Apparent 2nd law violation? (thermodynamics)

[Curl]

This might be easy but apparently I haven't thought about long enough:

Suppose a collection of particles with significant thermal energy are vibrating such that they emit electromagnetic radiation. Because of this, they cool down. Cooling means that their entropy decreases (classical entropy). But, you might say, the photons are scattered randomly, which represents an increase in entropy.

I point out that this collection of particles (a metal ball i.e.) is at the focal point of a polished parabolic mirror. The E&M waves are reflected parallel, and can be collected and used to do work (create a current in a wire, charge a capacitor, whatever).

Apparently this is a heat engine with no cold reservoir. Whats the problem here? I haven't been able to figure it out.

 

[mikelepore]

When they say that a heat engine requires a cold reservoir, they are talking about making a device operate repeatedly, performing a cycle over and over.

 

[Curl]

My example is repeatable, the process can continue until the thermal energy of the ball is exhausted (cooled to the point where electromagnetic radiation is insignificant).

Or it can be placed in thermal contact with a reservoir of higher temperature and the process repeated.

 

[K^2]

Curl, radiation has a temperature, related to its spectrum. It can only be used to do work if the collector for that radiation is colder than the source of the radiation. A solar battery at 300K, for example, cannot convert to energy radiation from a 200K source. Any other device you might come up with will face similar difficulties.

 

[AJ Bentley]

My example is repeatable, the process can continue until the thermal energy of the ball is exhausted (cooled to the point where electromagnetic radiation is insignificant).

Or it can be placed in thermal contact with a reservoir of higher temperature and the process repeated.

Repeatable means that it returns to the same state after each cycle. Once your ball is cold, that's the end of it.
Going to a new reservoir means bringing in something new from outside - that's not what is meant by a 'cycle'. Eventually you will run out of reservoirs.

 

[Curl]

Curl, radiation has a temperature, related to its spectrum. It can only be used to do work if the collector for that radiation is colder than the source of the radiation. A solar battery at 300K, for example, cannot convert to energy radiation from a 200K source. Any other device you might come up with will face similar difficulties.

Yes but it doesn't matter. If the wire is superconducting with ~0 resistance the "solar cell" will not increase in temperature, therefore the cold reservoir is never exhausted. This still violates the 2nd law, since entropy is not increased in the cold reservoir but entropy is decreased in the hot reservoir.

 

[Mapes]

Yes but it doesn't matter. If the wire is superconducting with ~0 resistance the "solar cell" will not increase in temperature, therefore the cold reservoir is never exhausted. This still violates the 2nd law, since entropy is not increased in the cold reservoir but entropy is decreased in the hot reservoir.

Even at perfect efficiency (superconducting wire, the whole works), the solar cell will heat up when it absorbs incoming photons (and the entropy increase will equal, at the very least, the entropy carried by the radiation). There's no Second Law violation here.

 

[Curl]

Okay explain how it will "warm up" the wire. The waves coming by the wire will create an electric field in the wire which gives rise to a current. The potential difference between ends of wires can draw charge from a capacitor, storing useful energy. The only way any of this will rise in temperature is if there is resistance in the wire or in the capacitor plates, so I don't see what you're saying.

 

[Mapes]

If your wire is absorbing radiative energy, its entropy will increase unless this entropy is transferred away by the refrigeration unit keeping the wire at constant temperature. It has nothing to do with Joule, or resistive, heating.

 

[Curl]

If your wire is absorbing radiative energy, its entropy will increase unless this entropy is transferred away by the refrigeration unit keeping the wire at constant temperature. It has nothing to do with Joule, or resistive, heating.

?

the wire is not absorbing energy, the capacitor is. All the wire is doing is conducting electrical charges from one capacitor plate to another, with the help of the electric field supplied by the bypassing EM waves.

 

[Mapes]

?

the wire is not absorbing energy, the capacitor is. All the wire is doing is conducting electrical charges from one capacitor plate to another, with the help of the electric field supplied by the bypassing EM waves.

You're just playing a word game. In your thought experiment, radiation impinges upon a wire, and some of the radiative energy is converted into electrical energy. This is universally described as absorption of radiation.

Do you know what I meant when I said that heating an object with light does not depend on the object having a non-zero resistance? You are effectively claiming that superconductors do not heat up when you shine light on them; do you have a reference for this claim?

 

[K^2]

Yes but it doesn't matter. If the wire is superconducting with ~0 resistance the "solar cell" will not increase in temperature, therefore the cold reservoir is never exhausted. This still violates the 2nd law, since entropy is not increased in the cold reservoir but entropy is decreased in the hot reservoir.

Yes it will. Solar cells have limited efficiency. The limits actually come from thermodynamics.

 

[Curl]

omg why is this tough to understand?

The wire doesn't need to be touched by anything, I can make a loop and shoot the EM beam through it and induce a current. The wire will not warm up since its resistance is ~0. All energy absorbed from the light beam will be put onto the capacitor.

Doesn't even matter, there is still an apparent violation because the particles are cooling off without the expense of a cold reservoir. How is this possible? The entropy of the photons does not count because they can easily be ordered without doing work ( by a mirror, for example).

 

[Mapes]

I ask again, could you provide a reference for your claim that shining light (i.e., any EM wave) at a superconductor does not heat it up? This forum is for discussing consensus physics. It sounds like you're less interested in finding out where your mistake is and more interested in arguing that you've found some exception to the Second Law.

 

[Curl]

It is obvious you chose to ignore my previous post. If you are interested in super conductors read here; there are many references on that page:
http://en.wikipedia.org/wiki/Superconductivity

If you go back to read my post, I have said that it is not necessary to shine a beam AT the conductor itself, just inside a loop (can be 10 meters across) to induce an electric field within the superconductor.

But even if you aren't familiar with superconductivity and Faraday's law, then as I said above, there is still an apparent violation because you can DECREASE entropy of an object without doing work or exhausting a cold reservoir.

A parabolic mirror does no work on light as it reflects it. Its free and it causes order in photons (parallel). You cannot say the photons have carry the particles' entropy because they can be captured in a mirror box if you wll. That's where I'm having the difficulty.

It's okay if you don't know, we'll just wait for someone who can figure this out.

 

[Mapes]

You cannot say the photons have carry the particles' entropy because they can be captured in a mirror box if you wll.

You are veering away from legitimate physics here.

 

[Curl]

Okay then explain it, that's what I've been searching for in the past few days. All you have done is shout "physics" but failed to explain anything.

 

[pallidin]

I'm having a hard time understanding the question(s) here.
With questions properly put forth without vagueness or unnecessary convolution, you will eventually get legitimate answers here at PF.
But that's up to you. You MUST frame your questions correctly AND be open to new understanding and corrected perspective.

 

[cesiumfrog]

Suppose a collection of particles with significant thermal energy are vibrating such that they emit electromagnetic radiation. Because of this, they cool down. Cooling means that their entropy decreases (classical entropy). But, you might say, the photons are scattered randomly, which represents an increase in entropy.

I point out that this collection of particles (a metal ball i.e.) is at the focal point of a polished parabolic mirror. The E&M waves are reflected parallel, and can be collected and used to do work (create a current in a wire, charge a capacitor, whatever).

Apparently this is a heat engine with no cold reservoir. Whats the problem here? I haven't been able to figure it out.

My example is repeatable, the process can continue until the thermal energy of the ball is exhausted (cooled to the point where electromagnetic radiation is insignificant).

Or it can be placed in thermal contact with a reservoir of higher temperature and the process repeated.

The cold reservoir is the surrounding 0K darkness into which you assume the radiation heads. The entropy and thermal energy of the surrounds increases no less than the entropy and thermal energy of your object decreases, and eventually the system will approach an equilibrium (picture the ball absorbing as much radiation, even from the cosmic background, as what it is emitting).

It might help to explain if you would explicitly specify what the parabolic mirror is pointing at? If it is a solar generator, what type? Or is the radiation simply harnessed to heat up a different object? Whatever you choose, you'll find the process only works efficiently if your original ball is much hotter than the receiving system, but as the process proceeds it approaches a point where the reverse process (your generator shining heat back at the ball) occurs at the same rate (or in other words, energy ceases to be harnassed for useful work).

 

[Andy Resnick]

This might be easy but apparently I haven't thought about long enough:

Suppose a collection of particles with significant thermal energy are vibrating such that they emit electromagnetic radiation. Because of this, they cool down. Cooling means that their entropy decreases (classical entropy). But, you might say, the photons are scattered randomly, which represents an increase in entropy.

I point out that this collection of particles (a metal ball i.e.) is at the focal point of a polished parabolic mirror. The E&M waves are reflected parallel, and can be collected and used to do work (create a current in a wire, charge a capacitor, whatever).

Apparently this is a heat engine with no cold reservoir. Whats the problem here? I haven't been able to figure it out.

This appears to be an interesting paradox, but it is ultimately flawed. Here's why:

First, let's list your assumptions (in no particular order):

"I point out that this collection of particles (a metal ball i.e.) is at the focal point of a polished parabolic mirror. The E&M waves are reflected parallel, and can be collected and used to do work"

Assumption 1: the distribution of thermal radiant energy has been converted from isotropic to collimated.

Assumption 2: no work has been performed by the radiation during the process of reflection.

Assumption 1 is false; light emitted from an extended object cannot be perfectly collimated.

Even so, this is a weak assumption- one could make it stronger by only requiring that the entropy associated with the radiance decreases. IIRC, the more narrow the radiant intensity, the lower the entropy associated with the radiation field- but I can't quickly find a reference. Then, assumption 1.1 may be true.

Unfortunately, assumption 2 is false due to radiation pressure. The light exerts pressure on the mirror, and if it were free to move, it would get pushed backwards. So work is performed when the light is reflected- anchoring the mirror won't save you because the radiation pressure is then stored as elastic energy (elastic deformation of the support).

 

[cesiumfrog]

Andy,

2. If the mirror is arbitrarily heavily anchored, you know no work will be performed on it. (Elastic sink is just silliness, implying that constant pressures produce constantly increasing deformation perpetually?)

1. Isn't it enough that as the collimation is improved the beamwidth grows? (A pitfall here may stem from imagining the entire finite extent of the ball object to be at the singular point of a parabolla's focus.)

 

[Curl]

1. cesiumfrog is right. Its foolish to point out the "work" done by the radiation pressure. I can have the system in a box, which cannot move by conservation of momentum.
Also energy/momentum ratio is extremely large for photons: that's why nobody uses flashlights for rocket engines.

2. Doesn't matter if the beams are "perfectly" parallel, although if we assume the radiation is coming normal to the sphere's surface, the focal point will be the center of the sphere which is a point of zero size. Therefore they WOULD mathematically be perfectly parallel by the definition of a parabola.

However, it doesn't matter if they are parallel. I can make a loop of radius 10 meters and I would still capture all the rays which would have very small deviation.

I already thought of these debunks, but none of them work. Normally I can figure these type of things out on my own, but this one is giving me trouble. I KNOW it cannot work I just don't know WHY. I need someone intelligent to notice something that I"m missing.

 

[jajknight]

question: is this perpetual motion?

Foucault pendulum

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

 

[cesiumfrog]

I already thought of these debunks, but none of them work. Normally I can figure these type of things out on my own, but this one is giving me trouble. I KNOW it cannot work I just don't know WHY. I need someone intelligent to notice something that I"m missing.

Please, would you simply (and concisely) state the entire complete closed cycle system? What each component is? What your problem is (that is, how you expect each component to act)?

 

[Andy Resnick]

Andy,

2. If the mirror is arbitrarily heavily anchored, you know no work will be performed on it. (Elastic sink is just silliness, implying that constant pressures produce constantly increasing deformation perpetually?)

Not true.

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

Also, as you (should) recognize, changing the direction of propagation means the *momentum* has changed. The momentum imparted to a mirror by light is a well-understood phenomenon.

 

[Andy Resnick]

1. cesiumfrog is right. Its foolish to point out the "work" done by the radiation pressure. I can have the system in a box, which cannot move by conservation of momentum.
Also energy/momentum ratio is extremely large for photons: that's why nobody uses flashlights for rocket engines.
...

I already thought of these debunks, but none of them work. Normally I can figure these type of things out on my own, but this one is giving me trouble. I KNOW it cannot work I just don't know WHY. I need someone intelligent to notice something that I"m missing.

I indicated the flaw; you are apparently wedded to the idea that you have invented a second-law violation. Which you have not.

 

[Mapes]

Okay then explain it, that's what I've been searching for in the past few days. All you have done is shout "physics" but failed to explain anything.

I already said that your hypothetical system (that absorbs radiation to produce power) will heat up from the incident radiation. This entropy increase will be transferred to the surrounding environment.

You said, No, it's a superconducting wire with zero resistivity. But Joule, or resistive, heating is not the only way to heat an object. Incident radiation heats up objects that aren't totally reflective. The heating increases with absorbed energy, and the whole point of your system is to absorb energy to provide stored power from a capacitor.

You said, No, I'll make a really big wire loop, much bigger than the beam. But there has to be some interaction with the radiation, otherwise the system couldn't absorb energy.

You said, No, photons don't carry entropy. And this is just flat wrong. The entropy doesn't just mysteriously disappear; you just keep asserting it does.

 

[Andy Resnick]

I agree with Mapes- the OP could have taken credit for coming up with an interesting scenario that has many parallels- Archimedes' burning mirror, supposed violations of Kirchoff's law in a cavity, etc. etc. The OP could have learned a lot.

Instead, the OP simply demands we understand the system for him/her. The OP can't be bothered to calculate the change in entropy from a purely thermal radiation field (i.e. isotropic) to one that propagates with a given set of beam parameters. That's lazy and boring.

 

[Curl]

I have already explained it 3-4 times. It is a simple scenario and it shouldn't require a formal essay to describe.

If you honestly believe that radiation pressure can prove that my system does not violate the second law, all I can do is laugh and move on. Apparently this is the wrong place to ask.

 

[pallidin]

It is a simple scenario and it shouldn't require a formal essay to describe.

Sorry, but ANY proposed suggestion that describes a process that violates the second law DOES INDEED require a formal essay!
You must PROVE it, not just suggest it. Up to the task?

 

[cesiumfrog]

Gah, Curl is so annoying to talk to. He keeps telling everyone else they need to read his posts again, but hypocritically ignores what everyone else has posted. Multiple people have said the radiation sink will heat up and cease being a sink. Multiple people have said the apparatus description is unclear (being spread over several posts and changing along the way). He fixates on the single criticism that actually does sound dubious, as if that proves his revolutionary idea is beyond criticism.

Not true.
http://en.wikipedia.org/wiki/Radiation_pressure
Also, as you (should) recognize, changing the direction of propagation means the *momentum* has changed. The momentum imparted to a mirror by light is a well-understood phenomenon.

Andy, how patronising, surely we can presume we both know how to calculate radiation pressure: how much wave energy is lost to redshift as the mirror recedes, how much momentum is imparted (by the dance of EM forces on the charges composing the mirror), etc. So I'm a bit confused by your posts. Yes, the mirror is continually changing the momentum of the light beam. Consequently, momentum is perpetually being accrued to the mirror at a known rate. So we can ask, how much power is involved? (A hint would be to ask, other than parity symmetry, how has the beam been altered?) How much kinetic energy has the mirror+anchor received? We know momentum is linear in velocity, but KE is not. Therefore, the lighter the mirror+anchor system, the greater the rate that it will absorb energy from the beam (even though, at least initially, the rate at which it accrues momentum is independent of this). Therefore, as we make the anchor arbitrarily heavy, the rate of energy it absorbs by this process can be made arbitrarily low. But nevermind that. Just mount the mirror on the same optical bench as the source and the receiver. Now it isn't arbitrarily low, it is exactly zero.. And by all means, let the mirror be mounted via a spring. When the device is turned on, sure, for a period energy will be lost compressing the spring, but as the spring compresses it will increase its force, approaching equilibrium with the radiation pressure, and then the elasticity will not sink any further energy. If you think about it, I believe you'll see these were red-herrings rather than the true justifications for the conclusion you're aiming toward. But if I'm not understanding you, please try to help me.

 

[Andy Resnick]

So I'm a bit confused by your posts.

Ok, I'll try again.

Extracting work from thermal radiation is trivial- that's what a solar panel does. The OP claimed (perhaps implicitly) that shaping the radiation field will somehow make this process more efficient- that is, *more work* can be extracted by a collimated beam than by an isotropic radiator- that the efficiency would then be greater than allowed by the second law of thermodynamics. Because solar panels exist.

It's the same faulty reasoning behind 'unlimited' solar concentrators, Archimedes' mirror, etc- by shaping the light beam, *more work* can be extracted (alternatively, more heat is transferred) than could ordinarily be permitted. For example, it is claimed that Archimedes' mirror was able to heat up a ship much faster than would occur by simply being in the sun- like you can burn ants. Similarly, with a solar concentrator I could boil a lot more water than I normally could, and generate much more useful work. To a certain point- given by thermodynamic arguments- this works. Ultimately, this limit is given by the optical invariant (sometimes called the etendue)- a combination of beam divergence and beam diameter.

So I focused on that essential assumption; the change in entropy of the radiation field caused by collimating a portion of a spherical field. IIRC, a collimated beam (with it's low divergence angle) has a lower entropy than a spherical beam- therefore, that loss must be compensated (at least...) by an increase in entropy somewhere else, and the only thing available (that I can think of) is the mirror.

So I proposed a form of 'workless dissipation' which allows the total entropy, before and after the reflection, to remain constant. Perhaps you have an alternative idea?

 

[Curl]

It's not as easy as pointing at the mirror and say it somehow causes an increase in entropy elsewhere. Actually the micro-state definition of entropy you learn from reading books and memorizing formulas can be misleading during thought experiments such as this.

I have another thought experiment which can separate gas particles by velocity (you pick a velocity, and all particles with speeds above this will be put on one side of a container, and the particles with lower speeds will remain in the other half of the container). It is similar to what Maxwell's daemon tries to do, except in my system there is no need for any moving parts and no work needs to be done. It seems like entropy is decreased right? Right. Is the 2nd law violated? No. It turns out that the process is not cyclic, and work CANNOT be done by this separation of gas particles.

The experiment I'm asking about in THIS thread might have some trick like that too, although I cannot tell what it is because the process seems cyclic and work CAN be extracted.

P.S. I'm not talking about solar cells like those in your calculator, I'm talking about a conducting loop (like a coil antenna) which takes advantage of the changing magnetic field present in an EM wave and uses magic called Faraday's law to set up a current. Capacitor, for example, can make use of that current to collect energy.

Also I already said that I know for a fact this cannot work, I'm trying to DISPROVE it, not prove it. However I want a legitimate disproof, I need to point out exactly why this cannot work. It helps me understand thermodynamics.

This might not even be obvious, for example in Maxwell's daemon, it had to be shown that it is IMPOSSIBLE to monitor a daemon at such scales without doing a greater amount of work. This is a deep disproof. Also the ratchet engine, it had to be show that a ratchet with such low sensitivity CANNOT exist. The answers don't come out of some thermo textbook formula, they are often deep. I'm not saying my experiment is deep, but it could be...

 

[cesiumfrog]

P.S. I'm not talking about solar cells like those in your calculator, I'm talking about a conducting loop (like a coil antenna) which takes advantage of the changing magnetic field present in an EM wave and uses magic called Faraday's law to set up a current. Capacitor, for example, can make use of that current to collect energy.

Since when does shining thermal radiation at a wire loop ever produce a useful current? That won't even work to begin with. You'll need more than a capacitor.. And I suppose it's that "more" which is critical in explaining why this process doesn't only proceed in one direction..

 

[Curl]

Finally you are on to something.

A changing B-field produces a current in a loop of wire. A current can be made to do work. Radios are a good example, although they use op amps to make the sound since the energy is very small.

EM radiation has a changing B field (derivative nonzero). It comes from Maxwell's equations.

 

[cesiumfrog]

Radios use rectifiers..
I guess you could hook your loop directly to a resistance heater, that way the analysis is simpler. Of course, it's going to be ridiculously ineffective at extracting power from the radiation even from the beginning (since it's such a bad model for a solar power collector). The larger point is that it also works in reverse: the resistance heater can absorb heat, the thermal movement of the charges therein can cause currents in the loop and create its own radiation, back toward (and limiting the cooling of) your source ball.

 

[Curl]

Don't use a resistance for heating.

The current can go (far away) to an electrical motor that can do work.

 

[cesiumfrog]

The same problem occurs, just through that different mechanism.
(I'd try to spell out the details for you, but you still haven't spelt out the details for me. Let's see, you have a ball, a parabola, a loop, and now a motor, and who knows what you'll add next? Why don't you write down in one post your entire system, and how each part is finally connected? Please attach a diagram? For one example, where goes the radiation left when it isn't all absorbed by the loop? That way we can start giving you specific answers, instead of vague ones.)

 

[Curl]

Okay when I find time I'll make a 3D model and post the binary files and rendered images.