get hot. There’s even a fire starter that uses adiabatic heating - it looks a lot like a bicycle tire hand pump.

Dave Lovell said:

I think you are wrong there Mike. It’s forty years since I used Boyle’s law, but I remember a square law in there somewhere. Surely if PV is constant, halving the volume and doubling the pressure requires the input of a considerable amount of work.

I suspect you may be conflating energy and force. Pressure multiplied by area (e.g., newtons per square meter multiplied by square meters) gives force.

Pressure multiplied by volume (e.g., newtons per square meter multiplied by cubic meters) has units of energy (work).

Think of the volume boundary moving. Pressure times area gives force, but then force times the distance the boundary moves is work.

Static pressure within or outside a volume does no work unless the volume changes. Once the volume explodes or implodes, energy is released.

Mike Elzinga said:

Dave Lovell said:

I think you are wrong there Mike. It’s forty years since I used Boyle’s law, but I remember a square law in there somewhere. Surely if PV is constant, halving the volume and doubling the pressure requires the input of a considerable amount of work.

I suspect you may be conflating energy and force. Pressure multiplied by area (e.g., newtons per square meter multiplied by square meters) gives force.

Pressure multiplied by volume (e.g., newtons per square meter multiplied by cubic meters) has units of energy (work).

Think of the volume boundary moving. Pressure times area gives force, but then force times the distance the boundary moves is work.

Static pressure within or outside a volume does no work unless the volume changes. Once the volume explodes or implodes, energy is released.

I don’t disagree with any of that Mike, but maybe I misunderstood what you meant when you said “potential energy stored .…. is just the pressure multiplied by the volume. Intuitively I feel if I double the pressure in a gas bottle it will have more like four times the stored energy, because you have to work a lot harder to pump the extra gas in. P1V1=P2V2=Constant, but every change in volume surely requires a change of potential energy because it can only be achieved by moving a force through a distance.

Dave Lovell said:

I don’t disagree with any of that Mike, but maybe I misunderstood what you meant when you said “potential energy stored .…. is just the pressure multiplied by the volume. Intuitively I feel if I double the pressure in a gas bottle it will have more like four times the stored energy, because you have to work a lot harder to pump the extra gas in. P1V1=P2V2=Constant, but every change in volume surely requires a change of potential energy because it can only be achieved by moving a force through a distance.

Energy stored in a compressed gas is roughly analogous to energy stored in a compressed spring with friction.

Consider a simple case of a piston in a cylinder with an ideal gas inside, and an initial pressure of P0 and an initial volume of V0.

Now push on the piston and compress the gas to a volume of Vf.

The pressure will increase according to the idea gas law, PV = nkT (Note: both sides of this equation has units of energy); or, in terms of the pressure, P = nkT/V.

The work done is the pressure times the area of the piston integrated (continuously summed) over the distance the piston moves (pressure is continually increasing, so we must integrate). Note that this has units of pressure times area times distance; in other words, force times distance.

How the pressure changes depends on whether or not we allow the temperature to change. In an adiabatic compression, the temperature rises and all the work done on the gas is stored in the kinetic energy of the molecules of the gas (1/2 kT is the kinetic energy per degree of freedom of a molecule).

In an isothermal compression, we allow heat (energy) to flow out into an external reservoir; so only part of the work done by the piston is stored in the kinetic energy of the molecules of the gas, with the rest flowing out of the cylinder into the reservoir as heat.

Since I don’t know what your math abilities are, I am trying to put this into words; which, I believe, is the superior way to do it (it is not uncommon for people to be fooled into thinking they understand something if they can do the math). Concepts first, math later if necessary.

The potential energy stored in a volume of compressed gas – or, conversely, a volume under external pressure – is simply pressure times volume. It is potential energy much like energy stored in a compressed spring. No work is done unless the volume changes (or the spring changes length).

Dave Lovell said: The energy comes from letting your 1000 kg slab of depleted ruby red unobtanium plummet to the seabed, As an extremely dense material of negligible volume, you will have to restore its potential energy without the benefit of its crystal blue unobtanium floatation device before you can repeat your experiment.

Yeah, I finally realized that this morning.

Not having a good conceptual idea where the potential came from, I sat down and used the old engineers trick of tallying up the energy in the various states, and trying to figure out what was missing…

State 1) Cube just above the surface of the water. 1000Kg mass @ 0m height.

State 2) Cube just under the surface of the water. 1000Kg mass @ -1m, entire surface of the ocean @ +1angstrom. Not much stored energy

State 3) Cube at bottom of ocean. 1000Kg mass @ -11000m, entire surface of the ocean still @ +1angstrom. Lots of stored energy

State 4) Imploded cube at bottom of ocean. 1000Kg mass @ -11000m, entire surface of the ocean back at 0m. Lots of energy liberated.

I can understand, from a mathematical perspective, where the energy is coming from, but there’s still sometime unsettling unsettling to the logic.

If I had lifted the 1000kg eleven kilometers into the sky I could readily see where I had “earned” the potential energy in the system. I would have done an enormous amount of work.

But it just doesn’t seem as if I’ve really done anything to earn the potential energy change between states 2 and 3.

yes, I know that 1000 Kg moved, but there was no force required. It took no work to make it happen.

At least if I had chucked 1000 bricks down an 11Km deep mine shaft I’d feel like I was doing something to justify the energy stored as the bricks fell and released in the crash at the end.

Dave Lovell said:

Intuitively I feel if I double the pressure in a gas bottle it will have more like four times the stored energy, because you have to work a lot harder to pump the extra gas in. P1V1=P2V2=Constant, but every change in volume surely requires a change of potential energy because it can only be achieved by moving a force through a distance.

Factors like � or other such factors come from specific conditions (such as whether the compression is adiabatic or isothermal).

For example, in the case of a spring, the energy stored is � kx2, where, in this case, the spring constant has units of force per distance. So force per distance multiplied by distance squared is force times distance, or simply energy (work).

It is the same with compressed gases. But the point is not to worry about constants until one is considering specific cases and needs to know the specific constant involved. The better way to do it is to think of the process conceptually. In that way, one is better prepared to set up and do a calculation properly and make fewer mistakes.

There’s something similar to this in electrical engineering.

In electronics 101 you learn about basic components, some of which, like capacitors and inductors, can store energy.

One of the (in)famous thought experiments involves taking 2 identical, ideal, capacitors, one of which has a charge(therefore stored energy) and one of which does not, and connecting them together.

The charge will redistribute but otherwise remain the same, but half the energy in the system will seemingly vanish for no obvious reason.

I’ve been an engineer for 30 years now, and this one still bothers me.

stevaroni said:

There’s something similar to this in electrical engineering.

In electronics 101 you learn about basic components, some of which, like capacitors and inductors, can store energy.

One of the (in)famous thought experiments involves taking 2 identical, ideal, capacitors, one of which has a charge(therefore stored energy) and one of which does not, and connecting them together.

The charge will redistribute but otherwise remain the same, but half the energy in the system will seemingly vanish for no obvious reason.

I’ve been an engineer for 30 years now, and this one still bothers me.

This is a “fun” example of an oversimplified and idealized case.

In reality, wires have resistance and accelerating charges radiate energy. When the capacitors are connected, charge has to accelerate and then decelerate as the voltage across the two capacitors comes to equilibrium.

In fact, the charge distribution between the two capacitors oscillates. Even if the wires had no resistance, the accelerating charges oscillating back and forth between the capacitors will produce electromagnetic radiation that carries away half the energy if the two capacitors are identical. As that energy radiates away, the charges finally distribute equally on the two capacitors.

Kevin B said:

So was the Flood really the tsunami caused by the turtles imploding?

There’s an obvious weak point where the two shells join. The radius changes fast and that’s going to result in a stress build-up during the pressure from giant floods.

Mike Elzinga said:… the accelerating charges oscillating back and forth between the capacitors will produce electromagnetic radiation that carries away half the energy if the two capacitors are identical. As that energy radiates away, the charges finally distribute equally on the two capacitors.

That’s another thing I learned in circuits 101.

Radio waves are voodoo.

Dave Lovell Wrote:

P1V1=P2V2=Constant, but every change in volume surely requires a change of potential energy because it can only be achieved by moving a force through a distance.

The case of

P1V1 = P2V2 = constant

is the case in which no net work is done on the gas whatsoever. One such case is the “free expansion” against no resistance case; so no work is done. The other case is the isothermal case in which all work done on the gas is transported out of the gas as heat.

The temperature remains constant; which means the internal energy of the gas remains constant. PV = nkT is constant when the temperature is constant and the number of molecules remains constant.

stevaroni said:

Radio waves are voodoo.

:-)

State 2) Cube just under the surface of the water. 1000Kg mass @ -1m, entire surface of the ocean @ +1angstrom. Not much stored energy

State 3) Cube at bottom of ocean. 1000Kg mass @ -11000m, entire surface of the ocean still @ +1angstrom. Lots of stored energy

But it just doesn’t seem as if I’ve really done anything to earn the potential energy change between states 2 and 3.

My suggestion is suggest forget about the height of the surface of the ocean; think about its center of gravity instead. Or to simplify even more, forget the whole ocean, and consider only the portion of it directly above the sub. The center of gravity of that column has been pushed up by the height of the sub. I suppose that mathematically, it’s as if the water displaced by the sub has been elevated to the surface, acquiring the potential energy lost by the sub due to its descent. (Can that be considered analogous to lifting something by use of a pulley with weights on one end of the rope matching the weight of the cargo?)

Henry

stevaroni said:

That’s another thing I learned in circuits 101.

Radio waves are voodoo.

Then call an exorcist!

Henry J said:

Radio waves are voodoo.

Then call an exorcist!

Exorcist. RF engineer. Same thing.

That, and the guys who do USB drivers. I’m working on one of those right now.

Black. Freakin’. Magic.

Work, shmork. I am beginning to understand the original question. As the box sinks, the internal pressure has to rise, or else the box will be crushed. Because pV/T is a constant, the temperature must rise to guarantee (bring about?) an increase in pressure. What mechanism makes the temperature rise? To make the point more precisely, assume a very well insulated box that is submerged quickly. Will it be crushed by the pressure of the water? If not, what forces the internal pressure to go up? Regards, Naive Realist

Matt Young said:

Work, shmork. I am beginning to understand the original question. As the box sinks, the internal pressure has to rise, or else the box will be crushed. Because pV/T is a constant, the temperature must rise to guarantee (bring about?) an increase in pressure. What mechanism makes the temperature rise? To make the point more precisely, assume a very well insulated box that is submerged quickly. Will it be crushed by the pressure of the water? If not, what forces the internal pressure to go up? Regards, Naive Realist

The internal pressure and temperature doesn’t have to rise. It depends on whether the structure of the box can withstand the external pressure without deforming. For example, the pressure inside a submarine, or a bathyscaphe, does not increase as the vehicle descends, even 11 kilometers. These vehicles can return to the surface quickly, without the passengers getting the bends, because the internal pressure never changed.

The internal pressure goes up if the structure of the box deforms (collapses). Assuming a well insulated box, the work involved in squeezing the air inside the box (raising its pressure) is deposited into the air (in the now smaller volume), thus raising the temperature of the air as well.

Good, thanks! Something said above - I do not remember what - made me think that the internal pressure had to be high, and I could not see how that condition came about. In fact the structure is strong enough to withstand the water pressure, and when the box collapses, the potential energy that is released is that due to the stress on the structure. The interior could have been evacuated, I suppose, and in fact is comparatively at a very low pressure at the bottom of the ocean. I must have watched too many old movies with diving suits in them.

Mike Elzinga said:

Dave Lovell Wrote:

P1V1 = P2V2 =Constant, but every change in volume surely requires a change of potential energy because it can only be achieved by moving a force through a distance.

The case of

P1V1 = P2V2 = constant

is the case in which no net work is done on the gas whatsoever. One such case is the “free expansion” against no resistance case; so no work is done. The other case is the isothermal case in which all work done on the gas is transported out of the gas as heat.

The temperature remains constant; which means the internal energy of the gas remains constant. PV = nkT is constant when the temperature is constant and the number of molecules remains constant.

I knew we must agree really. You slyly slip from “potential energy” to “internal energy” and our difference are clear! :-)

As a Physics graduate who has made a living in Engineering, I see “potential energy” as what I can get out of the system as useful work. If I fill a bottle with compressed ideal gas, you are saying only a fraction the work I put in goes into the “internal energy” of the gas. The rest is “lost” as waste heat as the gas cools back to ambient, and the higher the final pressure the higher the fraction of the input work becomes lost heat. But when I then let the gas out to drive an air turbine, I not only get the “internal energy” of the gas, but also create a heat engine to pull energy from the environment as the expanding gas cools. Theoretically doubling the pressure in the air bottle quadruples the total work output of the air turbine it is powering.

Dave Lovell said:

As a Physics graduate who has made a living in Engineering, I see “potential energy” as what I can get out of the system as useful work.

Potential energy and internal energy are not different in this case. The internal energy contained in the kinetic energy of the gas molecules is available for work provided that momentum transfers by the gas molecules are primarily in the direction of an outward moving piston or can transfer their momentum to a turbine.

How much of that internal energy is available depends on whether or not heat is allowed to flow out of the gas. If it is adiabatically compressed (no heat flowing in or out), then the internal energy added to the gas during compression (i.e., the work done on the gas) is available as work when the gas is allowed to expand. If heat is allowed to flow out of the gas as it is compressed, then the energy in the heat that flows out is no longer available to do work unless some heat is put back in.

One can extract much of the internal energy from the compressed gas by cooling it to a temperature below the temperature of the environment in which the desired work is to be done. In fact, one can cool the gas until the pressure inside the cylinder is below the pressure outside the cylinder. In this particular case, one can get some work by allowing the outside pressure to push the piston in farther until the inside pressure becomes equal to the outside pressure. But that work is more than offset by the work needed to extract the heat from the gas in the first place. So there is a net loss, as is almost always the case.

It’s just thermodynamic energy bookkeeping. Classical thermodynamics generally divides the energy of heat engines into three parts; (1) mechanical work, (2) internal energy of the “working medium,” and (3) heat.

However, thermodynamics is more general than just heat engines because it applies to all forms of energy, including the energy required to polarize electromagnetic materials or to put atoms and molecules into various excited states.

Because matter interacts with matter, there is always some kind of internal energy in the form of molecular vibrations or translations that can show up in ways that transmit energy in the direction of momentum transfers. Heat engines are but a very special case of the general nature of energy transmission and “storage.”

So the distinction between internal energy and potential energy is simply a matter of context. If there is a way to extract the internal energy to do “useful work” (an anthropomorphic requirement), then internal energy is potential energy. Energy will flow in the direction of momentum transfers – higher temperatures to lower temperatures. If there is a way to harness that flow for human purposes, then the historical term “potential energy” applies because such a condition has the “potential” for doing “useful work.”

Physicists don’t usually wallow in the quagmires of the meanings of the meanings of meanings. The similarities and distinctions are usually obvious from context.

However, as we have learned from the obsessive/compulsive word-gaming of ID/creationists, misuses of words – e.g., entropy, the second law, etc. – have pedagogical consequences that physicists are then left to clean up.