Does Optic Focusing Contradict the Second Law of Thermodynamics?

[the4thamigo_uk]

I was thinking again about the enclosed black body thought experiment. It seems for a 'steady state' when the outer body is maintained at constant temperature, we can equate the net energy flow for the inner body and make the following equation :

total power emitted from outer body = total radiative power lost by inner body.

However, if neither body is maintained at a constant temperature we could argue that we could still make this identity. Niaevely we will get the same result, that the temperatures of the two bodies in thermal equilibrium are different. Which is a contradiction in terms.

It would seem that the crucial difference is that there is a finite distance between the inner surface of the outer body and the outer surface of the inner body. Hence the radiation must travel a distance (R-r) and therefore take a finite time (R-r)/c.

So we have a subtle set of differential equations :

\frac{dQ_{i}(t)}{dt} = k_{i}\frac{dT_{i}(t)}{dt} = 4\pi R_{o}^{2} \sigma T_{o}^{4} (t - \Delta t) - 4\pi R_{i}^{2} \sigma T_{i}^{4} (t)

\frac{dQ_{o}(t)}{dt} = k_{o}\frac{dT_{o}(t)}{dt} = 4\pi R_{i}^{2} \sigma T_{i}^{4} (t - \Delta t) - 4\pi R_{o}^{2} \sigma T_{o}^{4} (t)

\Delta t = \frac{R_{o} - R_{i}}{c}

Q - net heat flow into body
T - temperature of body
t- time (brackets denote function arguments)
k - specific heat of body
R - radius of body
subscripts denote _{i}nner and _{o}uter black body

It seems to me that this must be the crucial difference between the two systems. Problem is I have no idea how to go about solving this set of equations? What techniques are required when there is a shift \Delta T to the variables? I wonder if there is potential for a harmonic type damped oscillation to thermal equilibrum or would it be a nice smooth decline?

 

[Dale]

We could have a theoretical flat black body sat on a hot plate at temperature T, we could use four flat mirrors to angle the radiation from this surface onto a second flat black body of quarter the area. It receives 'roughly' the same power although on 1/4 of the surface area. It therefore must heat up to a higher steady state temperature. It doesn't matter that some radiation is lost in the optics, in fact all we really require is that there is a higher power per unit area hitting the second black body than emitted by the first. We quadrupled the power with the four mirrors but even if we only increased the flux falling on the second black body by 1 Watt, it would still achieve a higher steady state temperature than the source. That the two surfaces are not in thermodynamic equilibrium is fine. They are not meant to be.

This is a great idea for a simplification. I would recommend that you actually go through the geometry rather than using the "roughly" argument. Since you are violating the 2nd law of thermo I think it merits more than a hand waving argument.

My guess is that when you do the actual geometry you find that the 2nd law wins out after all, but I could be wrong.

 

[the4thamigo_uk]

The flat plate idea is just to give a more real world example than the enclosed BB idea. They are both equally valid test cases. Geometrical arguments shouldn't be used to prove or disprove thermodynamics anyway as they are not general enough. As I said before I also don't believe there are any violations of the laws of thermodynamics as there is an external heat supply (namely the hot plate).

 

[the4thamigo_uk]

So we have a subtle set of differential equations :

\frac{dQ_{i}(t)}{dt} = k_{i}\frac{dT_{i}(t)}{dt} = 4\pi R_{o}^{2} \sigma T_{o}^{4} (t - \Delta t) - 4\pi R_{i}^{2} \sigma T_{i}^{4} (t)

\frac{dQ_{o}(t)}{dt} = k_{o}\frac{dT_{o}(t)}{dt} = 4\pi R_{i}^{2} \sigma T_{i}^{4} (t - \Delta t) - 4\pi R_{o}^{2} \sigma T_{o}^{4} (t)

\Delta t = \frac{R_{o} - R_{i}}{c}

Q - net heat flow into body
T - temperature of body
t- time (brackets denote function arguments)
k - specific heat of body
R - radius of body
subscripts denote _{i}nner and _{o}uter black body

I think the solutions must oscillate. As \frac{dQ_{i}(t)}{dt} tends to zero we end up with the following tending to equality :

4\pi R_{o}^{2} \sigma T_{o}^{4} (t - \Delta t) = 4\pi R_{i}^{2} \sigma T_{i}^{4} (t)
4\pi R_{i}^{2} \sigma T_{i}^{4} (t - \Delta t) = 4\pi R_{o}^{2} \sigma T_{o}^{4} (t)

which is essentially of the form:

X(t - \Delta t) = aY(t)
Y(t - \Delta t) = bX(t)

So X will eventually become proportional to what Y was a short time ago and Y will eventually become what X was a short time ago. Obviously it wouldn't work if X and Y both became flat. I would hope that the oscillations are damped though, to allow them to come to the same temperature.

Id like to be able to do this experiment to find out what really happens... I suppose the initial oscillations might be detectable although over time I would expect the oscillations to tend to a very high frequency 1 / \Delta T (as it is light speed that is mediating the heat transfer) for a lab sized experiment...

 

[Dale]

Geometrical arguments shouldn't be used to prove or disprove thermodynamics anyway as they are not general enough.

In the context of the conversation I don't understand this comment at all. In post 29 you specifically posited that you could get thermal energy transfer from a large cold blackbody to a small hot blackbody by using mirrors. That is inherently a geometrical argument.

As I said before I also don't believe there are any violations of the laws of thermodynamics as there is an external heat supply (namely the hot plate).

If you have passive radiative heat transfer from a cold blackbody to a hot blackbody then you are violating the 2nd law of thermodynamics by definition.

 

[the4thamigo_uk]

In the context of the conversation I don't understand this comment at all. In post 29 you specifically posited that you could get thermal energy transfer from a large cold blackbody to a small hot blackbody by using mirrors. That is inherently a geometrical argument. If you have passive radiative heat transfer from a cold blackbody to a hot blackbody then you are violating the 2nd law of thermodynamics by definition.

No, I wonder, does anyone here know what I am talking about? /

Im simply trying to show that it is theoretically possible to direct the radiative power from one source black body at fixed temperature T onto a second smaller black body, in order that the smaller black body achieves a 'steady state' temperature greater than T. The source black body is NOT passive, it is supplied heat from a hot plate. It all seems fairly obvious to me now, but some people disagree it seems?

Avoiding geometry, from only a thermodynamic argument, I 'could' simply state, that these two black bodies are the only things that exist in the world and that all the radiative power that each body emits is directed onto the surface of the other body. This is sufficient for the argument. There really is no need for geometry/optics.

Does anyone disagree with this on a 'purely thermodynamic' basis? This is what I want to find out. If its wrong, then its wrong, but exactly why is it wrong?

However, some people seem have countered that this is impossible, by invoking geometrical arguments about mirrors/lenses and such. Hence, to challenge this geometical argument, and 'only' in order to challenge this geometrical argument, we can use the enclosed black body example, which does not rely on mirrors/lenses. I think it is a fairly robust example.

Unfortunately again, some people may still think that this is an unrealistic counter-example even though it is a perfectly good enough example as far as I can see. We could easily build this experiment I believe.

In fact what the enclosed BB example shows is a perfect example, in that 'All' the radiative power from each body is directed to the other body. But, in fact you can relax this condition anyway. You 'dont even' need to capture all the radiation from the source body. All you need to show is that there is a way to increase the flux emitted from the surface of the source BB, such that it illuminates the entire surface of a smaller black body. This is what the mirrors example shows. You 'dont even' have to double/quadruple the flux, all you need to do is increase it by some amount. The flat BB is a sufficient example I think.

So, for a large BB maintained at T by a source of energy, it *is* possible to heat a smaller BB such that it achieves a higher temperature in a steady state. The two bodies do not have to be in thermal equilibrium as there is heat supplied.

If there is no heat supplied, then the black bodies will (eventually) achieve the same temperature, based on some system of differential equations like those given above.

Does anyone agree with this? ( or are you all bored by it? D ) ...

If you have passive radiative heat transfer from a cold blackbody to a hot blackbody then you are violating the 2nd law of thermodynamics by definition.

Second law of thermodynamics

'Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature.' (Clausius)

For illustration take the enclosed black body example. The condition for steady state is that the (total power emitted by inner BB) = (total power emitted by the outer BB). There is *zero net heat flow* between the two BBs.

It might be the wording of the Clausius statement that is confusing, a BB at non-zero temperature will always emit radiation, yes? There is nothing to stop it? Its charges are jiggling about so it generates radiation. Radiative energy therefore is 'spontaneously flowing' from each body, it is just that they are exactly equal in the 'steady state'

 

[sylas]

Does anyone disagree with this on a 'purely thermodynamic' basis? This is what I want to find out. If its wrong, then its wrong, but exactly why is it wrong?

You are wanting the transfer of energy to occur by spontaneous heat flow, from a cold object to a hotter one. It doesn't matter that there's an energy source to maintain the temperature of the colder object. It still violates thermodynamics.

The problem is that there's no way to focus the heat the way you want. We've looked at a couple of concrete examples, using the Sun, where the size of the Sun means that when you focus it the image also has a finite size. Whatever geometry you pick, you aren't going to get a flux of energy greater than what is coming from the surface already, so you will not be able to focus the heat as tightly as you require.

It is a bit like perpetual motion machines. People can come up with all kinds of new designs and clever tricks, and eventually with analysis we can see where the design fails, but the general rule for knowing you can't do it is not based on evaluations of all designs, but rather on the general thermodynamic principle that no design, no matter how clever, is going to violate.

In the same way, you can try picking your geometries however you like. We know in advance, from the second law, that there's going to be some way in which the design fails to heat something up to hotter that the source of your heat flow. If you propose a particular design in enough detail we might be able to explain where it fails and that may help you appreciate the power of the general principle.

But we know that we're always going to be able to find some flaw in any specific concentrating or focusing system trying to get that heat to flow into a hotter object.

Cheers -- sylas

 

[the4thamigo_uk]

In the same way, you can try picking your geometries however you like. We know in advance, from the second law, that there's going to be some way in which the design fails to heat something up to hotter that the source of your heat flow. If you propose a particular design in enough detail we might be able to explain where it fails and that may help you appreciate the power of the general principle.
Cheers -- sylas

Ive just said above at the bottom of my previous post that there *isnt* a violation of the second law as far as I can see. I don't think I am being dumb.

I think my suspicion that nobody really reads forum posts before replying to them is true...

 

[Yeti08]

The radiation exchange between blackbodies, from object i to object j is given by

q_{ij}=A_{i}F_{ij}\sigma\left(T_{i}^{4}-T_{j}^{4}\right)

where A is the surface area, F_{ij} is the view factor from i to j, and \sigma is the Stefan-Boltzmann constant. From the above equation, which can be derived from more basic principles, it is obvious that when there is no temperature difference, there is no heat exchange, thus no further change in temperature. Furthermore, the view factor are restricted by reciprocity:

F_{ij}A_{i}=F_{ji}A_{j}

So you can't have all the heat transfer from i go to j and have all the the heat transfer from j go to i. For your BB example, the view factor from the BB to an enclosure would be one as you said. However, the enclosure would be at least partially radiating to itself thus the view factor would have to be less than one.

 

[sylas]

Ive just said above at the bottom of my previous post that there *isnt* a violation of the second law as far as I can see. I don't think I am being dumb.

I think my suspicion that nobody really reads forum posts before replying to them is true...

No, I read it all. I am saying you are incorrect, and there is a violation of the second law. I appreciate that you don't see that as yet, but I think you are wrong, and I AM reading your posts.

Cheers -- sylas

 

[atyy]

Case 2. Big mirrors for a solar furnace

Now we bring in some perfect mirrors, line them all up behind the little ball, and focus them all directly on to the ball. These mirrors have a cross section area against the Sun of that is 10⁵ times greater than the surface area of the ball.

Without the mirrors, the ball is getting 1343/4 watts for each square meter of its own surface area. But the mirrors are getting 1343 * 10⁵ Watts for each square meter of the ball's own surface area. So the ball has to heat up to shed 1.343 * 10⁸ W/m², which gives a temperature of

\left(\frac{1.343\times 10^8}{\sigma}\right)^{0.25} = 6976 \; K​

Bingo. We've heated the ball up to be hotter than the Sun. Clearly, this is wrong. It is a violation of thermodynamics. So what was the error?

Is it the work needed to hold the mirrors in place?

 

[sylas]

Is it the work needed to hold the mirrors in place?

No; it is the unstated assumption that the mirrors will be able to focus the light from the large ball of the Sun into a sufficiently small area that the flux will exceed what is at the surface of the Sun. The case 3 is intended to illustrate this.

Cheers -- sylas

 

[atyy]

No; it is the unstated assumption that the mirrors will be able to focus the light from the large ball of the Sun into a sufficiently small area that the flux will exceed what is at the surface of the Sun. The case 3 is intended to illustrate this.

Huh! That is cute!

 

[the4thamigo_uk]

No, I read it all. I am saying you are incorrect, and there is a violation of the second law. I appreciate that you don't see that as yet, but I think you are wrong, and I AM reading your posts.
Cheers -- sylas

You should be a politician... )

Sylas I would find it really helpful if you could examine the steps in my argument below and tell me at which point you disagree :

If you say, as you did above, that the general principles of thermodynamics are the reason my argument fails, then the argument must be proved to fail without reference to optics, since the laws of thermodynamics are independent of optics.

* If you refute this, then you are saying that it is 'optics' and not pure 'thermodynamics' that is the problem with the argument. I would be more amenable to this, but you cannot then tell me that the argument fails because of the second law of thermodynamics. It would fail because of optics alone. Furthermore, I would also hope to counter with my enclosed black body example which relies on geometry to prove that it is still theoretically possible *
If you accept this, we can assume the ideal gedanken experiment with the following conditions :

(1) two BBs in a vacuum of different surface areas
(2) The larger BB (L) is maintained at temperature T by an external heat source
(3) the smaller BB (S) is passive
(4) all the radiation from the larger one is directed onto the surface of the small one
(5) all the radiation from the smaller one is directed onto the surface of the larger one

* If you refute these assumptions then why? Bear in mind that you can't refute (4) or (5) since you have accepted that optics/geometry does not play a part in a thermodynamic argument *

At 'steady state' for body S :

(total radiative power emitted by S) = (total radiative power received from L)

i.e. 'total radiative power' meaning total integrated flux from the BB over its entire surface

* If you refute this then you are saying that there is net heat loss/gain from S so its temperature would change hence it is not in a steady state, hence you are refuting the possibility of a steady state *
and by assumptions (4) above :

(total radiative power received from L) = (total radiative power emitted by L)

Hence by Stefans Law :
(area of S) * sigma * (temp of S)^4 = (area of L) * sigma * (temp of L)^4

* If you are refuting Stefans Law then I would ask you on what grounds you are doing so *
By implication of the formula above :

(temp of S) = (temp of L) 4throot[ (area of L) / (area of S) ]

Hence if (area of L) > (area of S) then (temp of S) is greater than (temp of L)

* If you refute the conclusion then it is a logical absurdity *

And for the second law...

It states :

'Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature.', Clausius

* I will assume you arent going to refute this *
A black body at non-zero temperature always emits radiation

* If you refute this then you refute the idea of a black body emitter*

At steady state, S is transferring all its radiation onto the surface L
At steady state, L is transferring all its radiation onto the surface S

* If you refute this you are saying something is preventing a BB from radiating when at 'steady state' and you are now refuting (4) and (5) which have already been accepted*
At steady state by the above calculations, there is 'zero net power/heat transfer' between the bodies so the second law is satisfied

* If you refute this, then you are presumably saying that you are wanting no radiation to be transferred, in either direction, between the bodies. I am not sure what else you can disagree with. *

The heat transfer is zero but the BBs are different temperatures!

* If you refute this then it is a logical absurdity *

 

[sylas]

You should be a politician... )

Now that hurt!

(1) two BBs in a vacuum of different surface areas
(2) The larger BB (L) is maintained at temperature T by an external heat source
(3) the smaller BB (S) is passive
(4) all the radiation from the larger one is directed onto the surface of the small one
(5) all the radiation from the smaller one is directed onto the surface of the larger one

* If you refute these assumptions then why? Bear in mind that you can't refute (4) or (5) since you have accepted that optics/geometry does not play a part in a thermodynamic argument *

I deny number 4, because it is an assumption that let's you violate the second law. As I said previously, based on the second law I am confident that if you try to be specific about the details of your optics and geometry, it will always be possible to find where your proposed design fails to achieve what you want.

You haven't actually given any optics/geometry argument. You've merely said that you can do this, but haven't provided the geometry or optics necessary.

If you ever do provide the optics and geometry, it will be possible to use the optics and geometry to show the flaw.

If you merely assert that you have some unknown design that works, then we can know, without looking at your design, that there's something wrong with it. That is because no amount of optics and geometry can violate the second law. The same applies for someone claiming to have a design for a perpetual motion machine.

Cheers -- sylas

 

[Yeti08]

The only situation that I can think of where (4) and (5) are both true is for infinite parallel plates (hence reciprocity in real, finite-size bodies), which would have equal (well, both infinite...) surface areas. It is definitely not true for your BB's and, though I can't speak for sylas, I would say that thermodynamics/heat transfer and geometry are intrinsically linked. Radiation heat transfer is very much dependent on shapes and dimensions which can be used to derive view factors (probably more of an engineering method as opposed to the basic physics).

 

[Dale]

Im simply trying to show that it is theoretically possible to direct the radiative power from one source black body at fixed temperature T onto a second smaller black body, in order that the smaller black body achieves a 'steady state' temperature greater than T.

That is exactly what you have not yet shown. You have only asserted that it is possible. Note, the word "smaller", it is inherently a geometric argument. You cannot avoid that.

we can use the enclosed black body example, which does not rely on mirrors/lenses. ... In fact what the enclosed BB example shows is a perfect example, in that 'All' the radiative power from each body is directed to the other body.

It doesn't work. If you actually sit down and draw the geometry you will find that most of the energy emitted by the enclosing object misses the small object and hits the other side of the enclosing object. This is a common effect for concave radiating surfaces.

Specifically, consider a differential element on the surface of the enclosing object. This element radiates over a half-sphere solid angle. The small object occupies a smaller solid angle which is a function of its diameter and distance. The remainder of the radiation emitted by the differential element does not hit the small object.

 

[Dale]

The radiation exchange between blackbodies, from object i to object j is given by

q_{ij}=A_{i}F_{ij}\sigma\left(T_{i}^{4}-T_{j}^{4}\right)

where A is the surface area, F_{ij} is the view factor from i to j, and \sigma is the Stefan-Boltzmann constant. From the above equation, which can be derived from more basic principles, it is obvious that when there is no temperature difference, there is no heat exchange, thus no further change in temperature. Furthermore, the view factor are restricted by reciprocity:

F_{ij}A_{i}=F_{ji}A_{j}

So you can't have all the heat transfer from i go to j and have all the the heat transfer from j go to i. For your BB example, the view factor from the BB to an enclosure would be one as you said. However, the enclosure would be at least partially radiating to itself thus the view factor would have to be less than one.

Excellent reply. That really says it all.

@ the OP: I would encourage you to study Yeti's post in detail.

 

[the4thamigo_uk]

(1) Ok, you are all denying it on the basis of optics. To prove it in all cases you would *at least* need to prove that it is false for every possible shape, size of BB, and every configuration of mirrors, lenses. Hey you then might have a new law of thermodynamics only it wouldn't be, because it isn't general enough to other modes of heat transfer (see (3) and (4) below)
(2) My argument relies on the laws of thermodynamics only and Stefans law. Not on optics. Therefore you certainly cannot deny it on the basis of the second law. If you can't follow this logic then I have no hope for you... I mean it, I really have no hope for you... )
(3) The 4 laws of thermodynamics do not concern themselves with shapes of objects, optics, geometry. They talk about heat and temperature. They don't even mention the surface area. That is Stefans law which isn't one of the 4 laws.
(4) The 4 laws of thermodynamics do not even mention conduction, convection, radiation. They are independent of the means of heat transfer.
(5) It is the 'additional laws' of heat transfer that we apply to the 4 laws of thermodynamics, we have a law of thermal conduction for example and a law of black body radiation.
(6) My argument explicitly proves that for 'purely radiative transfer' it is possible (in principle) to achieve a 'steady state' with different temperatures that satisfies the second law. You don't even really need to capture the whole energy emitted by the source object, you simply make your passive BB so much smaller to achieve the higher temperature. As said before 'steady state' is not 'thermal equilibrium' because the system has an external heat supply.
(7) For thermal convection however the situation is different. A hot body maintained at temperature T would heat up a passive body to temperature T and no higher. I think you have all got it into your head that this applies to purely radiative transport too, since purely radiative transport is an uncommon situation.
(8) The only 'geometry' in the argument is the surface area of the body. There is no necessity to define a shape at all.
(9) My argument *explicitly proves* that it *does not* violate the second law of thermodynamics as shown in my argument. I don't know how many times I can keep saying this. But yet you persist in denying it? I find this very shocking... There is no net heat transferred between the BBs in the 'steady state'
(10) The form factor laws that you quote are not the laws of thermodynamics they are laws of geometry/optics. Furthermore they do not allow for any focussing or reflection to amplify the intensity of the radiation. This can be easily achieved. I repeat there is no real necessity to capture all the emitted radiation from the source you just need to make the flux on the passive BB more intense over its whole surface.
(11) If you want a geometrical argument (it actually IS unnecessary), but since you think that everything hangs on it, I will repeat it yet again.

Geometrical argument
==============

(1) small spherical black body radius r
(2) large spherical shell radius R. Inner surface is a radiative black body.
(3) small BB is at centre of large shell (though not a requirement it makes calculations easier)
(4) outer surface of the shell is in a heat bath at constant temperature T.
(5) There is no radiation emitted to the outside world
(6) Steady state implies the same equations as above. Inner body achieves a higher steady state temperature.
(7) No net power transfer between both BBs, hence NO violation of second law.

Q.E.D. Merry christmas... I will leave you to think about it...

 

[Yeti08]

(1) No, I'm not.
(2) This has nothing to do with optics. It does have to do with geometry though. You may rely on the Stefan-Boltzmann law, but you are applying it incorrectly.
(3&4) Okay, the "4" laws make general statements.
(5) The details are worked out through additional equations. The laws by themselves are worthless unless you know how to mathematically represent the physical phenomena.
(6) No, it doesn't
(7) Are you saying the laws of thermodynamics apply differently to different modes of heat transfer?
(8) Surface area and orientation - surfaces pointing in opposite directions won't transfer heat radiatively.
(9) Yes, it does violate the law. The Clausius statement associated with the 2nd law states that "Heat generally cannot flow spontaneously from a material at lower temperature to a material at a higher temperature" (the exception is extremely small scales, though it always stands at macroscopic scales), therefore you are violating the second law no matter how you look at it, regarless the mode of heat transfer.
(10) View factors apply just as much as cross sectional area applies to conduction or orientation applies to free convection - you can't do much without them

Your geometrical argument fails for the reasons I have already stated. View factors are not optional - they are a simplification of very real effects. I just don't have the time or patience to explain their derivation through integration of solid angles between differential elements.

I will leave you to think about it...

With all due respect, I have thought about this. I've read several books and taken several classes concerning this sort of thing, and I work in a field that deals with this.

 

[the4thamigo_uk]

I guess I am just a little dissatisfied with the explanation is all... I can't see what is wrong with it?

 

[the4thamigo_uk]

So you can't have all the heat transfer from i go to j and have all the the heat transfer from j go to i. For your BB example, the view factor from the BB to an enclosure would be one as you said. However, the enclosure would be at least partially radiating to itself thus the view factor would have to be less than one.

Ok yes I see your argument now. It comes down to the fact that there is a spread of rays in all directions from each point on the inner surface of my enclosing BB, so my simple calculation is clearly flawed as it assumes radial rays. So some will miss the surface of the inner body and be reabsorbed by the enclosing BB. I wish someone would have put it in those terms... but yes that was an excellent post.

An interesting one and I stand corrected!... Is there a 'general proof' of this for all geometrical arrangements?

I very much enjoyed it though and I learned quite a bit too... Youve got to keep questioning and pushing in order to get a good understanding of something. Thanks for your patience everyone... I will write this up and stick it on the internet somewhere.

 

[Roger44]

So, I was apparently wrong when I challenged Mgb Phys who said :

"For example, you can only heat a blackbody target using a blackbody source to the same temperature as the source. So however much you concentrate the light with lenses/mirrors you can't use the sun to heat something to a higher temperature than the surface of the sun. Because at that point the target would emit back at the sun."

I stand corrected but no regrets because I very much enjoyed the debate too. Thanks everbody for these two days of pure pleasure.

 

[the4thamigo_uk]

I stand corrected but no regrets because I very much enjoyed the debate too. Thanks everbody for these two days of pure pleasure.

If you want some more fun have a look at my thread on stefans law...? See where it might lead?

 

[the4thamigo_uk]

I am writing a few notes on this but a thought came to me. Please humour me once more...

It seems that the truth of the 4 laws, rests on their ability to prevent nonsensical situations arising in the world. It also lies in their consistency, meaning that any deductions we make from them must not be self-contradicting. Finally it lies in their completeness at describing the world. We as humans, observe the world and extract from it these basic postulates, axioms or laws. The 4 laws don't explicitly mention geometry, but since they have been extracted from empirical evidence about the real world, so they necessarily have geometry embedded deep down in them somewhere/somehow.

So, if we come across some imaginary geometrical experiment (like we have seen), that appears to contradict the 4 laws, can we 100% always immediately say on the basis of the laws that this imaginary experiment cannot exist in reality. In other words does a fundamental proof lie in reference to the 4 laws, or in reference to a more complete understanding of the geometry?

I now understand that the Stefan-Boltzman law can be derived purely from the 4 laws (http://en.wikipedia.org/wiki/Stefan–Boltzmann_law), so there is no new essential physics contained within it. Its just a convenient formula to work with and make calculations easier. So it would appear to me now that a contradiction of the 4 laws is sufficient to disprove a given experiment.

So it looks like there is no need to 'prove for all geometrical arrangements that you cannot have all the radiation transmitted from one BB to another BB'. If you ignore geometry completely you get the second law contradiction and that is sufficient argument, *because* contradiction of the second law leads to absurdities that are not observed in nature.

I know that's what you were saying Sylas, Yeti but it takes some time to come to terms with it. I haven't studied this stuff since my college days.

Sorry if its a bit philosophical... Thanks again everyone

 

[Nabo00o]

Sorry I know this is a bit old, but I just got to say; they got to you.
Optic focusing 'will' contradict the second law, but you nor nobody else wants to face that burden...

 

[Mapes]

Sorry I know this is a bit old, but I just got to say; they got to you.
Optic focusing 'will' contradict the second law, but you nor nobody else wants to face that burden...

Probably because this argument has been rehashed many times, including in the physics literature. See, for example, S. Panse ("Non-spontaneous radiative heat transfer," J. Phys. D: Appl. Phys. 25 (1992) 28-31), which claimed to present an optical focusing system that contradicted the Second Law, and K.M. Browne ("Focused radiation, the second law of thermodynamics and temperature measurements," J. Phys. D: Appl. Phys. 26 (1993) 16-19), which refuted Panse's argument and showed that in fact the Second Law was not violated in these systems because the finite size of the radiating body prevented focusing its rays to a point.

If you think you have a better approach that avoids Browne's refutations, publish it.