06 November 2011
|No, Virginia, Cooler Objects Cannot Make Warmer Objects Even Warmer Still (Updated)|
|Supplemental email correspondence-pg 2|
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Intro by John O'Sullivan: It is my great pleasure to provide for publication the following robust analysis and counter-argument of former NASA scientist, Dr. Pierre Latour, to Dr. Roy Spencer’s unscientific claims regarding the alleged heating properties of ‘back radiation.’ Latour’s detailed assessment affirms those aspects of Slayers’ science (John O’Sullivan, November 6, 2011).
"No, Virginia, Cooler Objects Cannot Make Warmer Objects Even Warmer Still"
[Author's note: Revised and updated November 28, 2011, with additional supplemental email correspondence with Dr. Roy Spencer-see end of article].
Pierre R Latour, PE, PhD Chemical Process Control Systems Engineer rebuts Dr. Roy Spencer’s article,’Yes, Virginia, Cooler Objects Can Make Warmer Objects Even Warmer Still’ (published July 23, 2010). [1.]
I have admired and learned from Roy Spencer's work on AGW & GHG for several years. He taught me a lot. He is well recognized in his field. Now I write to return the favor and teach him about the errors in his posting and how he can learn from my field. I read all 350 blog responses, and identify the correct ones at the end.
Spencer’s setup through paragraph 11 is OK, assume start is steady-state, all dT/dt = 0. Spencer does not say whether the chiller chamber surroundings at 0F are held there by constant heat removal rate (= plate power input rate) or constant T = 0 (adjusting power input rate). Spencer’s paragraph 12 claim that the radiating plate temperature will increase from 150 to 160F by absorbing some back-radiation from the inserted non-radiating 100 plate is merely a claim, without scientific theory or evidence to back it up.
His statement “This is because the second plate reduced the rate at which the first plate was losing energy.” is provably false. And the answer to his subsequent question in parentheses is: no. His statement “Again, the reason the heated plate became even hotter is that the second plate has, in effect, “insulated” the first plate from its cold surroundings, keeping it warmer than if the second plate was not there.” is not true.
If the claim were true, the total surroundings, including cooler plate, would receive more radiation from T difference = 160 – 150 = 10F and the chiller chamber temperature would increase to T > 0, even if the portion of surroundings blocked by the cool plate gets colder. The rest gets warmer. The chiller would have to remove more heat to maintain 0, but input electrical energy to the 150 plate is constant, so this requires creation of energy. The 100 plate does not insulate the 150 plate from all 0 surroundings.
The Stefan-Boltzmann law radiation law says radiation rate is proportional to its absolute temperature **4, no T difference involved; the radiation rate of 150 is proportional to its radiating T = (65.6 + 273)**4, no matter what the surroundings. However, the absorption rate of real bodies depends on whether the absorber T (radiating or not), is less than the intercepted radiation T, or not. If the receiver T > intercepted T, no absorption occurs; if the receiver T < intercepted T the absorption rate may be as great as proportional to (T intercepted – T absorber), depending on the amounts reflected, transmitted or scattered.
What actually happens is the chiller radiates to the hot plate, but the plate cannot absorb any of it because it is too cold. The hot plate reflects, transmits or scatters colder radiation, just like my roof does for cold radio waves. Insertion of the 100 plate blocks hot radiation to the portion of the surroundings behind it, cooling them to T < 0. But the 100 plate also radiates to the rest of the surroundings, heating it to T > 0. The combined effect is no change in radiation absorbed by total surroundings and average radiating temperature remains 0. The hot plate does indeed intersect 100F radiation from the cold plate, just as it intersects 0F radiation from the surroundings, but it cannot absorb any of it and warm since the incident radiation is too cold, < 150.
Examples are all around us. Chemical engineers design and operate radiant, convection and conduction furnaces, kilns, forges, chemical reactors and boilers for refining petroleum, manufacturing chemicals and generating electricity since 1920. We no longer need more experiments. No back-radiation is observed. Conducting this experiment will allow nature to tell which prediction is correct. This has been done already by Prof Nasif Nahle, reported on 26 Sep 11 [2.]. Findings confirm the prediction T remains 150 is correct because a warm body cannot absorb cooler back-radiation.
An easy proof experiment is to park your car along a busy road at night with the headlights on. Move 5 meters in front and watch or measure your headlight emission brightness as approaching cars shine on them. Have you ever noticed your headlights getting brighter; then flickering back down as the oncoming car passes? No! Why? The hot bulb filaments do not absorb the low intensity, T, radiation from oncoming headlights, and reradiate it, brightening them.
Mathematics. Back-radiation may be represented by finite difference equations:
fi = f0 + K*Fi-1, and Fi = F0 + k*fi, where:
i is the iteration number, i = 1, 2, 3, …. infinite
Fi+x is the energy rate from the first bar at iteration i+x (x = 0|-1). Given F0 > 0.
fi+x is the energy rate from the second bar at iteration i+x (x = 0|-1). Given f0 => 0.
K is the fraction of radiation from the first bar absorbed by the second colder bar, 0 < K <=1.
k is the fraction of re-radiation from the second bar absorbed by the first hotter bar, 0 <= k <=1.
Substitute the first equation into the second to get
Fi = F0 + k*[f0 + K*Fi-1]
Delta Fi = Fi - Fi-1 = - (1 - kK)*Fi-1 + F0 + k*f0
This sequence converges to Fj - Fj-1 = 0 = - (1 - kK)*Fj + F0 + k*f0, and
Fj = [F0 + k*f0]/(1 - kK) => F0, constant, provided kK < 1, and
fj = f0 + K[F0 + k*f0]/(1 - kK) => f0.
The change in radiation energy rate to surroundings, Es, is the final rate minus initial rate minus amount initially diverted from surroundings to the injected cold plate, K*F0,
Es = (Fj - F0) + (fj - f0) - K*F0 = [(1 + k)*K*F0 + (1 + K)*k*f0]/(1 - kK) - K*F0.
For any K > 0 and k > 0, Es > 0. This would constitute creation of energy, a violation of the first law of thermodynamics.
Since K may be > 0, Es = 0 if and only if k = 0.
Since this is the only possible solution, k must be identically zero, so no cold back-radiation is absorbed and T remains 150. Quod Erat Demonstrandum, QED.
Chemical Engineering. Here is the corresponding radiation energy transfer engineering (Perry, John H, “Chemical Engineers Handbook”, 1950, H C Hottel, Section 6, Radiant Heat Transmission , pp. 483-498; Bird, R Byron, Warren E Stewart & Edwin N Lightfoot, “Transport Phenomena”, John Wiley, 1960, Chapt 14, Energy Transport by Radiation; Bennett, C O & John E Myers, “Momentum, Heat and Mass Transfer”, McGraw-Hill, 1962, Chapt 28, Radiant Heat Transfer, p371):
Hot emitter rate at T is
Qe = 5.7*X*T**4, S-B relation.
where X is radiating area, m2, T = 65.6 + 273 = 338K.
Hot radiation absorbed by cold at t < T is
Qa = a*b*Qe
where a = view factor of q from Q, < 1. Fraction of Q emission intercepted by q.
b = absorption factor of q, < 1. Depends on amount of incident radiation > t. Amount < t is not absorbed. Rest, (1-b), is reflected, transmitted or scattered.
Hot radiation re-emitted by q at t is
qe = c*Qa = 5.7*x*t**4
where x is radiating area, m2, t = 37.8 + 273 = 311K.
c = emission factor of q, < 1.
The rest (1-c) is converted to thermal heat to warm the cold body, increasing thermal t, and releasing heat to its colder surroundings by convection or conduction, until they equilibrate. Any change in radiating t depends on the nature of the radiating body and the absorbed radiation; it can be complex. I shall assume t remains constant for simplicity, no thermal effects, just like Spencer.
Re-emission energy from q intercepted by Q is
qi = A*qe, where
A = view factor of Q from q, < 1, fraction of q emission intercepted by Q.
Amount of re-radiation from q absorbed by Q is
qa = B*qi = B*A*qe = B*A*c*Qa = B*A*c*a*b*Qe = abcAB*Qa < Qa , where
B is absorption factor of Q, < 1.
This describes radiation from a furnace flame to boiler tubes and fire walls then onward from fire walls (not backward) to tubes.
Physics says when T > t, B = 0. So Qa = 0. There is no back-radiation energy transfer from cold to hot. QED.
Radiant energy transfer rate from Q that is absorbed by q and re-radiated by q to surroundings ts < t is
QT = Qa – qe = ab*Qe – c*Qa = abX5.7T**4 – cx5.7t**4 = 5.7[abX*T**4 – cx*t**4]
Some call this QT the net radiant energy transfer from Q to q accounting for qe because it has a temperature difference factor. This is not the difference between hot radiation emitted and cold back radiation re-absorbed by the hot emitter. When the surroundings are black, x = X, and when the radiating body is grey, c = a*b, so
QT = abX5.7[T**4 – t**4], provided T > t.
Note S-B law is not used for this analysis; it is a side information issue because it just assigns a radiating T for a particular Q/X. It is only needed to verify whether B = 0.
All these equations are first law conservation of energy balances.
Black and grey bodies are introduced to simplify the analysis, neither exists in nature. Engineers determine view factors a and A. That geometry is the hard part for furnace duty. Conduction and convection modeling is harder still, and significant. Since materials that behave like black and grey bodies are most useful for radiant energy transfer equipment, these assumptions with experimental adjustment factors are used for commercial engineering design of furnaces, kilns and forges.
Major furnace constructors like Babcock & Wilcox, Foster - Wheeler, Stone & Webster, Selas, KTI, KBR, Combustion Engineering, and Lummus have developed and built proprietary furnace designs world-wide for decades. Earth’s surface and atmosphere radiation may deviate from black and grey as well. And engineers never assume radiators get hotter by absorbing their own generated energy re-radiated back from colder absorbers. If one assumes everything is a theoretical black body, everything works like a black body, but nature may not quite.
Kirchhoff’s law assumes absorbed radiation is completely re-emitted (none is converted to thermal energy) and then proves the obvious, the ratio of emissive power to absorptivity is the same for all such bodies; equivalently the fraction of incident radiation absorbed, absorptivity, equals fraction emitted, emissivity. While emissivity depends only on the nature of the emitting body, absorptivity also depends on the nature of the incident radiation absorbed (but if this can be neglected, it is called a grey body, to simplify analysis). So emissivity can be less than absorptivity for real, non –grey bodies, they convert the difference to thermal heat. I have not assumed it or violated it in this analysis.
Spencer’s statement of Kirchhoff’s law is not precisely correct and was irrelevant to his claim hot bodies absorb cold radiation, just an interesting comment about the weather.
Unlike Spencer, I tend to include the physics of what happens on the molecular, atomic and photon level; it often overturns common sense and experience, leading to a more complete understanding of physics and natural phenomena. I do not arbitrarily dismiss physics because I do not understand it; only if I do and know it to be irrelevant. I am aware professional radiation physicists may have more precise descriptions of the un-absorbable colder T criteria from particle physics. Claes Johnson gave a plausible explanation of cutoff frequencies in “Slaying the Sky Dragon”, 2011. Irwin Hasenwinkle (30Jul10, 6:38 am) provided a convincing supporting explanation from Maxwell’s field equations.
Spencer imagined a physical situation and claimed what would happen; a radiating plate would get warmer if another colder, non-radiating plate were introduced, with no supporting physics or evidence. Then he claimed it was correct because he claimed it to be so. This is a circular argument, an invalid tautology; claim something and use it to prove the claim. Logic shows this proves nothing. Circular arguments should be avoided in a court where the judge and jury understand and reject invalid tautology.
Conclusion, the hot plate remains at 150. All physics I know supports it; no physics offered refutes it. Spencer mistakenly assumed the 150 plate absorbs incident 100 radiation. Introducing change to surroundings, like a new 100 plate, will simply change the temperature of the rest of the surroundings (cooling them to < 0), absorbing the same radiation from the 150 plate. Not only did Spencer fail to prove his claim but I have offered an alternative theory that refutes it. The generalized claim that a cooler object placed near a warmer object cannot result in a rise in temperature of the warmer object stands.
Another Spencer misstatement is revealed in paragraph 14 and repeated in subsequent blog comments: an unclear description of the first law conservation of energy ODE: input rate – output rate = accumulation rate = mCp*dT/dt. So imbalance does not cause T, it causes dT/dt or temperature change. T will keep changing until a T is reached that restores the balance; this always occurs because an input and/or output rate always depends on T.
If not T would go to 0 K or infinity. Surely every climatologist, weatherman, climate change artist, Congressman, engineer and high school graduate worth his salt knows how to quantify change and what a derivative is, (Newton, I, “Principia”, 1687). While this may seem picky, AGW promoters have claimed since 1997 ice melts because the atmosphere is warming, temperature is increasing, dT/dt >0, when in fact ice melts because the atmosphere is too warm, when T >0C, and at a rate proportional to T, not because atmosphere is warming, dT/dt > 0. Further, [CO2] significantly affects Cp of air, which affects the lag time of T responses to energy imbalances but may not affect the steady-state equilibrium value much. AGW debate is filled with sloppy language, inconsistent definitions and hence confusion.
Just because the K-T energy flow diagram balances does not prove GHG back-radiates 333 w/m2 from the cold sky GHG’s, or warmer Earth absorbs all of it and as a consequence warms further, as indicated at the far right of K-T diagram. The 396 w/m2 emitted by the surface and 333 w/m2 back-radiation absorbed could just as well have been 63 w/m2 emitted and 0 w/m2 reabsorbed.
What I feel with a warm blanket is reduction in heat transfer rate, not higher temperature. (Skin may sense T change but mostly Q change.) A blanket reduces the conductive heat transfer coefficient, U, between my body and air. Since Q = UA*(T body – T air), Q decreases with U so long as T body > T air. Metabolism adjusts Q to hold T body constant 98.6F (37.0° C for Europeans). When you die, Q = 0, and T body = T air, no matter what U is or how thick the blanket is. Blankets, coats and gloves reduce the rate of heat loss from one’s body, and hence the required shivering metabolism rate to maintain 37°C. They do not warm cold stones. To confirm my opening sentence, turn a fan on. You feel cooling because the fan increases the convective heat transfer coefficient at your skin, increasing Q at constant T. You feel increase in Q. Besides your experiment is about radiant energy transfer only, you ruled out conduction and convection, so the blanket conduction analogy is invalid if radiant and heat transfer are different mechanisms. Radiant energy transfer does not work the same way as conductive & convective heat transfer, as you know. Energy from colder cannot heat hotter further because the second law of thermodynamics says so, because nature says so; always and everywhere.
Spencer attempted to show how his claim relates to how much CO2 affects atmospheric temperature.
His opening universal statement about energy transfer to outer space “Putting anything between that (essentially infinite) heat sink and the Earth’s surface will cause the surface to warm.” should say space is an infinite radiation energy transfer sink, but it is an empty infinite barrier to conductive and convective heat transfer, since there is nothing out there to conduct or convect heat. Further, the statement for radiation would be false for any atmosphere that is transparent to the emitted radiation, like transparent gases for visible light, a tent for radio waves or my body for x-rays.
Since all atmospheres must get colder with altitude as kinetic energy is transformed into potential energy in a planet’s gravitational field, the lower atmosphere must be warmer than upper atmosphere, even if there is no radiation involved. This follows from the perfect gas law, PV = nRT. (The slope of the h vs. T line, the lapse rate, is –g/Cp.) Since air heat capacity, Cp, increases with exchange of O2 for CO2, the slope gets more horizontal and the surface T may increase. And the length of the line increases with the amount of atmosphere, also warming the surface.
This is not how a blanket works; is not even Spencer’s mischaracterization of how a blanket works. A planet’s surface temperature increase due to the presence of an atmosphere depends on the amount of atmosphere and it’s Cp. Its average re-radiation rate is set by the atmospheric energy balance dominated by solar input, adjusted for changes in reflectivity, surface inputs like respiration, combustion and mantle eruptions and outputs like photosynthesis, stabilized by ocean CO2 and energy sinks and sources. Short term weather has nothing to do with this because weather is a natural result of energy, mass and momentum transport within a turbulent three phase system driven by planet surface changes, rotation and orbit, lightening, ionosphere ionization and auroras.
So not only was the cold heats hot statement not proven to be correct, it is actually not true. In fact there is no heat transfer (heat means thermal energy, not radiation energy) involved from Earth’s surface to stratosphere on average either, because heat cannot escape to space and average dT/dt > 0, always. Of course there is tremendous mass, energy and momentum underway within Earth’s turbulent three-phase atmosphere, causing weather. The only mechanism I can see for Spencer’s assertion is if the atmosphere converts thermal heat to radiation to space, just as the surface does. And how much [CO2] affects that transformation. Which leaves us with total energy leaving Earth is that radiated by its surface and atmosphere. There is no back-radiation energy transfer from cold sky absorbed by Earth’s warmer surface.
Spencer did not prove his claim “ANY infrared absorber that gets between the Earth’s surface and space will cause the surface to warm.” He just asserted it. If that IR absorbing gas absorbs solar IR rather than letting the Earth surface absorb it, (thereby cooling surface) would not the gas re-emit all of it, even at a somewhat lower T and spectrum, as colder radiation and thermal heat? Thereby releasing all the energy it absorbed, and not influencing Earth energy balance one whit? Would it not just modify the distribution between radiant and thermal energy? Maybe more thermal T and less radiant T? According to Kirchhoff’s law!
Spencer’s far right downward orange arrows get wider because the amount of atmosphere overhead increases as you go down, not because warm lower atmosphere absorbs and reemits colder IR. Upper atmosphere IR in the widest arrow down has cooled more by dispersion and is not absorbed by the warmer surface below, just scattered. And the orange upward arrows are correspondingly narrower.
The statement “As a result of the atmosphere’s ability to radiatively insulate the Earth’s surface from losing infrared energy directly to the “cold” depths of outer space, the surface warms to a higher average temperature than it would have if the atmosphere was not there.” is an unproven assertion. I accept the next statement “This, then, constitutes the basic mechanism of the Greenhouse Effect. Greenhouse gases represent a “radiative blanket” that keeps the Earth’s surface warmer than it would otherwise be without those gases present.” because Spencer is more expert than I on that subject. But I have proven the basic mechanism is wrong.
I inserted clarifications in next paragraph: “Many well-meaning people think that one of the consequences of Kirchoffs Law of radiation is that an individual layer of the atmosphere that absorbs infrared energy at a certain rate must also emit energy at the same rate. This is NOT true. OK, because it is not a black or grey body. It is true for every molecule though, because of conservation of energy.
The rate of emission becoming the same as the rate of absorption occurs in the very special case where (1) the temperature has reached thermal (change thermal to radiant) equilibrium, and (2) that equilibrium is the result of only those two radiative flows, in and out of the object. And this condition is met at the molecular level.
Interestingly, this condition of a layer emitting the same amount of IR as it is absorbing is virtually never met anywhere in the atmosphere instantaneously, but it is satisfied in aggregate, on average, for well mixed gases. This is because of the vertical, convective flows which are also transporting energy between layers that affect local conditions but not average behavior.”
Then Spencer asserts, “In the global average, air below about 5,000 feet in altitude is absorbing more infrared energy than it emits, while air above that altitude (up to the top of the troposphere, the 80% of the atmosphere where weather occurs) is losing infrared energy faster than it is gained.” without explanation or evidence. If true, wouldn’t air below continue warming forever; and air above continues cooling forever? Since I don’t know, I must remain skeptical.
Can Energy “Flow Uphill”? Spencer says “In the case of radiation, the answer to that question is, “yes”. While heat conduction by an object always flows from hotter to colder, in the case of thermal radiation a cooler object does not check what the temperature of its surroundings is before sending out infrared energy. It sends it out anyway, no matter whether its surroundings are cooler or hotter. Yes, thermal conduction involves energy flow in only one direction. But radiation flow involves energy flow in both directions.”
I say “In the case of radiation, the answer to that question is, “no”. While heat conduction by an object always flows from hotter to colder, in the case of thermal radiation a cooler object does not check what the temperature of its surroundings is before sending out infrared energy, but the receiving absorber does and will only absorb radiation hotter than itself, otherwise it reflect, transmits, or scatters it. It sends it out (emits) anyway, no matter whether its surroundings are cooler or hotter.” Yes, thermal conduction involves energy flow in only one direction. But radiation flow involves energy flow in both directions, but actual transfer in only one from hot to cold, just like conduction and convection.”
Spencer offers “But, if ANY flow of energy “uphill” is totally repulsive to you, maybe you can just think of the flow of IR energy being in only one direction, no, it emits in all directions, but with it’s magnitude being related to the relative temperature difference between the two objects. OK. The result will still be the same: The presence of a cooler object can STILL cause a warmer object to become even hotter.” Nope, if you agree the magnitude of actual transfer is related to T hot **4 – T cold **4 then you cannot then assert the contrary. Contradiction is not allowed.
To recap, Spencer did not correctly describe how radiating plates work; how a blanket works or how the atmosphere works. There is no Green House in the sky. Cooler objects cannot make warmer objects even warmer still. QED.
Anyway, that’s my story, and I’m sticking to it, until someone convinces me otherwise. I trust this clears up the controversy. It is hard to translate the language of nature, mathematics, into the language of humans, like English. If it’s all about semantics, get the definitions right. History since Socrates teaches high standards of skepticism are warranted because most speakers and writers are wrong, including scientists. That is why establishing the truth is difficult. Call it wisdom if you please.
I am left to assume Spencer devised this provocative plate experiment claim to test how many student bloggers can rebut it correctly. I think Vangel, Dusty, Eilert, Anonymous (25Jul10, 1:51am, 6:17am), Tom Rowan, jae, Brian Strong, Andrew S, Eilert (25Jul10, 3:29am), Joletaxi, Colin Henderson, old construction worker, Spencer (27Jul10, 9:58 am), william, KuhnKat, Gord, robjMitchell, Irwin Hasenwinkle (30Jul10, 6:38 am), John Onsager, Gerlich and Tscheuchner, and Rudolf Clausius would. I hope his daughter would too. I would not want to deliberately mislead Virginia either.
By the way, I worked for NASA, Apollo, 1967-69. In 1997, I proved using fossil fuel combustion for Earth’s thermostat cannot work because the system is un-measurable, unobservable and uncontrollable.
[1.] Rebuttal of Roy Spencer’s ‘Cool Things Can Warm Hot Things’
http://www.drroyspencer.com/2010/07/yes-virginia-cooler-objects-can-make-warmer-objects-even-warmer-still/ Posted by Roy Spencer, PhD, 23 Jul 10 to 27 Jul 10
By Pierre Latour (4 Nov 2011)