By Christopher Monckton of Brenchley
The monthly satellite lower-troposphere temperature anomaly from Remote Sensing Systems, Inc., is now available.
Taking the least-squares linear-regression trend on this dataset (the bright blue horizontal line through the dark blue data), there has now been no global warming – at all – for 17 years 5 months.
Would readers like to make a projection of how many mainstream media outlets will report this surely not uninteresting fact?
It shows that the Hiatus hernia for true believers in the New Religion continues.
My own prediction is that the number of media reporting 17 years 5 months without any global warming will be approximately equal to the number of general-circulation models that predicted such a long Pause notwithstanding ever-rising CO2 concentration.
Print out the graph as a postcard and send it to the editor of a newspaper near you that has shut down democratic debate by announcing that it will refuse to print any letters at all from “climate deniers”.
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Joe Born said @ur momisugly <February 14, 2014 at 2:18 am
It appears more adverse than that. 1.), The isolated particle modeling didn’t provide a useable scientific ‘handle’ on the problems of interest (statistics did), and 2.), Loschmidt clung to particle-descriptions, because he was committed to creating a perpetual motion machine.
Currently, Visiting Physicist continues to invoke the Loschmidt ‘particle magic’, because he too wants to obtain a result that science can’t support.
Once a guy says “a particle” or “one molecule”, academic referee flags fly like a blizzard. ‘Does not compute’ … and everything that comes after the opening ‘single particle’ “premise”, is therefore itself based on an invalid premise. You’re a lawyer, eh? 😉
I don’t myself really have a big personal problem with this kind of stuff (‘magic’, Zero Point, etc), but I’m reluctance to get drawn into ‘endless’ examinations of it, especially if it seems not to be recognized for the attempt to make an ‘end-run’ around science, that it is But climbing over the approved playground fence & exploring off-limits terrain is not without some attraction. 🙂
Loschmidt got a raw deal, but he was explicitly after a Perpetual Motion Machine outcome, and indulged in “extreme rendition” to get his model to “confess” what he wanted to hear. One wants to avoid falling into that ol’ pitfall … it’s always lurking out there.
tc
rgbatduke: “whether or not heat flows from the bottom to the top of the wire is determined by one thing only. Whether or not the bottom and top are at the same temperature.”
In my last comment, I may have argued past you. Let me try it differently.
First, let’s accept what you said in the passage just quoted, but with one difference. What you say is true of conduction only: the total (zero) flow is made up of a conduction flow but also a counteracting, gravity-caused drift flow. This is analogous to the (lack of) current flow across a semiconductor diode that isn’t in a circuit: a diffusion current occurs across the junction, I’m told, because of the different charge-carrier populations in the differently doped semiconductors, but that causes an electric field that in turn cause a drift current that cancels out the diffusion current.
That’s one way of looking at it. The other way doesn’t accept your premise. In your “refutation” post you said, “Such a wire admits the thermally driven conduction of heat according to Fourier’s Law [which is] an empirical law, and in no way depends on whether or not the wire is oriented horizontally or vertically.”
How could its independence of orientation have been empirically determined when the gravity-caused gradients of interest here are too small to measure?
See, there’s a logical flaw. You assume (1) that there’s an equilibrium gradient in the gas column but (2) that there’s none in the silver wire. So you’ve essentially assumed a contradiction from the beginning. No wonder you end up with one.
Now, you observe, reasonably, that it’s not too plausible that the gas column and the silver wire would have equal equilibrium gradients in isolation, even if you were to accept that such gradients are possible. But an initial, temporary heat flow, similar to the diode’s initial current flow when the two differently dope semiconductors are joined, could establish a new, common gradient–and eliminate the perpetual motion.
Do I know the exact microscopic mechanism for such an adjustment? No. But you haven’t given a good reason why one could not occur–and you have identified no step in which the Velasco et al. paper went wrong.
Velasco et al Eur. J. Phys. 17 (1996) 43–44. Not a Paper.
It’s an item in Eur. J. Phys. LETTERS AND COMMENTS.
It looks like a normal “paper”. But it isn’t; and thus it isn’t part of the formal scientific literature. It’s not peer reviewed; it cannot be cited as such.
It’s scuttlebutt. Possibly intelligent & insightful scuttlebutt … but not an authoritative scientific reference.
Ted 11:20am: It is the substance that really counts. If the substance is novel & good enough, physics will grant a Nobel Prize on the basis of even a short paragraph at the end of a May 1965 Letter to the Editor as shown in the 1978 Nobel Prize awarded Penzias & Wilson for finding the CMB “hiss” aka “excess temperature” in a certain horn antenna.
http://adsabs.harvard.edu/abs/1965ApJ…142..419P
The Eur. J. Phys. site does tell us: ”Comments will be subject to the normal refereeing procedures.”
Trick:
I just realized that I had in fact failed to post the comment I thought I’d posted.
The substance of it was that your link to Bohren worked, and (I resent it but can’t deny it) you were right in your inference that I’ll need to study some before I can comprehend the equation to which you referred.
Ted Clayton: “Once a guy says “a particle” or “one molecule”, academic referee flags fly like a blizzard. ‘Does not compute’ … and everything that comes after the opening ‘single particle’ “premise”, is therefore itself based on an invalid premise. You’re a lawyer, eh? ;)”
Each of us makes judgments based on his own experience, and, since I undoubtedly don’t have the same experiences as you, I can’t say I wouldn’t have assumed a similar point of view if my experiences were the same as yours.
As a result of my experience, though, the practices of an “academic referee” leave me singularly unimpressed. Yes, I was a lawyer. In that role I dealt intimately with the theories of a large number of technical experts, and significant investments not infrequently depended on those theories’ accuracy. By detecting errors in the theories of PhD.s from among the most-prestigious institutions, I have more than once saved investors from misdirecting resources to enterprises based on those theories. Conversely, I have received profound physics insights from at least one person who was a step away from being a street person.
So, although I understand your viewpoint, you may perhaps forgive me if my own experience set leads me to give credentials and other matters of form mean rather less, well, credence.
Trick said @ur momisugly February 14, 2014 at 11:53 am
The discovery of Cosmic Microwave Background radiation was substantiated, big-time. It wasn’t scuttlebutt.
It was real observational data; plainly pointing to an epochal discovery; gathered with a physical antenna-instrument.
The Scientific Tectonic Plates trembled perceptibly, as a million-head herd of peer & colleague wild buffalo stampeded in delirium across the primal intellectual prairie.
Penzias & Wilson’ initial report could be verified, validated, and repeated. And was, quickly, at 100s of leading labs, by thousands of scientists.
For sure, what sets P&W apart from Velasco et al, is the horn antenna they used to gather ‘actual’ data & facts. If a test could be offered, that would put Velasco’s conjecture on a data-driven, instrumented, test-hypothesis basis – and their ideas panned out – they too could become scientific celebrities.
Nobody would be more tickled than me, to see Velasco’s work shake the tectonic plates. So far, though, there is no way to test it; no data, no verification, no validation … no substance.
That leaves us with unsubstantiated ‘talk’. Scuttlebutt.
Ted 1:42pm: “…leaves us with unsubstantiated ‘talk’.”
And Bohren’s rigorous 1998 work, Verkley’s 2004 extensional work, Akmaev follow-up preciseness in 2008. Can you point to something wrong with the Velasco “scuttlebutt” (Ted term)? Or a subsequent paper/editor letter/comment/blog post that does? This to extend the atm. science work to generate a better understanding of the FLAT in top post. You know like Penzias & Wilson did even if by “accident.”
Joe Born said @ur momisugly February 14, 2014 at 1:11 pm
My apologies, Mr. Born. That was not meant as a dig or put-down. Is was meant as a ‘nod’ to the logic & deductive training of a lawyer.
… That, in the legal world, a flawed initial premise means that subsequent findings based on the flawed initials, will also be flawed. I regret not being more clear.
Specifically, in your case, the validity of a train of logic beginning with a single molecule, relies on the validity of the initial assumptions about the molecule. When we ‘start with one molecule’, and then pose a series of ‘such-thats’ and ‘therefores’, our eventual conclusions reflect the assumptions inherent in the first molecule. Whether they were stated or not …
What happens is, by adjusting the assumptions about the initial state or premise or molecule, we can, and people repeatedly do, arrive at virtually “any” outcome. (Such as, as we see argued, the assertion of the ability to create a Perpetual Motion Machine (by selecting the right assumptions about the molecule). As Loschmidt did.)
That’s the weakness or failing of the “Given an isolated molecule…” approach. It doesn’t reliably produce “an” outcome, but instead produces “almost any kind of outcome that can be imagined”. Rhetorically, it ends up tells us whatever we want to hear.
There has to be/are assumptions about the hypothetical single particle, etc. Whether they are recognized and planned, or not. As the cause-effects series plays out, what emerges is a chimera or shape-shifter, which varies unpredictably & unreliably based on the assumed initial nature of the particle.
That’s why this approach was abandoned, and replaced with statistics, during the later part of the 19th C. That’s why we honor Boltzmann & Maxwell, because it is they who saw the problem in this approach, and found a workable alternative, using statistics.
tc
Trick said @ur momisugly February 14, 2014 at 2:01 pm
“Scuttlebutt” isn’t a synonym for wrong/false. Some ‘talk’ ends up true, but we don’t know until additional information validates & verifies it.
Additional scuttlebutt (new but also unsubstantiated – untested/untestable – talk or discussion) about the original scuttlebutt, does not validate or verify it. It stays scuttlebutt … until a test or experiment or data can give it substance.
tc
I believe we’ve reached an impasse. But let me summarize so that I’m sure we’ve communicated.
I believe it is clear that Trick and I think (1) an isolated vertical gas column in a gravitational field will exhibit a (minuscule but non-zero) translational-kinetic-energy gradient, (2) a thermally conductive wire extending through the same height range may also exhibit a translational-kinetic-energy gradient, although probably not the same one, and (3) when respective ends of those two erstwhile-isolated systems are brought into thermal communication, an initial, short-lived flow of heat serves to equalize the two systems’ gradients, after which heat flow will cease.
On the other hand, Dr. Brown and Mr. Clayton believe that assumption of (1) and (2) necessitates the conclusion that a non-vanishing level of heat flow would continue indefinitely: the composite system would be a perpetual motion machine. They therefore conclude that statement (1), which is the ultimate issue, cannot be true.
My reason for thinking (1) is that I believe Velasco et al. say it’s a result of conventional statistical mechanics. Specifically, they say that in the microcanonical ensemble subject to a uniform gravitational field the mean translational kinetic energy is a diminishing function of elevation.
I infer from their remarks that Dr. Brown and Mr. Clayton believe that Velasco et al.’s conclusion is not conventional statistical mechanics. If so, perhaps they could cite some authority for precisely uniform translational kinetic energy in the microcanonical ensemble subject to a uniform gravitational field.
Joe Born 5:22pm: “..a thermally conductive wire extending through the same height range may also exhibit a translational-kinetic-energy gradient,”
Not exactly, the thin wire is a solid, no translation KE, constituents will vibrate in place. Wire can still come to thermodynamic equilibrium at max. entropy w/no heat flow in the system any longer AND thermal equilibrium with the gas if left alone long enough now that there are two bodies in there. Tougher solution. I’ll gladly let Joe be the 1st to rigorously solve. Go for the glory Joe, sufficiently armed with the Bohren 1998 text.
Next on your reading list is the Bohren 2006 text on atm. radiation…to be really dangerous on the blogs. If you like the guy’s writing as I do, first tackle ‘Clouds in a Glass of Beer’ and then ‘What light through yonder window breaks’. Interesting clips available for free if you look.
After all that, you will not need the Velasco stuff anymore to better understand FLAT in top post.
Thanks for the pointers, Trick.
Having failed to get a creditable answer from the physicists when this came up a couple years ago, I have from time to time thought of trying to teach this stuff to myself–and maybe then submitting a WUWT response to Dr. Brown’s “Refutation” post. As you can see, though, it’s been over two years, and I haven’t yet grasped the nettle; all those equations make my head hurt. So don’t hold your breath.
Still, even though my brief review hasn’t revealed a statistical-mechanics treatment in it, Bohren does look like a good source, so it may inspire me.
In any event, thanks again for the link.
Joe Born said @ur momisugly February 14, 2014 at 7:58 pm
It isn’t in your interests, to gaze up at the Ivory Tower and try to interpret the hand-signals and incantations. And you don’t have to, in this particular case, for very solid reasons.
Thermodynamics was originally a practical matter, and then the practicality of it remained intensely relevant. “Theory” came panting along after-the-fact, trying to hen-scratch explanations for existing, working, applied reality.
All along, because of the practical role of thermodynamics, it was urgent to inform & prepare non-academic engine-operators. Steam is dramatically unforgiving, and the machinery is expensive. You have to ‘fly’ or ‘ride’ a steam machine. Our ancestors ‘drove’ wagons and carts, but they ‘rode’ horses … and they full-well knew the difference. One is static, the other is dynamic.
Loschmidt was a businessman, first. He was a serial business-failure, before he returned to the campus at 33. His motive for crafting the gravity-thermal-gradient concept, was “applied” in nature. He was not pursuing science or practicing theory-art. He was trying to free humanity from the grinding pursuit of energy (and possibly aiming to strike a blow against the Capitalists).
Loschmidt’s thermal gradient in a gravity field idea was published in 1876. People have been playing with it, ever since. Nobody has ever gotten it to work. My personal opinion is, the phenomenon he describes – if real – would leave various kinds ‘signals’ or signs, in the environment at large (the atmosphere, eg). These ‘signals’ would have been investigated, and the phenomenological underpinnings of Loschmidt’s proposal – thermal gradient in a gravity field – exposed. Long ago, really.
That nothing has ever come of Loschmidt’s idea, does not prove that it is false. But that Loschmidt was actually not looking for, nor particularly interested in, ‘the truth’, is an inauspicious “signal”, right from Day One.
Loschmidt was not only working from several non-scientific ‘ulterior motives’, but he furthermore had the advantage of having Boltzmann & Maxwell at his elbow … “Nooo, Josef, that doesn’t look right at all”. Yet he persisted, without a speck of observational support, and in direct opposition to the sharpest colleagues around.
Remember, farm boys and street-kids run the steam & nuke plants on Navy vessels. And they know their thermodynamics (and their nuclear physics, to-boot). Don’t get too hung-up on the Ivory Tower … which actually is not and never was the leader, in the thermodynamics game. (Radioactivity, nuke-phys, a little different situation…)
tc
To Joe:
. This precisely analogous to Ohm’s Law: 
. Heat flows if a system with a finite thermal conductivity has a temperature difference across it. Current flows if a system with a finite electrical conductivity has a potential difference across it. In both cases, thermal equilibrium and electrostatic equilibrium are established if the ends are by a thermal or electrical conductor if and only if the ends are isothermal or equipotential, respectively.
(in spite of the fact that it shorts itself out because it has a finite thermal conductivity). Thermal equilibrium is the state where no net heat spontaneously flows, because heat only flows within a system that is not in equilibrium. There is precisely one self-consistent temperature field in which no heat or matter will flow. Consequently, if you change the temperature difference from 
to something else, heat will flow until the temperature difference is once again 
.
\ne T_A$. Again, if you place any other temperature difference across system B, heat will flow not to where it once again comes into thermal equilibrium with a new temperature difference — it will flow until the temperature difference 
is once again obtained. Again, nothing fancy here — this is straight up Fourier’s Law (except that FL clearly requires $latex \Delta T_A = \Delta T_B = 0, but we’re pretending that this isn’t true for the moment to see the contradiction).
(unless you want to claim that Fourier’s Law is false, and that there are many temperature differences for a single system that permit no heat flow, an assertion that is sufficiently absurd and in contradiction of moutains of empircal evidence that I’ll have to ask you to prove it). If it is in equilibrium, then system B is not and heat is flowing within it. If system B is in equilibrium, system A is not and heat is flowing within it.
Fourier’s Law (in 1 dimension, all that is relevant):
System A, in thermal equilibrium with a proposed vertical thermal lapse
System B, in thermal equilibrium with a different proposed vertical thermal lapse
Connect the two systems thermally at the top and bottom and wait for the two systems to stop changing. System A will have zero spontaneous internal heat flow only if the temperature difference is
There is no state of “mutual” thermal equilibrium in which no heat flows in both at some interpolatory temperature difference because thermal equilibrium in A has nothing to do with what is going on in B and vice versa. They are not well-mixed systems — they are distinct systems with a thermally conductive contact connecting them at certain points, just like the ones pictured repeatedly in thermo texts to make some of these exact points. Equipartition in one has nothing to do with equipartition in the other. Their specific heats are different. The physical mechanisms that lead to equilibrium can be different (or at least, differently weighted). All A knows of B are the temperatures at the points of thermal contact. Those temperatures in contact with B could just as well be produced by tiny electrical heaters or refrigerators as by system A.
Do you seriously think that no heat will flow through A or B for an arbritrary range of temperature differences between the ends? Because that is what you and Trick are asserting.
rgb
rgbatduke 1:59pm: “Do you seriously think that no heat will flow through A or B for an arbritrary range of temperature differences between the ends?”
No, not me. Not an arbitrary T( z) range. Nature’s range of temperatures will no longer be arbitrary when the isolated system of interest entropy value has been left alone long enough thereby increased to the maximum achievable entropy where heat no longer flows. The unique temperature field T(z) will be exactly and ideally determined as derived by Poisson long ago. For the ideal gas T field derivation, google this string: isentropic wiki
When the entropy stops increasing in the isolated system of interest here, heat will no longer flow, the system is said to be isentropic. For an isentropic (meaning unchanging entropy value) single system of gas in a gravity field, Poisson derived that T(p) as a function of p(z) long ago. Drop a thin silver wire in there and the system will still achieve max. entropy. I know as the wire diameter is increased to fill the system, an alternate solid solution increasingly emerges and your intuition & Fourier conduction becomes more and more applicable.
This latest post of yours shows my point that you cannot be dislodged even by dynamite from intuitively thinking about Fourier conduction in solids being applicable to gas. The Fourier conduction “law”* is not strictly applicable to fluids (due to their translational KE). Except at the no slip boundary in fluid flow, where it is useful. Just do the research, I should have provided enough hints by now. Instead of taking the trouble to read Fourier’s words, you merely repeat what others have said. A good example of error propagation in practice like Newton’s law of cooling when Newton never annunciated it at all.
Again, if want to discuss and/or contribute to further understanding FLAT in top post, one has to do the basic work correctly, i.e. pass the pre-req.s for admittance.
*”Law” in quotes because it is not applicable universally so strictly it is not a law. THIS could be one source of confusion.
Dr. Brown:
I’m afraid I can’t respond further to your argument, because I have merely inferred, from (what I currently see as) the fact that the equilibrium gas column in a gravitational field will exhibit a translational-kinetic-energy gradient, that a new equilibrium, no-net-heat-flow state will be established when the two systems are joined. That is to say, I have no explanation for that result except that the fact I’ve assumed dictates it.
That’s not much of an answer, I know, but unfortunately I’ll need to get smarter about the statistical mechanics before I can contribute more effectively to the discussion.
That said, I will mention that I don’t view the analogy to current flow in the same way you do. To me, heat flow is more like a diffusion phenomenon, while it is the gravitational effect that is more like flow in response to an electric field.
Specifically, you say, “Current flows if a system with a finite electrical conductivity has a potential difference across it,” i.e., I = V/R. And who am I to argue with Ohm’s Law? Yet no current flows through the junction of an unconnected semiconductor diode even though there’s a potential difference across that junction (but not across the diode as a whole). So you have to add a gloss to Ohm’s Law: there is indeed a drift, i.e., Ohm’s-Law, current, but it’s canceled by an opposite, diffusion current. You may similarly want to consider the possibility that on occasion Fourier’s Law also needs a gloss if it is to be applied properly.
Again, though, these plausibility arguments have reached an impasse. Resolution can come only from a rigorous analysis. I currently believe that the Velasco et al. papers do provide such an analysis from a statistical-mechanical perspective, and my guess is that Bohren et al. do from the more-traditional dS = dQ/T perspective. But I never quite mastered the former completely, and I’ve only just cracked open the latter, so I’m not yet able to argue further
Yet no current flows through the junction of an unconnected semiconductor diode even though there’s a potential difference across that junction (but not across the diode as a whole).
Try (imagine) shorting it out.
rgb
When the entropy stops increasing in the isolated system of interest here, heat will no longer flow, the system is said to be isentropic. For an isentropic (meaning unchanging entropy value) single system of gas in a gravity field, Poisson derived that T(p) as a function of p(z) long ago. Drop a thin silver wire in there and the system will still achieve max. entropy. I know as the wire diameter is increased to fill the system, an alternate solid solution increasingly emerges and your intuition & Fourier conduction becomes more and more applicable.
, basically), while the density and pressure increase, the average kinetic energy per particle does not.
Obviously you are never going to get the point of the silver wire.
Look, this problem has been solved literally forever. It is literally a textbook problem. One of many treatments of the correct solution can be found in the following article in the American Journal of Physics:
http://scitation.aip.org/content/aapt/journal/ajp/53/3/10.1119/1.14138
This one is particularly simple — intended to help instruct undergraduates seeking to understand precisely this question. In it, the authors provide a clever, very short proof that should make even Joe happy. If one has an ideal gas in an isolated container etc etc that has been left for a very long time, and imagine that the gas particles have a Maxwell distribution (that is, are at a well-defined temperature) at a single height and are completely non-interacting, the molecules from that height still have a Maxwell distribution at the same temperature after they have risen to a new height. This works because the Maxwell distribution is exponential in the kinetic energies — shifting all the kinetic energies by the same constant amount ends up shifting the distribution by an overall scale factor but does not affect the distribution itself. That is, the average kinetic energy is not a function of height!
Adding perfectly elastic collisions of course is not going to change anything, although if you want to go through the brute force proof then you should acquire e.g. the venerable The Mathematical Theory of Non-Uniform Gases by Chapman and Cowling (for example) and learn how to solve e.g. the Boltzmann equation with a uniform field present for the stationary velocity distribution for at least ideal gases — the general problem of solving the Boltzmann equation, like the general problem of solving the closely related Navier-Stokes equation, is mathematically extremely difficult and a lot of people are still working on it in many different contexts.
The argument of Coombes and Laue is sufficient, however, to address the most common argument made in favor of a lapse — that as particles fall they should speed up so surely there should be more kinetic energy, on average, per particle, at lower heights. Because they all shift their kinetic energies up by the same amount (and because the distribution function is an exponential of the kinetic energy over
For the (I sincerely hope) last time, we did not need even this much of the apparatus of statistical mechanics to demonstrate that equilibrium is isothermal (as is clearly stated and proven over and over again in the literature and textbooks). If equilibrium is not isothermal, it is possible to build perpetual motion machines of the second kind. It is not possible to build perpetual motions period, first or second kind. Therefore equilibrium is isothermal. Q.E.D. — pure symbolic logic. Only if equilibrium is isothermal do you eliminate the possibility of perpetual motion heat/energy loops in equilibrium, because we know perfectly well that heat flows from hotter places to colder places given any opportunity. All I have to do is provide one such pathway that shorts out the supposedly equilibrium lapse and heat will flow forever, because as fast as it flows out at the bottom of the gas column, up through the silver, and out into the gas at the top of the gas column, gravity will sort it out again spontaneously.
No, it doesn’t. The silver is in thermal equilibrium when it is isothermal, with both ends at the same temperature. As the argument above shows, so is the gas! If it has any well-defined temperature at any height, the isothermal Maxwell distribution is uniquely precisely stationary, preserving the probability distribution of kinetic energies at all heights at a constant temperature even if the gas molecules are in completely free non-interacting motion.
rgb
rgbatduke – There is no difference in potential across the junction, there is a difference of potential. These are completely different statements. viz, nothing to short.
rgbatduke 12:42pm: “One of many treatments of the correct solution…”
Coombes&Laue?? Not held to be correct anymore. You are living in the past. See not even the dynamite Velasco et. al. used refuting this paper you cite works to get you to the physical truth of this matter. The more modern Bohren 1998 sec. 4.4 generally refuted your 1985 cite also, Verkley 2004 refuted it for the 3rd time along with Akmaev 2008 for the 4th time. You are way behind in your reading as I have repeatedly informed.
If there really are other texts out there showing your views that refute these papers, please list them. I will go get them. I have ordered up a copy of Chapman you cite not on my shelf – but is way outdated – I have ordered the updated 1995 edition.
“…because we know perfectly well that heat flows from hotter places to colder places given any opportunity…”
I do agree in solids, this is a perfectly correct result of the 2nd law which is built on the foundation of entropy increase for all real systems. The 2nd law tells us an isolated system such as the big universe will increase entropy until it reaches the max. then die a natural heat death where heat no longer can be made to flow. 2nd law says nothing about the time or the temperature field for that to occur. The tall column is entirely isolated, a universe unto itself. Entropy increases to max. and heat ceases to flow; Poisson gave us the gas temperature field as a function of the pressure field at that max. entropy value (isentropic).
This is just your understanding limitations at play, your insistence that solids are like gases for heat flow at isentropic condition – which Poisson proved long ago is not the case. Did so despite your incorrect assertions.
This is why Fourier developed first the solid heat flow “law”, then the needed IGL PV=nRT was added for gases along with the 2nd law to keep your thin silver wire from being a perpetual motion machine where it cannot become one even if the tall top is at a different temperature than the bottom in the isentropic gas column as shown by Poisson eqn. and some max. entropy calculus.
Inspect a real 1768 foot or more radio tower. Do you really think the metal is the exact same T at the bottom as the tip top? Or it is a perpetual motion machine? No. Not isothermal. There are two bodies in this case, the air and metal can come into thermal equilibrium along the 1768 foot length. They do not come into thermodynamic equilibrium as this situation is not isentropic, one system nor isolated, all by inspection.
Here is a video of a maintenance worker climbing up a metal tower (no safety straps for good reason):
NB: You continue to confuse the heck out of these long standing terms below found in the literature. The tall column is just one isolated max. entropy system. The silver wire may be isothermal in two body thermal equilibrium at the beginning but as the isolated single system increases to max. entropy as it must, the column with or without thin wire becomes isentropic not isothermal as rigorously proven by the four cites I gave and you have yet to read 3 of them.
Thermodynamic equilibrium = applicable to single isolated object, body or system (call it what you will) at max. entropy.
Thermal equilibrium = applicable to at least two objects, bodies, systems.
Zeroth law = applicable to three objects, bodies, systems.
Musatroglophobia; diagnosis and treatment
Musatroglophobia is the fear of, or taboo against, giving the monkey the banana. In this malady, it is thought the monkey can only optimally realize the boon of the fruit, after he apprehends the underlying nature of banananess, and its array of relationships to the Known Universe.
It’s a boutique disorder, having only become widespread (in Modern Times), in the changes brought to social, political, scientific & academic institutions, in & around The 1960s. Drugs are thought to have played a role.
Pre-WWII scientific texts are often heavily-freighted with bananas. Monkeys have learned to pilot spaceships, eg, by studying these sources. The discovery of FLAT has been associated with unauthorized recent consumption of this high-octane, intellectually stimulating nutrient.
The Internet has of course greatly expanded the natural range & productivity of non-institutionalized varieties of the banana. Sadly, some monkeys still avoid these free-growing forms of the fruit, which musatroglophobia falsely warns can cause reduced blood-flow to the brain, and halitosis.
But the truth is out there.
tc
rgbatduke: “Try (imagine) shorting it out.”
I have (mentally). No difference. The unconnected diode exhibits no potential difference across its terminals, so shorting its terminals has no effect. The potential difference I mentioned exists across the junction, not across the terminals.
What I envisioned was a quasi-sigmoid potential curve centered on the junction, but this may not be precisely correct; I’m not a solid-state (or any other kind of) physicist. So, in response to your comment, I Googled “semiconductor junction potential,” and this popped up: http://en.wikipedia.org/wiki/P%E2%80%93n_junction. I commend it to your attention.
rgbatduke 12:42pm: “…you should acquire e.g. the venerable The Mathematical Theory of Non-Uniform Gases by Chapman and Cowling (for example)…demonstrate that equilibrium is isothermal (as is clearly stated and proven over and over again in the literature and textbooks).”
Yes, of course when the gas vessel is not in a gravity field. When the hydrostatic condition & gravity field is added, the small percentage non-isothermal temperature field result at thermodynamic equilibrium is rigorously proven over and over again in the modern literature.
My copy of Chapman 3rd. ed. 1970 reprinted 1995 came in today. A column in gravity field is not mentioned in the TOC, gravity not even mentioned by index. The only column ref. is to a separation column p. 268 and the reader is referred to other authors. The Earth atm. is mentioned only in context of strong electric field phenomena in its upper atm. p. 383.
Perhaps you have a page and section number in Chapman 1970 with which to turn my attention? Otherwise, you will need supply another cite (besides the outdated C&L 1985) purporting to support your hypothesis about FLAT in top post.