The Maxwell Boltzmann Distribution Effect

How carbon dioxide cools the atmosphere

Vincent J. Curtis

16 Oct 23

Maxwell-Boltzmann statistics are used in Statistical Thermodynamics.  The Maxwell-Boltzmann partition equation that we shall use is as follows:

N_i = N[exp – (ΔE/kT)] = N[exp – (hυ/kT)];

where N is the total number of molecules; Ni is the number of molecules in state i; ΔE is the difference in energy between the ground state and excited state i; h is Planck’s Constant, υ is the frequency, k is the Boltzmann constant, and T is absolute temperature in degrees Kelvin.  N_i/N is the ratio of the number of molecules in excited state i over the total number of molecules..

This equation shows the partition into ground and excited states for the temperatures relevant to the earth’s atmosphere.  Excitation arises from thermal collisions, and the one excited state of CO₂ is all that’s relevant to the problem at hand.

We obtain υ for the transition of a CO₂ molecule from the ground state to the vibrationally excited state represented by the absorption at 667 cm^-1 from the universal wave equation:

c = υƛ; 

where c is the velocity of light, υ the frequency, and ƛ the wavelength

Rearranging and substituting:

υ= c/ƛ = (3 x 10⁸ ms^-1/15 x 10^-6 m) = 2 x 10¹³ s^-1

Substituting into the Maxwell-Boltzmann equation:

N_i = N{exp – [(6.626 x 10^-34 x 2 x 10¹³)/(1.38 x 10^-23 x T)]}

N_i = N[exp – (960/T)]

For properly normalized results, we have to sum over the two states: the ground and excited state.  Since the ground state is deemed to have ΔE = 0, the exponential of that value gives 1.

Stated precisely, the normalized results for our two state system is given by:

            N_i/N = [exp –(960/T)]/[1 + exp –(960/T)]

Hence, the proportion of the excited state (N_i/N) at various temperatures are as follows:

T = 220K: 1.25 %

T = 288K: 3.45 %

T = 303K: 4.04 %

The values hold good at any pressure; at atmospheric pressure, this state is thermally quenched before emission.[1]  At low pressures, say, at 0.02 Torr, which obtains at 250,000’ altitude, radiation becomes the dominant[2] means by which an excited CO₂ molecule returns to the ground state; and in the upper atmosphere, this radiation can be emitted to space.

The effect of the Maxwell-Boltzmann distribution is the basis for the 220K curve in the blackbody radiation of the earth, as seen from outer space.  The CO₂ of the lower atmosphere completely absorbs all the radiation at 15 microns (667 cm^-1); but that in the upper atmosphere emits radiation at that frequency to space.  One can observe a spike in the middle of the big absorption peak at 667 cm^-1 that arises from the emission at high altitudes.  Emission of radiation to space is ultimately how the earth cools itself from solar radiation received during the day.

Because the proportion of CO₂ in the upper atmosphere is nearly the same as in the lower atmosphere, an increase in atmospheric CO₂ would eventually increase the amount of emission by CO₂ in the upper atmosphere to space, cooling the upper atmosphere more efficiently.  A cooler upper atmosphere would speed up the cooling of the lower atmosphere; hence, any warming from the increase of CO₂ (which I deny as a violation of the law of conservation of energy[3]) would be off-set by a faster rate of heat transport from the lower to the upper atmosphere.  And if the cooling effect in the upper atmosphere occasioned by a higher concentration of CO₂ was all there was, then increasing CO₂ would cool the atmosphere faster, and this does not violate the law of conservation of energy.

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[1] See 17 September 2023 entry “Carbon Dioxide Saturation and Global Warming.”

[2] See 28 September 2023 entry “There is no greenhouse effect, Part 1”

[3] See “There is no greenhouse effect, Part 3” to be published.

Hamilton School Board chooses reconciliation over education.

 

No wonder!

Vincent J. Curtis

16 Oct 23

RE: Majority of public school students score below previous year on EQAO. By contrast most Catholic board pupils surpassed provincial average. By Kate McCullough 14 Oct 23.

RE: School Board commits to Truth and Reconciliation.  New strategic direction reflects broad input, education director says. By Richard Leitner 16 Oct 23.

You look at these two headlines, and you wonder why public school students in Hamilton are doing so poorly?  The Public Board has taken its eyes off the ball, and instead of improving educational outcomes, they’re chasing fashionable chimera of no benefit to the students they’re responsible for educating.  It’s reconciliation over education.

Of course the senior directors "stood up and applauded the unanimous acceptance" of the (echoes of the Soviet Union) Five Year Plan: it’s their plan!  They want “Growing Together:” precisely what aboriginals don’t want.  First Nations want to maintain a separate identity; they don’t want to be submerged in Canada.  They don’t want us to “grow together;” they want to remain separate and distinct.

The education planners hired no fewer than three consulting firms; and the only groups they didn’t consult with were aboriginal groups. There’s no report of an agreement to the effect that ‘if we do this, you be reconciled.’ And if there’s no agreement saying if ‘we do this, every aboriginal in Canada be reconciled to someone, something, somehow,’ then without such an agreement, why bother?

Why mess up student education with progressive nonsense if there’s no benefit somewhere to someone at the other end?

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REPOST

Hamas in Gaza: Who are the puppet masters?

Serious Means for Serious Ends

Vincent J. Curtis                                                                       23 July 2014

 

War is a serious means for attaining serious ends.  The waves of rocket attacks by Hamas against Israel are certainly serious means, but what serious end is in view for Hamas?

Territorial gain cannot be the goal, certainly not the immediate goal of the acts of war committed by Hamas against Israel.  For the foreseeable future, Hamas and the Palestinian people they govern will be confined to the Gaza strip, a well-defined piece of territory.  Israel would gain no respite should territory be ceded to Hamas as a gesture, and Hamas lacks the military power to seize and hold Israeli territory.  Gain of territory cannot be the serious end in view. 

The sheer inconveniencing of Israeli citizens and Israeli commerce, while it may be occurring, is not a serious goal because it cannot be maintained.  It is not a step towards something higher.  Israeli retaliation against Gaza makes that goal not a paying proposition in the interim.

The declared goal of Hamas is the complete destruction of the Israeli state, and these rocket attacks will not achieve that.  Israel is not going to surrender to Hamas because of these attacks.  Indeed, the success of the Iron Dome anti-missile system is making Hamas’s barrages look feeble.  On the other hand, serious destruction is being meted out by Israel against Gaza.  Air attacks, artillery, and now a ground invasion of Gaza by Israel provoked by the Hamas rocket offensive is proving what an illusion it was to believe that Israel would surrender to a rocket barrage.

What goals could possibly be aimed at by Hamas, since neither the surrender of Israel, the gain of territory, retaliation, nor the relief of other pressures by Israel is in the offing?

Several goals come to mind.  The first is that Hamas is proving its worth to its supporters and paymasters.  Israel is hated by many other countries in the Middle East; the destruction of Israel is the declared national goal of Iran, for example.  Hamas did not build the missiles it is firing into Israel.  The missiles Hamas is launching into Israel had to be supplied by someone, and manufactured somewhere other than Gaza.

A missile capable of reaching Tel Aviv from Gaza takes up a lot of space.  Thousands of rockets somehow had to be transported by sea and delivered to Gaza through an efficient Israeli naval blockade.  This fact suggests that the missiles were delivered through Egypt and moved past the border controls between Egypt and Gaza.  These missiles would not have been delivered to Gaza at such cost and risk unless it was understood that Hamas would launch them against Israel.  Thus Hamas is acting as an agent to the state which supplied them the missiles.  It is doing what is expected of it.

 

The benefit to the state which supplied Hamas the missiles is that it gets to see Israel harassed at no physical cost to itself.  It is the Gazans who suffer Israel’s wrath, not Iran for example.

Hamas also is enforcing its control over the Palestinians of Gaza.  The goal that Israel must be destroyed is resisted at the cost of one’s life in Gaza.  Hamas will tolerate no dissent, on this point above all.  The Palestinians of Gaza have been dragooned into a war with Israel.  They are obliged to use their women and children as human shields protecting Hamas’s missile storage sites, an act contrary to the Geneva Conventions.  Being able to show civilian casualties to the world and offering these as examples of Israeli brutality is another goal of Hamas in this campaign.

Who would be convinced by such a thing?  The scenes of destruction and the sight of wounded children have certainly raised emotions all around the world.  Emotions would most likely be raised favorably for Hamas among those who are already convinced of the evil of Israel.

Thus Hamas by this rocket offensive against Israel is proving its worth as an agent and client of its supporters.  It is demonstrating its power over the Palestinians of Gaza by dragooning them into the war with Israel.

But Gaza and its Palestinian population clearly are things to be used by Hamas.  The destruction of Gaza and the creation of misery for its population are useful to Hamas since it can justify repression of dissent as a necessary war emergency.

Hamas governs Gaza, but to the benefit of itself not to the benefit of the people of Gaza.

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The Iceni Tribe

Vincent J. Curtis

12 Oct 23

RE: Sinforia Ancaster presents ‘Land Acknowledgement’ concert.  By Leonard Turnevicius.  The Hamilton Spectator 12 Oct 23.

It was awfully kind of SA music direct Jeffery Pollock to assign Ancaster to nations other than Canada.  This is what he seemed to say in “composers who come from nations on which the AMAC land sits.”  ‘Land sitting on nations’ is a rather awkward formulation, but it somehow forms the basis for holding a “Land Acknowledgement recognition concert” to acknowledge that Ancaster is illicitly squatting on Indian land.

Apparently, 357 Wilson St. E., Ancaster, and, by implication, all of Ancaster, is Anishinaabeg and Haudenosaunee land, (whoever they are); that’s the working theory.  This is rather like saying that East Anglia, England, is Iceni land because that was the indigenous Celtic tribe in occupation when the Romans arrived.

Actually, the Ancaster area was found to be in the possession of the Mississaugas of the Credit, and whatever title they were deemed to have had to it was purchased from them by the descendants of the Iceni in 1792, as part of the Land between the Lakes acquisition.  Land tenure was a foreign concept to the local indigenous, and it would be doubly impossible for 357 Wilson St. E. to be Asishinaabeg or Haudenosaunee land: first, because it was Mississauga; and, second, no individual from any local indigenous tribe can be said to have owned that parcel then, or now.  It’s Iceni, and licitly so..

Rather than give their part of illicit Ancaster back, they’re going to sing for reconciliation; but there’s no incentive on the Indian side to reconcile.

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For shame!

Vincent J. Curtis

11 Oct 23

RE: It’s time for oil & gas to get real about Net Zero. Op-ed by Catherine McKenna The Hamilton Spectator 11 Oct 23.

The latest tactic among the most extreme of the climate crazies is to shame Big Oil, and to demand that they stop doing their shameful things.  Catherine McKenna, Canada’s own climate Barbie and former federal Minister of the Environment and Climate Change, is one of those extreme climate crazies.  (She is CEO of Climate Solutions and Chair of the UN Secretary General’s expert group on Net Zero emissions.)  In her column she demands that Suncor “get real” on net zero.

Oil companies have a fiducial responsibility to their shareholders, which include many pension plans, to make a profit and to pay a dividend.  They have something approaching a moral responsibility to supply product to an oil-thirsty world.  The modern world cannot function without oil: wind mills need lubricating oil, electrical transformers need dielectric oil, hydraulic systems need hydraulic oil, and even the wheel bearings on a Tesla need lubricating grease.  You can’t just stop oil unless your plan is to demolish the modern world.

I don’t give McKenna credit for thinking that far ahead.  She can’t see that Net Zero means nothing if China, India, and Russia utterly ignore it, as they are ignoring this white, liberal fetish and guilt trip.  Canada is responsible for 1.6 percent of world CO2 emissions, and if Canada disappear tomorrow it would have no effect on world climates in the year 2100.

Net Zero is the prescription the beautiful people have to remedy their guilt feelings, which they believe other people should be having.  Net Zero won’t hurt the wealthy, but it will eviscerate the middle class.

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It’s never been about science

Vincent J. Curtis

7 Oct 23

RE: Denying science for fortune and fame. Opinion piece by Jay Robb, Communications Manager for McMaster University Faculty of Science.  The Hamilton Spectator 7 Oct 23

Since the Rio 92 conference, which was headed by Canada’s Maurice Strong, climate science has never been about science; it’s always been about finding a justification to humble the Western world by crippling its economic success.  That’s why the operative word in IPCC is Intergovernmental and that the lead chapter in every IPCC report is Advice for Policy Makers.  When Michael Mann produced the hockey-stick graph in 1998, it was like manna from heaven, the smoking gun, the pot of gold at the end of the rainbow, that justified crippling Western electric power generation and transportation fleets.

It turned out that Mann’s hockey stick was fool’s gold, and Steve McIntyre was the one who pointed that out.  The hockey stick was brandish around the world by the IPCC.  However, nobody previous to McIntyre had checked Mann’s work, not even for computational errors, and McIntyre, who knows a lot about statistical analysis, thought he spotted fraud; and he asked Mann for his raw data so that he could replicate the hockey stick himself.  It took a long while, but he got it, and asked economist Ross McKittrick to confirm his findings.  They found mathematical errors and statistical folly.  Together, McIntyre and McKittrick wrote a paper that demolished the scientific validity of the hockey stick, and their claims were upheld upon review by the US National Academy of Sciences.  For that, they’ve never been forgiven by the hockey-stickers, for without the hockey stick, they’ve no cause at all.

No climate “denier” denies the earth has a climate; in fact the earth has many climates.  What is denied is that CO₂ is a weather control knob.  What’s also denied is a strong connection between CO₂ and global warming; these two theories are busts, and it’s unscientific to uphold them, as Jay Robb does.

This malicious review condemns two Canadians as being climate deniers simply for fame and fortune, the late Dr. Tim Ball and Mr. Steve McIntyre on account of their effective attacks on the work of one Dr. Michael Mann, who was awarded his Ph.D. for the hockey stick paper.  Attacking Mann’s work is an attack on science, according to Robb.  Mann sued Ball, and lost the case, but, to my knowledge, never paid Ball before his death the legal fees he was assessed in losing the case.

In the Tom Nelson podcast #30 featuring Dr. Ross McKittrick, McKittrick goes through in detail the analysis of Mann’s work; the whole story is an appalling indictment of the state of climate “science,” which remains mostly valid today.  The whole discipline is corrupted from top to bottom, driven entirely by a political agenda, and rife with professional incompetence.  The professional incompetence and corruption was complained about by UAH Professor John Christy before a congressional committee in 2010. (There’s a presently a movement among retired physics professors to declare climate “science” as not a sub-discipline of physics.)

The climate “crisis” is driven, in part, by money.  Billions in research grants have been wasted in phoney or worthless climate research, and on modelling with expensive supercomputers.  In return for their grant money, the job of the researchers is to justify the Marxist idea that the economic success of the Western countries needs to be humbled, by making everything more expensive, particularly electrical power generation.

The search for fame and fortune is all by the climate crazies, those who claim the climate change is responsible for the rise in cases of dandruff.  It especially low for someone allegedly involved in science to lack the fineness of thought to understand the objections to the hockey-stick “science.”  But that’s it, isn’t it?  It’s been about politics from the start, and the use of the cancel weapon became routine, and first exposed in the climategate email scandal that involved Mann and Phil Jones.

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Heard it before

Vincent J. Curtis

2 Oct 23

RE: The impact of climate change on Ontarians. Spectator editorial 2 Oct 23.

The first question that arises from this provocative title is, ‘what climate change’?  The global average temperature now is the same as it was in 1999.  Then we read that it’s another one of those reports speculating about the future, like those speculations that forecasted the Arctic Ocean would be ice-free by 2014, and that lower Manhattan would be flooded due to rising sea levels by 2018; that  The Maldives and Tuvalu would be submerged by now.  Yeah, those kinds of reports.

These forecasts are based on climate modelling, the ones that have greatly overestimated global warming.  We have two decades of history with these models, and their lack of conformance to actual measured temperature data is noteworthy.  They can’t tell what the weather will be next month, but they can tell us what the weather will be in 75 years?  Really?  And what exactly makes the climate of today the absolutely optimum one, that there can be none better?  What is the ideal amount of rainfall, drought, and temperature for all Ontario?

The plan to spend money on hardening infrastructure is one I’ve recommended for years.  Don’t waste money on useless things like windmills, solar panels, and rainbows.  Even if the CO2-is-a-weather-knob theory is true, because of China and India, there’s nothing heroic Ontario can do about it.

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