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### Author Topic: Is this a new paradox of energy?  (Read 27240 times)

#### Anukshan Ghosh

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##### Is this a new paradox of energy?
« on: 19/02/2011 03:42:19 »
On lifting a system from the floor to a height does the energy I expended get added to the system's internal energy? Cause change in Internal Energy in a isothermal process is given by nCv(T2-T1),which predicts ΔU to be zero.

#### CPT ArkAngel

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##### Is this a new paradox of energy?
« Reply #1 on: 19/02/2011 09:15:27 »
where do you see a paradox? More explanations, please... It seems to be a simple problem.

#### yor_on

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##### Is this a new paradox of energy?
« Reply #2 on: 19/02/2011 15:40:58 »
No, they are two different processes. You may lift a book from the floor to the table, while you're acting on the book you loose some 'energy' but the book gain no energy from you. The only thing changing for the book is the position it have relative gravity, that is, you just moved it a little further away from 'gravity's center'. That means that its 'potential energy' might be seen to grown a little versus Earths center although if measured you will find no extra 'energy' expressed as mass in that book. At the same time as you lifted that book and put it on the table you also, if you like, decreased its 'potential energy' relative the moon if doing so at night, daytime you might assume that you increased its 'potential energy' relative the moon as the moon then could be in a opposite position relative the direction you moved that book.

If you on the other hand define gravity as a 'force', you actually decreased that 'force' by removing the book from the Earths floor, relative Earth/book at the same time as you, if at night, increased the moons 'force/gravity' acting on that book. And that's why I find myself mixing those two at times. It's hard not looking at gravity as a 'force' as that is exactly as we experience it normally, it acting on us. but it's no 'force' in a normal manner, it's more like a invincible dynamic topology.
==

It's slightly confusing as I ignore Earth when discussing the moon/book. But it is true in that you can define any two objects as a system if you like, depending on what you try to define. I had to look at this twice to get it right :) Also it is a question about how to define the possible interaction from that 'potential energy' to me. If I move something away from gravity we can assume that it, if following the geodesics moving into that 'gravity well' its 'interaction' will become stronger the further it have to travel, hitting the ground. But when we have several gravity wells acting in different directions on that book it becomes more confusing to me. And that's why I ignore Earth for this moon/book. A cheap escape I know :)

==

The only way I know to increase the 'energy' aka mass of that book is if you 'compress' it and then somehow make it stay in a compressed state. The rest is variables of 'potential energy' relative what you define as your system, be it Earth/book or Moon/book, well, as I see it.
==

It naturally depends on how you define your system but even if defining it as a system including you, the book and the gravity wells acting on you you will find that the book do not gain any measurable energy, only a potential and that 'energy' not relative you, only relative gravity.
« Last Edit: 19/02/2011 16:43:17 by yor_on »

#### Anukshan Ghosh

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##### Is this a new paradox of energy?
« Reply #3 on: 20/02/2011 03:01:58 »
To summarize it, you say not a measurable potential energy gain in the system.
Thank you

#### Anukshan Ghosh

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##### Is this a new paradox of energy?
« Reply #4 on: 24/02/2011 06:42:03 »
I got my answer and everything else is crap actually what happens is that a systems internal energy is defined from a frame of reference in which the center of mass is at rest and hence adding potential energy to the system does not add to its internal energy. A steady state is established in terms of internal energy for these works performed.

#### Geezer

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##### Is this a new paradox of energy?
« Reply #5 on: 24/02/2011 08:14:05 »
Actually, if the book is part of the system which has the internal energy, because you did work to move the book, you did change the internal energy of the system. If you didn't, you'd have violated the first law of thermodynamics.

#### yor_on

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##### Is this a new paradox of energy?
« Reply #6 on: 24/02/2011 10:17:37 »
No Geezer, you're not transferring any energy to the book, and I think that was what this question was about? 'Potential energy' is a conceptual framework describing possible interactions under the influence of the arrow of time. Not 'now' but 'when/if' the book falls down. you can move the moon if you like, without adding any energy to it by moving it, same as you move a starship by 'expending' energy. The star-ships 'invariant mass' will not increase as far as I know, the possible exception to it being its Lorentz contraction that just might add a invariant mass.

We had this discussion before methinks :)
« Last Edit: 24/02/2011 10:31:46 by yor_on »

#### Geezer

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##### Is this a new paradox of energy?
« Reply #7 on: 24/02/2011 19:02:26 »
Yoron,

It's a thermodynamic question, and internal energy is a thermodynamic concept. Whenever work is done on a "system", it alters the internal energy of the system.

Check out

Daemons - Systems     at    http://www.thermofluids.net/

#### yor_on

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##### Is this a new paradox of energy?
« Reply #8 on: 25/02/2011 11:39:56 »
Nice site Geezer, and I agree on that looked at as a system the 'internal energy' have changed for it. But a system is very much a conceptual exercise wherein you are free to define it like you need, for the validation of your experiment, within limits of course but..

The 'internal energy' you refer too I see a as a common description for all relations involved between, and in, the objects you defined as belonging to that same 'system'. And you need only to change what objects you refer to to get a new and different 'system'. As I see it not unlike the idea of 'potential energy'. But even so, that book has no extra energy collected in it by you lifting it up on a table. The potential energy that it refer too is not measurable as any new mass, its atoms are not jiggling faster. In fact, nothing have changed for the book itself. The only thing changing is the relation it will have relative gravity. And that's the plain truth, nothing more :) But the 'systems' possible energy have changed, if we remember that it's the 'possible' energy we're talking about, that is the 'potential energy'.

Gravity is no force, to me it's more of a 'topology'. What you could assume, possibly, is that when getting compressed, like moved close to the event horizon, or past, it should express itself as more mass. At least it seems reasonable to assume that, also there is the question about what a Lorentz contraction does to a piece of lasting matter. Those two are really interesting :)

#### Geezer

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##### Is this a new paradox of energy?
« Reply #9 on: 25/02/2011 19:23:28 »
Nice site Geezer, and I agree on that looked at as a system the 'internal energy' have changed for it. But a system is very much a conceptual exercise wherein you are free to define it like you need, for the validation of your experiment, within limits of course but..

The 'internal energy' you refer too I see a as a common description for all relations involved between, and in, the objects you defined as belonging to that same 'system'. And you need only to change what objects you refer to to get a new and different 'system'. As I see it not unlike the idea of 'potential energy'. But even so, that book has no extra energy collected in it by you lifting it up on a table. The potential energy that it refer too is not measurable as any new mass, its atoms are not jiggling faster. In fact, nothing have changed for the book itself. The only thing changing is the relation it will have relative gravity. And that's the plain truth, nothing more :) But the 'systems' possible energy have changed, if we remember that it's the 'possible' energy we're talking about, that is the 'potential energy'.

Gravity is no force, to me it's more of a 'topology'. What you could assume, possibly, is that when getting compressed, like moved close to the event horizon, or past, it should express itself as more mass. At least it seems reasonable to assume that, also there is the question about what a Lorentz contraction does to a piece of lasting matter. Those two are really interesting :)

Yes, but I think you'll find that if the book was part of a system, and the work done to raise it came from outside the system, the internal energy of the system increased. If you can explain how it's possible to elevate the book without doing work, I might start to believe you.

#### yor_on

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##### Is this a new paradox of energy?
« Reply #10 on: 25/02/2011 20:01:05 »
I'm just saying that there is no 'energy' transfered to the book Geezer? Where the 'energy' used by lifting the book went? Where does any 'work done' go? We have this formulation of 'work' transforming into 'work done', and what differs between them is 'energy expended', but exactly where it goes in any system? It depends on what you define as it I guess, in a rocket you might say that it transformed into its 'speed' and 'heat/radiation'. In the case of a human chemical processes should be the most important I guess?

As for the 'energy' increasing?
Not sure I follow you there?

The only thing changing is work being done on the book? Maybe you're thinking of the books 'potential energy' relative gravity?
==

Let's make it simple.
I say there is no energy transfered to the book?
That was the original question as I understood it.

Are you saying that there is an added energy in the book?
Prove it.
==

Maybe you're thinking of a enclosed system? Like a container in where you pour something hot, increasing the systems energy, the pouring taking place from outside the defined system? Then I would agree. If we define it as lifting something really heavy inside a closed container then the systems 'energy' will transform, but not increase. If we define it as a open system, no physical enclosure, but still including someone lifting a book against gravity, then I expect the system to lose its 'energy expended', in form of heat and other chemical processes, diminishing the systems 'energy'. If we define the system as only the book versus gravity and let the lifter be outside our 'system' then work is being done on the book and its 'potential energy' relative gravity is increased but its own internal measurable mass/energy will not increase as far as I know? To actually increase the 'energy' for the system? If I compressed it I would expect the books internal energy to increase, no gravity needed other than the books own invariant mass/energy increasing, produced by a compression, just like making a black hole.

« Last Edit: 25/02/2011 20:42:07 by yor_on »

#### Geezer

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##### Is this a new paradox of energy?
« Reply #11 on: 25/02/2011 20:28:05 »
Hey! They're not my rules. I'm only applying the laws of thermodynamics

"The internal energy of a system can be changed by heating the system or by doing work on it;[1] the first law of thermodynamics states that the increase in internal energy is equal to the total heat added and work done."

From http://en.wikipedia.org/wiki/Internal_energy

#### yor_on

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##### Is this a new paradox of energy?
« Reply #12 on: 25/02/2011 20:44:51 »
Well, we define 'potential energy' too Geezer. We have a lot of laws describing transformations, but as for how they are measurable? A compression should be measurable.
==

"In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy necessary to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields."
« Last Edit: 25/02/2011 20:48:49 by yor_on »

#### Geezer

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##### Is this a new paradox of energy?
« Reply #13 on: 25/02/2011 20:49:31 »
Well, we define 'potential energy' too Geezer. We have a lot of laws describing transformations, but as for how they are measurable? A compression should be measurable.

Not quite sure I understand your point there Yoron, but I do know that work and heat are fairly easy to quantify.

#### yor_on

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##### Is this a new paradox of energy?
« Reply #14 on: 25/02/2011 20:55:22 »

#### Geezer

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##### Is this a new paradox of energy?
« Reply #15 on: 25/02/2011 21:01:58 »
Oh, I'm only saying it's not hard to quantify the amount of work or heat added to a system (in thermodynamics).

I didn't understand what you meant by "A compression should be measureable."

#### yor_on

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##### Is this a new paradox of energy?
« Reply #16 on: 25/02/2011 21:06:38 »
Conservation of energy.

"The first law of thermodynamics simply asserts that energy is conserved,[17] and that heat is included as a form of energy transfer. A commonly used corollary of the first law is that for a "system" subject only to pressure forces and heat transfer (e.g., a cylinder-full of gas), the differential change in energy of the system (with a gain in energy signified by a positive quantity) is given as the following equation:

***

where the first term on the right is the heat transfer into the system, defined in terms of temperature T and entropy S (in which entropy increases and the change dS is positive when the system is heated), and the last term on the right hand side is identified as "work" done on the system, where pressure is P and volume V (the negative sign results since compression of the system requires work to be done on it and so the volume change, dV, is negative when work is done on the system). Although this equation is the standard textbook example of energy conservation in classical thermodynamics, it is highly specific, ignoring all chemical, electric, nuclear, and gravitational forces, effects such as advection of any form of energy other than heat, and because it contains a term that depends on temperature. The most general statement of the first law (i.e., conservation of energy) is valid even in situations in which temperature is undefinable.

Energy is sometimes expressed as the following equation:

***

which is unsatisfactory[11] because there cannot exist any thermodynamic state functions W or Q that are meaningful on the right hand side of this equation, except perhaps in trivial cases.
==

What I meant was that if you compress a spring, and leave it compressed, that should be measurable as an added 'invariant' mass. But if we're discussing heat, fluids and gases it's different than with our 'lifting a book'.
« Last Edit: 25/02/2011 21:10:39 by yor_on »

#### Geezer

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##### Is this a new paradox of energy?
« Reply #17 on: 25/02/2011 21:38:54 »
All good stuff, but I'm not sure how to apply it in this particular case.

Try this:

We define a system consisting of the Moon, a table and a book only.

Initially, the book is sitting on the surface of the Moon. A big hand comes down from above and moves the book onto the table.

We then might try to answer questions like:
Was work done on the book?
Was work done on the system?
Did the internal energy of the system change?
Is it even possible to answer these questions by applying Thermodynamics? (I have a suspicion the answer may be no.)

#### yor_on

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##### Is this a new paradox of energy?
« Reply #18 on: 25/02/2011 22:03:55 »
:)

Sh*

I really liked that big hand, reminded me of MP:n. Sorry, I was away for a while, helped me mum. The first law is about conservation of energy as I think of it. You're probably all too right in it being tricky defining where the 'energy' went though :) heat? This one might help us, ah, maybe?

"The total energy of the universe does not change. This does not mean that the form of the energy cannot change. Indeed, chemical energies of a molecule can be converted to thermal, electrical or mechanical energies.

The internal energy of a system can change only by work or heat exchanges. From this the change in the free energy of a system can be shown by the following equation:

ΔE = q – w

When q is negative heat has flowed from the system and when q is positive heat has been absorbed by the system. Conversely when w is negative work has been done on the system by the surrounding and when positive, work has been done by the system on the surroundings.

In a reaction carried out at constant volume no work will be done on or by the system, only heat will be transferred from the system to the surroundings. The end result is that:

ΔE = q

When the same reaction is performed at constant pressure the reaction vessel will do work on the surroundings. In this case:

ΔE = q – w

where

w = PΔV

When the initial and final temperatures are essentially equal (e.g. in the case of biological systems):

ΔV = Δn[RT/P]

therefore,

w = ΔnRT

By rearrangement of the above equations one can calculate the amount of heat released under constant pressure:

q = ΔE + w = ΔE + PΔV = ΔE + ΔnRT

In this last equation, Δn is the change in moles of gas per mole of substance oxidized (or reacted), R is the gas constant and T is absolute temperature. "

From there it gets constantly more scientific :)
==

And as that hand is involved we probably need to look at 'Standard State Conditions in Biological Reactions'. It's easier to call it an 'Act Of God' and leave it be I think :)
« Last Edit: 25/02/2011 22:21:36 by yor_on »

#### Geezer

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##### Is this a new paradox of energy?
« Reply #19 on: 25/02/2011 22:36:26 »
Here's another one:

A system consists of a mechanical clock that is powered by a spring.

A big hand comes down from the sky and winds up the spring.

Was work done on the system? (Yes, I think.)
Did the internal energy of the system change? (Yes, I think.)
Is this really any different from the book and moon model? (No, I think.)

#### yor_on

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##### Is this a new paradox of energy?
« Reply #20 on: 25/02/2011 22:48:35 »
I would put this way. The hand expended energy drawing up the spring, the spring is now in a more or less compressed state, containing a very slight added invariant mass that it will expend, finally in form of mechanically induced 'heat' also driving levers, cogs etc in the process, moving the hands of the clock.

Was work done by the hand. Yep.
Did (some/most of) that work get stored as 'energy' by that spring. Yep
Did that spring finally lose that 'energy' to the rest of the machinery. Yep.
Did that machinery gain any energy? (final state) Nope.

Did the clock as a system gain energy? Yep, momentarily it did.

Your hand, did that expend energy? As long as it's mortal it did :)
Did the book gain any energy by being lifted. Nope
Where did the energy expended go then? I would say it got 'lost' into the universe as 'heat/radiation' ultimately that is. But if we really want to pinpoint where the he* it went we should ask Bored Chemist :)

I'm pretty sure he's having a good time reading us :)
« Last Edit: 25/02/2011 22:52:45 by yor_on »

#### Geezer

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« Reply #21 on: 25/02/2011 23:18:20 »

Did that machinery gain any energy? (final state) Nope.

Ah! But it did.

Imagine the system (the clock) is in a perfectly insulated box and we can read the temperature of the air in the box. After the spring has wound down again, the temperature of the system will have increased.

The reason for this is that all the mechanical energy that was in the spring is eventually converted into heat in overcoming friction in the mechanism. If you keep repeating the wind/unwind cycle the temperature will continue to increase with each cycle.

Now let's try it with a weight powered grandfather clock in a perfectly insulated box. We'll get a similar result. (We should really include the Earth in the insulated box to get the most accurate measurement, but that could be a bit tricky.)

#### yor_on

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##### Is this a new paradox of energy?
« Reply #22 on: 25/02/2011 23:36:54 »
Yes, I agree, in a enclosed system you will find the temperature go up as the energy gets expended transforming into radiation. If you define the universe as 'closed' you might want to define the same happening there. So loosely we can say that the hands 'energy' got transfered to the universe in form of heat, and assume that some of it momentarily was existing in form of 'energy' in the book too. But that kind of 'energy' is not there any longer time, and, as the universe is infinite, and conservation of energy assume that there always is a equilibrium?

You might want to argue that there should be a temperature difference to the universe after the hand expended its energy but even if so I don't expect it to be measurable and as the universe finally is expected to end in a Heat Death. in where nothing 'jiggle' anymore I would expect any heat/radiation coming from the hand lifting to dissipate very quickly. My view :)

#### Geezer

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##### Is this a new paradox of energy?
« Reply #23 on: 26/02/2011 00:04:37 »
If you define the universe as 'closed' you might want to define the same happening there.

I don't think that works. If the hand that wound up the spring is part of the system, it cannot alter the internal energy of the system. The internal energy of a system only increases if external work or energy is added to or removed from it. That's why the big hand has to mysteriously appear from nowhere.

The book situation is no different. You can lift the book against the force of gravity, or, if you prefer, you are doing work to distort space-time. Either way it's not so different from winding a spring or lifting the weight on a grandfather clock. If you allow the book to fall, all the work that went into changing the position of the book will be dissipated as friction (heat).

#### yor_on

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##### Is this a new paradox of energy?
« Reply #24 on: 26/02/2011 07:42:47 »
Well, I expect it to be different though :) To disprove it you have to show there is a measurable energy collected into that book, after lifting it. It's a interesting thought in that it also should mean that gravity was a 'force', and that we then could expect it to do different work on us throughout the universe. If that was so you might also assume that it could lose 'energy' itself, but as far as I know it doesn't? You have another 'force' reminding of gravity though, permanent magnetism doesn't lose 'energy' either as I understands it, levitating something. At least not by applying the magnetic 'force'.

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##### Is this a new paradox of energy?
« Reply #24 on: 26/02/2011 07:42:47 »