Tag Archives: thermodynamics

Open Cycle Minds and Thermodynamic Socialism

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On 21 May 2021, Mark Ashwill’s excellent and moving article, “Of Class Rings, Bone Fragments and Fish Ponds: the Interminable Search for US MIAs in Vietnam,” was published (https://www.counterpunch.org/2021/05/21/of-class-rings-bone-fragments-fish-ponds-the-interminable-search-for-us-mias-in-vietnam/). It is about the searches by both Vietnamese and American groups for the unrecovered remains of those killed during the Vietnam War, while at the same time Americans continue to studiously avoid searching through their 20th century history to face up to its ongoing contortion of their 21st century national life. Think: Gaza in Palestine, May 2021, bombed Guernica-style by an unopposed Israeli military massively armed and lushly funded by the American Government.

“History does not repeat itself, but it rhymes,” (misattributed to Mark Twain, but actually from 1970).

It is my belief that 1968 was the most pivotal year in United States history after 1945. The commitment then to continue pursuing the Vietnam War, and the refusal ever since to face up to the consequences of it — unlike Germany’s postwar forthrightness about its 1933-1945 period — have doomed the U.S. to sink with increasing madness into the delusional path of “exceptionalism” it has been on since.

The last time there seemed a faint chance of breaking free from our American neo-fascist trajectory was 1976-1978, during the Carter Administration — and, yes, I know he was far from “perfect.”

I don’t think the U.S. will break free of its current delusional-ideological trajectory until it has fully come to terms with its Vietnam War history — and war crimes — and I mean by much more than just erecting a Black Wall.

The Amerindian Genocide, Black Slavery + Jim Crow, and the Vietnam War are in my view the three major American-perpetrated Holocausts. American “sleep” is shame-based denial of historical American reality. We as a nation could awaken from that sleep and transcend its underlying pathology, to such great benefit to everybody everywhere.

A good friend of mine is a 1966-1967 US Marine combat veteran of the Vietnam War, who survived much heavy combat and encirclement during the 1st Battle of Khe Sanh. He is the fiercest peacenik-socialist I’ve ever met, and also a really sweet gentle guy. He knows the truth.

And that truth is that official US Government ideology operates as an open cycle through the propagandized American Public Mind: we are not to “connect the dots” between what “we” have done with what “we” are doing. Acknowledging such attitudinally-causal links would be to operate both the personal and public minds in a morally closed cycle manner — to actually understand what is happening and why — and such clarified thinking must be dispatched into the non-thought oblivion of the memory hole in order to preserve the artifice by our political class of their guilt-free righteousness in perpetrating and sponsoring the war crimes deemed essential to the success of American foreign policy.

Let me suggest one such open cycle sequence of rhymed histories:

the Wounded Knee massacre, South Dakota 1890;

the Moro Crater massacre, southwestern Philippines 1906;

the No Gun Ri massacre, Korea 1950;

any number of massacres and bombardments in Southeast Asia during the Vietnam War between 1965 and 1975;

the El Mozote massacre, El Salvador 1981, by a US trained and Reagan Administration sponsored Salvadoran Army;

the 2003-2011 Iraq War and its catastrophic aftermath;

May 2021: Palestinians apparently do not have a “right to exist,” but Israelis continue to have the right to destroy them with massive firepower gifted to them by the United States.

Imagine if closed cycle thinking had been applied after any of these catastrophes, and that had prevented subsequent ones because of the socially transformative moral effect of such thinking on the people and government of the United States. Give peace a chance. Is that funny? Why should the moral elevation of our American civilization be seen as an unrealistic and ridiculous fantasy? That is just a cowardly excuse to cling to barbarism and immaturity.

Our planet’s habitability is too rapidly and visibly decaying today, for us humans (and that includes you, unexceptional Americans!) to continue carrying on with the sociopathological behaviors exhibited by ancestors like Achilles, Genghis Khan, the Spanish Conquistadores, and the dictators of the 1930s. It is time we applied closed cycle moral thinking for the guidance of our political selves.

Thermodynamic Socialism

On 21 May 2021, The Santa Fe New Mexican newspaper reported that:

“Oil and gas operators’ required bond insurance in New Mexico would cover only a fraction of the potential cost of cleaning up wells and pipelines they might leave behind, which could stick the state’s taxpayers with a colossal bill [$8.3B], according to an independent study released Thursday.”
(https://www.santafenewmexican.com/news/local_news/oil-and-gas-cleanup-could-cost-new-mexico-8-3-billion-study-says/article_6b8a9918-b97f-11eb-b0b1-6786d9af4fb1.html)

In pointing out this news story, Jeffrey St. Clair commented (23 May 2021, FB): “Same old story, all across the West. The mining, oil and timber corporations rip it up, abscond with the cash, leave behind poisonous rubble and the bill for cleaning it up…if it can be cleaned up.”

This “profitable” business behavior by resource extraction corporations is consistent with the type of energy cycle being promoted: the open cycle.

In thermodynamics, the open cycle is defined as the operation of any isolated “engine” — for extracting “work” from the consumption of “fuel” — by drawing the energy-containing resource (fuel) from an assumed infinite external and unchanging source (i.e., Nature), consuming it within the engine at high temperature to extract work (such as torque, or thrust), and exhausting the waste products of the conversion process into an assumed infinite external and unchanging sink at lower temperature (i.e., Nature). It is left to unspecified external reality — Nature — to endlessly absorb all wastes from our engines, and produce all fuels for our engines, without alteration to itself while existing at a constant temperature.

This has been a very useful concept for designing thermodynamically isolated fossil-fueled engines, like for jet airplanes, but it fails when “the engine” becomes so gargantuan — like being the aggregate fossil-fueled powering of our entire industrialized civilization — that it becomes comparable in “size” to the source and sink it is supposed to operate between. In terrestrial reality there are no isolated engines. You can’t wash an elephant in a kiddie pool, pretending it is in a river.

The aerobic-respiration-photosynthesis cycle sustaining wild animal and plant life on Planet Earth operates as a closed cycle. The aerobic exhalation of carbon dioxide by animal life is inhaled by plant photosynthesis to in turn exhale oxygen, in a balanced closed loop energized by the “fuel” of sunlight, and which cycle generates food for all: sugars, cellulose and protein.

The need to transform our civilization and reduce the amount of energy we use to conduct it, is entirely the task of abandoning further reliance on open cycle thermodynamics — the fiction that all our billions of little engines are each thermodynamically isolated — and operate our civilization’s aggregate planetary engine in a closed cycle. Of necessity this would mean abandoning the fiction that all our millions of little polities are sociologically isolated and can function in an apartheid and exclusionary manner.

Mens sana in corpore sano.

To power our planetary civilization with planetary closed cycle thermodynamics — in the interests of maintaining the longevity of human and much other life on Earth — we have to conduct our various socio-economic lives in a politically closed cycle manner across this planet. Think of this as thermodynamic socialism.

We humans are physically and intellectually capable of rearranging our civilization to operate at this elegantly integrated more advanced level, and we are now morally tasked to do so. We must leave our barbarism in the past and become a nation of morally closed cycle thinking in a world of thermodynamic socialism.

Is that impossible? The toppling of moral impossibilities in past human society always began as gleams of morally closed cycle thinking in just a few minds.

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Ocean Heat, From the Tropics to the Poles

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The heat being captured by the increasing load of carbon dioxide and other greenhouse gases in the atmosphere is subsequently transferred into the oceans for storage. This process — global warming — has raised the temperature of the biosphere by 1°C (or more) since the late 19th century.

Heat introduced into any material body at a particular point will diffuse throughout its volume, seeking to smooth out the temperature gradient at the heating site. If heat loss from that body is slow or insignificant, then a new thermal equilibrium is eventually achieved at a higher average temperature.

Thermal equilibrium does not necessarily mean temperature homogeneity, because the body may have several points of contact with external environments at different temperatures that are held constant, or with other external thermal conditions that must be accommodated to. Equilibrium simply means stable over time.

The heat conveyed to the oceans by global warming is absorbed primarily in the Tropical and Subtropical latitudes, 57% of the Earth’s surface. The Sun’s rays are more nearly perpendicular to the Earth’s surface in those latitudes so they receive the highest fluxes of solar energy, and oceans cover a very large portion of them.

That tropical heat diffuses through the oceans and is also carried by ocean currents to spread warmth further north and south both in the Temperate zones (34% of the Earth’s surface) and the Polar Zones (8% of the Earth’s surface).

What follows is a description of a very idealized “toy model” of heat distribution in the oceans, to help visualize some of the basics of that complex physical phenomenon.

Heat Conduction in a Static Ocean

The model is of a stationary spherical globe entirely covered by a static ocean of uniform depth. The seafloor of that ocean is at a constant temperature of 4°C (39°F), the surface waters at the equator are at 30°C (86°F), and the surface waters at the poles are at -2°C (28°F). These temperature conditions are similar to those of Earth’s oceans. These temperature boundary conditions are held fixed, so an equilibrium temperature distribution is established throughout the volume in the model world-ocean. There is no variation across longitude in this model, only across latitude (pole-to-pole). (See the Notes on the Technical Details)

Figure 1 shows contours of constant temperature (isotherms) throughout the depth of the model ocean, from pole to pole. The temperature distribution is shown as a 3D surface plotted against depth, which is in a radial direction in a spherical geometry, and polar angle (from North Pole to South Pole).

Figure 2 is a different view of the temperature distribution. Three regions are noted: The Tropical Zone (from 0° to 23° of latitude, north or south) combined with the Subtropical Zone (from 23° to 35° of latitude, north or south); the Temperate Zone (from 35° to 66° of latitude, north or south); and the Polar Zone (from 66° to 90° of latitude, north or south).

The model temperature distribution is perfectly stratified — isotherms uniform with depth — in the Tropical-Subtropical Zones, from 30°C at the surface at the equator, to 4°C at the seafloor. On entering the Temperate Zones, the isotherms arc up into a nearly radial (vertical) orientation. In the small portions of the planetary surface covered by the Polar Zones the isotherms are now more horizontally stratified because the surface waters are chillier that the those at the seafloor.

Figure 3 shows the streamlines of heat flow (the temperature gradient) for this temperature distribution. At the equator the heat is conducted down from the 30°C surface to the 4°C seafloor. As one moves further away from the equator the streamlines become increasingly lateral, until they are entirely so at 35° of latitude (north or south) where the model surface waters are at 19°C. The heat flow is entirely horizontal at this latitude, which separates the Subtropical and Temperate Zones; tropical heat is being conducted laterally toward the poles. In the Polar Zones the heat flow is up from the lower depths because the surface waters are chiller than those at depth, and because there is too little temperature variation with distance along the surface to drive a lateral heat flow.

Thermally Driven Surface Currents

Much oceanic heat is distributed by currents, and many of these occur along the surface.

The average speed of the Gulf Stream is 6.4km/hr (4mph), being maximally 9kph (5.6mph) at the surface but slowing to 1.6kph (1mph) in the North Atlantic, where it widens (information from the National Oceanic and Atmospheric Administration, NOAA).

Heat-driven equator-to-poles surface currents on the model ocean were estimated from the combination of the pole-to-pole surface temperature distribution, and thermodynamic data on liquid water. (See the Notes on the Technical Details)

The pressure built up by tropical heat in the model ocean’s equatorial waters pushes surface flows northward (in the Northern Hemisphere) and southward (in the Southern Hemisphere): from a standstill at the 30°C equator; with increasing speed as they recede from the equator, being 2kph (1.3mph) where the surface waters are at 25°C (77°F); a continuing acceleration up to a speed of 2.8kph (1.7mph) at the 35° latitude (the boundary between the Subtropical and the Temperate Zones); and an ultimate speed of 3.6kph (2.2mph) at the poles.

The currents are converging geometrically as they approach the poles, so a speed-up is reasonable. Logically, these surface currents are legs of current loops that chill as they recede from the equator, plunge at the poles, run along the cold seafloor toward the equator, and then warm as they rise to the surface to repeat their cycles.

An equator-to-pole average speed for these model surface currents is 2.8kph (1.7mph). Their estimated travel times along the 10,008km surface arc (for a model world radius of 6,371km, like that of a sphericalized Earth) is 3,574 hours, which is equivalent to 149 days (0.41 year).

Greater Realities

The model world just described is very simple in comparison to our lovely Earth. Since it does not rotate, it does not skew the north-south flow of currents that — with the help of day-night, seasonal, and continental thermodynamic inhomogeneities — creates all of the cross-longitudinal air and ocean currents of our Earth.

The irregularity of seafloor depth on Earth also redirects cross-latitudinal (pole-to-pole) and cross-longitudinal bottom currents, as do the coastlines of the continents; and the very slight and subtle changes in seawater density with temperature and salinity — neither of which is distributed uniformly throughout the body of Earth’s oceans — also affect both the oceans’s volumetric temperature distributions, and the course of ocean currents.

Recall that the model ocean is bounded by constant imposed temperature conditions at its seafloor (4°C) and surface waters (a particular temperature distribution from 30°C at the equator, to -2°C at the poles). Since this model world is otherwise suspended in a void, if these boundary conditions were removed the oceanic heat concentrated at the equator would diffuse further into the watery volume, seeking to raise the temperatures of the poles and seafloor while simultaneously cooling the equatorial region. The ultimate equilibrium state would be an ocean with a constant temperature throughout its volume.

Additionally, if it is also assumed that the now “liberated” model ocean-world can radiate its body heat away — as infrared radiation into the void of space — then the entire planet with its oceanic outer shell slowly cools uniformly toward -273.16°C (-459.69°F), which is the “no heat at all” endpoint of objects in our physical Universe.

When our Earth was in its Post-Ice Age dynamic thermal equilibrium, the “heat gun” of maximal insolation to the Tropics and Subtropics warmed the oceans there; a portion of that heat was conducted and convected into the Temperate Zones and toward the Poles; where the “ice bags” of masses of ice absorbed seasonal oceanic heat by partially melting — which occurs at a constant temperature — and then refreezing. Also, the atmosphere did not trap the excess heat radiated into space. In this way cycles of warming and cooling in all of Earth’s environments were maintained in a dynamic balance that lasted for millennia.

What has been built up in the atmosphere since about 1750 is an increasing load of carbon dioxide gas and other greenhouse gases, which have the effect of throwing an increasingly heated “thermal blanket” over our planet. Now, both the heat conduction pathways and the heat convection currents, described with the use of the model, convey increasing amounts of heat energy over the course of time. As a result the masses of ice at the poles are steadily being eroded by melting despite their continuing of cycles of partial re-freezing during winter, and additional melting during summer.

Simple mathematical models can help focus the mind on the fundamental processes driving complex multi-entangled physical realities. From there, one can begin assembling more detailed well-organized quantitative descriptions of those realities, and then using those higher-order models to inform decisions regarding actions to be taken in response to those realities, if responses are necessary. This point of departure from physics plunges you into the world of psychology, sociology, economics, politics, and too often sheer madness. I leave it to another occasion to comment outside my field of expertise about all that.

Notes on the Technical Details

The cylindrically symmetric equilibrium temperature distribution for a static ocean of uniform depth, which entirely covers a spherical planet, was solved from Laplace’s equation. The temperature of the seafloor everywhere is 4°C, the surface waters at the Equator are at 30°C, and the surface waters at the poles are at -2°C. The variation of surface water temperature with respect to polar angle (latitude) is in a cosine squared distribution. Displays of the 3D surface T(r,ɵ) show isotherms down through the ocean depths at all polar angles (ɵ). The contour lines on the stream function associated with T(r,ɵ) are heat flow streamlines, the paths of the heat gradient (which are always perpendicular to the isotherms).

Bernoulli’s Theorem was applied to surface flow from the equator to the poles (no radial, nor cross-longitudinal motion) for incompressible liquid water with thermal pressure given by:

P(T°C)=[62.25kg/m-sec^2]*exp{0.0683*[T(R,ɵ)-Tp]}

for R equal to the planetary radius to the ocean surface; Tp=-2°C; and using thermodynamic data for water between 32°F (0°C) and 100°F (37.8°C) that indicates a thermal pressure equal to 62.25kg/m-sec^2 in liquid water at 0°C; and that the density of water is essentially constant at 1000kg/m^3 (for the purposes of this model) within the temperature range of the data surveyed.

Inserting P(T°C) into the Bernoulli Theorem definition of equator-to-pole lateral (cross-latitudinal) velocity gives a formula for that velocity as a function of polar angle:

v(ɵ)=±sqrt{(2*[62.25kg/m-sec^2]/[1000kg/m^3])*exp[0.0683*(Te-Tp)]*[1-exp(-0.0683*[Te-T(R,ɵ)])]}

v(ɵ)=±(1.0523m/s)*sqrt{1-exp(-0.0683*[Te-T(R,ɵ)])}

for Te=30°C, and ± for northward (in the Northern Hemisphere) or southward (in the Southern Hemisphere) surface flows.

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Remembering R. P. Kroon

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Rein Kroon and another Westinghouse engineer testing strain on celluloid model of mount for Hale Telescope. (Hagley)

 

Reinout Pieter Kroon (4 August 1907 – 4 August 1992) was my professor for turbomachinery during my Mechanical Engineering undergraduate years (1968-1972) at the Towne School of Engineering at the University of Pennsylvania (which is in Philadelphia). He was a kind, intelligent, witty and perceptive man, with great insights into what engineers — as public-minded, socially conscious citizens — could and should be. This web-page is my appreciative memorial for him.

“Reinout P. Kroon (1907 – 1992) was a Dutch mechanical engineer who immigrated to the United States in 1931 after earning his M.S. degree from the Federal Technical Institute in Zurich, Switzerland. Joining Westinghouse Corporation that year, he soon became a development engineer in the Steam Division.

“In late 1935, Westinghouse sent Kroon to Pasadena to work on the details of the mounting of the 200-inch telescope. During his six-month assignment, Kroon solved three major design issues. First, he designed the hydrostatic pressure system with which the telescope turns in right ascension on a thin film of oil. Second, he designed the horseshoe and ball bearings for the north and south ends of the yoke. Finally, he designed the spoked declination bearings that allow the telescope to travel north and south.

“Later, Kroon became head of engineering research at Westinghouse where he managed a team that in 1945 developed the first commercially viable American jet engine. In 1960, he joined the engineering faculty at the University of Pennsylvania where he rose to the position of chairman of the graduate division of mechanical engineering.” (http://www.astro.caltech.edu/palomar/about/personalities.html)

Reinout Kroon was the Team Leader at Westinghouse in the making of the first American jet engine. The story of that effort during the World War II years is described by Kroon in his lecture-pamphlet “What’s Past Is Prologue” (shown below), and the unsuccessful effort to commercialize the initial technical triumph of making that turbojet, during the years 1950-1960, is given in detail by Paul D. Lagasse in his 1997 Master’s thesis in American History (http://enginehistory.org/GasTurbines/EarlyGT/Westinghouse/WestinghouseAGT.pdf).

Professor Kroon was a tall, elegant and personable man; he was a fabulous instructor and an inspiring example of an engineer’s engineer. From him I learned more about fluid mechanics and thermodynamics, specifically about turbomachinery, and — most elegantly — dimensional analysis; he was very adept mathematically. A field trip to the Westinghouse plant where huge turbines (for steam turbine electric generators) were built, was memorable. The stamping machines for fashioning the turbine blades were awesome, and loud!

Reinout had one brother, Berend Jan Gerhard (Bert) Kroon; and he was married to Dora Kroon (born Kaestli, on 25 May 1910, in Bern, Switzerland) with whom he had children, one son being Berend Walter Kroon. Reinout Kroon lived in Kennett Square, Pennsylvania. Professor Kroon died tragically in 1992, on his 85th birthday, as a result of injuries sustained some days earlier in an automobile accident.

What’s Past Is Prologue

Kroon, Dimensional Analysis

PDF files of the two pamphlets displayed below are available from the web-links above.

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The Thermodynamics of 9-11

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When hijacked airliners crashed into the tall Towers of the World Trade Center, in New York City [on 11 September 2001], each injected a burning cloud of aviation fuel throughout the 6 levels (WTC 2) to 8 levels (WTC 1) in the impact zone. The burning fuel ignited the office furnishings: desks, chairs, shelving, carpeting, work-space partitions, wall and ceiling panels; as well as paper and plastic of various kinds.

How did these fires progress? How much heat could they produce? Was this heat enough to seriously weaken the steel framework? How did this heat affect the metal in the rubble piles in the weeks and months after the collapse? This report is motivated by these questions, and it will draw ideas from thermal physics and chemistry. My previous report on the collapses of the WTC Towers described the role of mechanical forces (1).

Summary of National Institute of Technology and Standards (NIST) Report

Basic facts about the WTC fires of 9/11/01 are abstracted by the numerical quantities tabulated here.

Table 1, Time and Energy of WTC Fires

ITEM                              WTC 1           WTC 2
impact time (a.m.)          8:46:30          9:02:59
collapse (a.m.)               10:28:22        9:58:59
time difference               1:41:52          0:56:00
impact zone levels          92-99            78-83
levels in upper block       11                 27
heat rate (40 minutes)     2 GW            1 GW
total heat energy             8000 GJ       3000 GJ

Tower 1 stood for one hour and forty-two minutes after being struck between levels 92 and 99 by an airplane; the block above the impact zone had 11 levels. During the first 40 minutes of this time, fires raged with an average heat release rate of 2 GW (GW = giga watts = 10^9 watts), and the total heat energy released during the interval between airplane impact and building collapse was 8000 GJ (GJ = giga-joules = 10^9 joules).

A joule is a unit of energy; a watt is a unit of power; and one watt equals an energy delivery rate of one joule per second.

Tower 2 stood for fifty-six minutes after being struck between levels 78 and 83, isolating an upper block of 27 levels. The fires burned at a rate near 1 GW for forty minutes, diminishing later; and a total of 3000 GJ of heat energy was released by the time of collapse.

WTC 2 received half as much thermal energy during the first 40 minutes after impact, had just over twice the upper block mass, and fell within half the time than was observed for WTC 1. It would seem that WTC 1 stood longer despite receiving more thermal energy because its upper block was less massive.

The data in Table 1 are taken from the executive summary of the fire safety investigation by NIST (2).

The NIST work combined materials and heat transfer lab experiments, full-scale tests (wouldn’t you like to burn up office cubicles?), and computer simulations to arrive at the history and spatial distribution of the burning. From this, the thermal histories of all the metal supports in the impact zone were calculated (NIST is very thorough), which in turn were used as inputs to the calculations of stress history for each support. Parts of the structure that were damaged or missing because of the airplane collision were accounted for, as was the introduction of combustible mass by the airplane.

Steel loses strength with heat. For the types of steel used in the WTC Towers (plain carbon, and vanadium steels) the trend is as follows, relative to 100% strength at habitable temperatures.

Table 2, Fractional Strength of Steel at Temperature

Temperature, degrees C      Fractional Strength, %
200                                     86
400                                     73
500                                     66
600                                     43
700                                     20
750                                     15
800                                     10

I use C for Centigrade, F for Fahrenheit, and do not use the degree symbol in this report.

The fires heated the atmosphere in the impact zone (a mixture of gases and smoke) to temperatures as high as 1100 C (2000 F). However, there was a wide variation of gas temperature with location and over time because of the migration of the fires toward new sources of fuel, a complicated and irregular interior geometry, and changes of ventilation over time (e.g., more windows breaking). Early after the impact, a floor might have some areas at habitable temperatures, and other areas as hot as the burning jet fuel, 1100 C. Later on, after the structure had absorbed heat, the gas temperature would vary over a narrower range, approximately 200 C to 700 C away from centers of active burning.

As can be seen from Table 2, steel loses half its strength when heated to about 570 C (1060 F), and nearly all once past 700 C (1300 F). Thus, the structure of the impact zone, with a temperature that varies between 200 C and 700 C near the time of collapse, will only have between 20% to 86% of its original strength at any location.

The steel frames of the WTC Towers were coated with “sprayed fire resistant materials” (SFRMs, or simply “thermal insulation”). A key finding of the NIST Investigation was that the thermal insulation coatings were applied unevenly — even missing in spots — during the construction of the buildings, and — fatally — that parts of the coatings were knocked off by the jolt of the airplane collisions.

Spraying the lumpy gummy insulation mixture evenly onto a web of structural steel, assuming it all dries properly and none is banged off while work proceeds at a gigantic construction site over the course of several years, is an unrealistic expectation. Perhaps this will change, as a “lesson learned” from the disaster. The fatal element in the WTC Towers story is that enough of the thermal insulation was banged off the steel frames by the airplane jolts to allow parts of frames to heat up to 700 C. I estimate the jolts at 136 times the force of gravity at WTC 1, and 204 at WTC 2.

The pivotal conclusion of the NIST fire safety investigation is perhaps best shown on page 32, in Chapter 3 of Volume 5G of the Final Report (NIST NCSTAR 1-5G WTC Investigation), which includes a graph from which I extracted the data in Table 2, and states the following two paragraphs. (The NIST authors use the phrase “critical temperature” for any value above about 570 C, when steel is below half strength.)

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“As the insulation thickness decreases from 1 1/8 in. to 1/2 in., the columns heat up quicker when subjected to a constant radiative flux. At 1/2 in. the column takes approximately 7,250 s (2 hours) to reach a critical temperature of 700 C with a gas temperature of 1,100 C. If the column is completely bare (no fireproofing) then its temperature increases very rapidly, and the critical temperature is reached within 350 s. For a bare column, the time to reach a critical temperature of 700 C ranges between 350 to 2,000 s.

“It is noted that the time to reach critical temperature for bare columns is less than the one hour period during which the buildings withstood intense fires. Core columns that have their fireproofing intact cannot reach a critical temperature of 600 C during the 1 or 1 1/2 hour period. (Note that WTC 1 collapsed in approximately 1 1/2 hour, while WTC 2 collapsed in approximately 1 hour). This implies that if the core columns played a role in the final collapse, some fireproofing damage would be required to result in thermal degradation of its strength.” (3)

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Collapse

Airplane impact sheared columns along one face and at the building’s core. Within minutes, the upper block had transferred a portion of its weight from central columns in the impact zone, across a lateral support at the building crown called the “hat truss,” and down onto the three intact outer faces. Over the course of the next 56 minutes (WTC 2) and 102 minutes (WTC 1) the fires in the impact zone would weaken the remaining central columns, and this steadily increased the downward force exerted on the intact faces. The heat-weakened frames of the floors sagged, and this bowed the exterior columns inward at the levels of the impact zone. Because of the asymmetry of the damage, one of the three intact faces took up much of the mounting load. Eventually, it buckled inward and the upper block fell. (1)

Now, let’s explore heat further.

How Big Were These Fires?

I will approximate the size of a level (1 story) in each of the WTC Towers as a volume of 16,080 m^3 with an area of 4020 m^2 and a height of 4 m (4). Table 3 shows several ways of describing the total thermal energy released by the fires.

Table 3, Magnitude of Thermal Energy in Equivalent Weight of TNT

ITEM                                  WTC 1              WTC 2
energy (Q)                          8000 GJ           3000 GJ
# levels                              8                       6
tons of TNT                       1912                 717
tons/level                           239                  120
lb/level                               478,000           239,000
kg/m^2 (impact floors)       54                    27
lb/ft^2 (impact floors)         11                    6

The fires in WTC 1 released an energy equal to that of an explosion of 1.9 kilotons of TNT; the energy equivalent for WTC 2 is 717 tons. Obviously, an explosion occurs in a fraction of a second while the fires lasted an hour or more, so the rates of energy release were vastly different. Even so, this comparison may sharpen the realization that these fires could weaken the framework of the buildings significantly.

How Hot Did The Buildings Become?

Let us pretend that the framework of the building is made of “ironcrete,” a fictitious mixture of 72% iron and 28% concrete. This framework takes up 5.4% of the volume of the building, the other 94.6% being air. We assume that everything else in the building is combustible or an inert material, and the combined mass and volume of these are insignificant compared to the mass and volume of ironcrete. I arrived at these numbers by estimating volumes and cross sectional areas of metal and concrete in walls and floors in the WTC Towers.

The space between floors is under 4 meters; and the floors include a layer of concrete about 1/10 meter thick. The building’s horizontal cross-section was a 63.4 meter square. Thus, the gap between floors was nearly 1/10 of the distance from the center of the building to its periphery. Heat radiated by fires was more likely to become trapped between floors, and stored within the concrete floor pans, than it was to radiate through the windows or be carried out through broken windows by the flow of heated air. We can estimate a temperature of the framework, assuming that all the heat became stored in it.

The amount of heat that can be stored in a given amount of matter is a property specific to each material, and is called heat capacity. The ironcrete mixture would have a volumetric heat capacity of Cv = 2.8*10^6 joules/(Centigrade*m^3); (* = multiply). In the real buildings, the large area of the concrete pads would absorb the heat from the fires and hold it, since concrete conducts heat very poorly. The effect is to bath the metal frame with heat as if it were in an oven or kiln. Ironcrete is my homogenization of materials to simplify this numerical example.

The quantity of heat energy Q absorbed within a volume V of material with a volumetric heat capacity Cv, whose temperature is raised by an amount dT (for “delta-T,” a temperature difference) is Q = Cv*V*dT. We can solve for dT. Here, V = (870 m^3)*(# levels); also dT(1) corresponds to WTC 1, and dT(2) corresponds to WTC 2.

dT(1) = (8 x 10^12)/[(2.8 x 10^6)*(870)*8] = 410 C,

dT(2) = (3 x 10^12)/[(2.8 x 10^6)*(870)*6] = 205 C.

Our simple model gives a reasonable estimate of an average frame temperature in the impact zone. The key parameter is Q (for each building). NIST spent considerable effort to arrive at the Q values shown in Table 3 (3). Our model gives a dT comparable to the NIST results because both calculations deposit the same energy into about the same amount of matter. Obviously, the NIST work accounts for all the details, which is necessary to arrive at temperatures and stresses that are specific to every location over the course of time. Our equation of heat balance Q = Cv*V*dT is an example of the conservation of energy, a fundamental principle of physics.

Well, Can The Heat Weaken The Steel Enough?

On this, one either believes or one doesn’t believe. Our simple example shows that the fires could heat the frames into the temperature range NIST calculates. It seems entirely reasonable that steel in areas of active and frequent burning would experience greater heating than the averages estimated here, so hotspots of 600 C to 700 C seem completely believable. Also, the data for WTC Towers steel strength at elevated temperatures is not in dispute. I believe NIST; answer: yes.

Let us follow time through a sequence of thermal events.

Fireball

The airplanes hurtling into the buildings with speeds of at least 200 m/s (450 mph) fragmented into exploding torrents of burning fuel, aluminum and plastic. Sparks generated from the airframe by metal fracture and impact friction ignited the mixture of fuel vapor and air. This explosion blew out windows and billowed burning fuel vapor and spray throughout the floors of the impact zone, and along the stairwells and elevator shafts at the center of the building; burning liquid fuel poured down the central shafts. Burning vapor, bulk liquid and droplets ignited most of what they splattered upon. The intense infrared radiation given off by the 1100 C (2000 F) flames quickly ignited nearby combustibles, such as paper and vinyl folders. Within a fraction of a second, the high pressure of the detonation wave had passed, and a rush of fresh air was sucked in through window openings and the impact gash, sliding along the tops of the floors toward the centers of intense burning.

Hot exhaust gases: carbon monoxide (CO), carbon dioxide (CO2), water vapor (H2O), soot (carbon particles), unburned hydrocarbons (combinations with C and H), oxides of nitrogen (NOx), and particles of pulverized solids vented up stairwells and elevator shafts, and formed thick hot layers underneath floors, heating them while slowly edging toward the openings along the building faces. Within minutes, the aviation fuel was largely burned off, and the oxygen in the impact zone depleted.

Thermal Storage

Fires raged throughout the impact zone in an irregular pattern dictated by the interplay of the blast wave with the distribution of matter. Some areas had intense heating (1100 C), while others might still be habitable (20 C). The pace of burning was regulated by the area available for venting the hot exhaust gases, and the area available for the entry of fresh air. Smoke was cleared from the impact gash by air entering as the cycle of flow was established. The fires were now fueled by the contents of the buildings.

Geometrically, the cement floors had large areas and were closely spaced. They intercepted most of the infrared radiation emitted in the voids between them, and they absorbed heat (by conduction) from the slowly moving (“ventilation limited”) layer of hot gases underneath each of them. Concrete conducts heat poorly, but can hold a great deal of it. The metal reinforcing bars within concrete, as well as the metal plate underneath the concrete pad of each WTC Towers floor structure, would tend to even out the temperature distribution gradually.

This process of “preheating the oven” would slowly raise the average temperature in the impact zone while narrowing the range of extremes in temperature. Within half an hour, heat had penetrated to the interior of the concrete, and the temperature everywhere in the impact zone was between 200 C and 700 C, away from sites of active burning.

Thermal Decomposition — “Cracking”

Fire moved through the impact zone by finding new sources of fuel, and burning at a rate limited by the ventilation, which changed over time.

Heat within the impact zone “cracks” plastic into a sequence of decreasingly volatile hydrocarbons, similar to the way heat separates out an array of hydrocarbon fuels in the refining of crude oil. As plastic absorbs heat and begins to decompose, it emits hydrocarbon vapors. These may flare if oxygen is available and their ignition temperatures are reached. Also, plumes of mixed hydrocarbon vapor and oxygen may detonate. So, a random series of small explosions might occur during the course of a large fire.

Plastics not designed for use in high temperature may resemble soft oily tar when heated to 400 C. The oil in turn might release vapors of ethane, ethylene, benzene and methane (there are many hydrocarbons) as the temperature climbs further. All these products might begin to burn as the cracking progresses, because oxygen is present and sources of ignition (hotspots, burning embers, infrared radiation) are nearby. Soot is the solid end result of the sequential volatilization and burning of hydrocarbons from plastic. Well over 90% of the thermal energy released in the WTC Towers came from burning the normal contents of the impact zones.

Hot Aluminum

Aluminum alloys melt at temperatures between 475 C and 640 C, and molten aluminum was observed pouring out of WTC 2 (5). Most of the aluminum in the impact zone was from the fragmented airframe; but many office machines and furniture items can have aluminum parts, as can moldings, fixtures, tubing and window frames. The temperatures in the WTC Towers fires were too low to vaporize aluminum; however, the forces of impact and explosion could have broken some of the aluminum into small granules and powder. Chemical reactions with hydrocarbon or water vapors might have occurred on the surfaces of freshly granulated hot aluminum.

The most likely product of aluminum burning is aluminum oxide (Al2O3, “alumina”). Because of the tight chemical bonding between the two aluminum atoms and three oxygen atoms in alumina, the compound is very stable and quite heat resistant, melting at 2054 C and boiling at about 3000 C. The affinity of aluminum for oxygen is such that with enough heat it can “burn” to alumina when combined with water, releasing hydrogen gas from the water,

2*Al + 3*H2O + heat -> Al2O3 + 3*H2.

Water is introduced into the impact zone through the severed plumbing at the building core, moisture from the outside air, and it is “cracked” out of the gypsum wall panels and to a lesser extent from concrete (the last two are both hydrated solids). Water poured on an aluminum fire can be “fuel to the flame.”

When a mixture of aluminum powder and iron oxide powder is ignited, it burns to iron and aluminum oxide,

Al + Fe2O3 + ignition -> Al2O3 + Fe.

This is thermite. The reaction produces a temperature that can melt steel (above 1500 C, 2800 F). The rate of burning is governed by the pace of heat diffusion from the hot reaction zone into the unheated powder mixture. Granules must absorb sufficient heat to arrive at the ignition temperature of the process. The ignition temperature of a quiescent powder of aluminum is 585 C. The ignition temperatures of a variety of dusts were found to be between 315 C and 900 C, by scientists developing solid rocket motors. Burning thermite is not an accelerating chain reaction (“explosion”), it is a “sparkler.” My favorite reference to thermite is in the early 1950s motion picture, “The Thing.”

Did patches of thermite form naturally, by chance, in the WTC Towers fires? Could there really have been small bits of melted steel in the debris as a result? Could there have been “thermite residues” on pieces of steel dug out of the debris months later? Maybe, but none of this leads to a conspiracy. If the post-mortem “thermite signature” suggested that a mass of thermite comparable to the quantities shown in Table 3 was involved, then further investigation would be reasonable. The first task of such an investigation would be to produce a “chemical kinetics” model of the oxidation of the fragmented aluminum airframe, in some degree of contact to the steel framing, in the hot atmosphere of hydrocarbon fires in the impact zone. Once Nature had been eliminated as a suspect, one could proceed to consider Human Malevolence.

Smoldering Rubble

Nature is endlessly creative. The deeper we explore, the more questions we come to realize.

Steel columns along a building face, heated to between 200 C and 700 C, were increasingly compressed and twisted into a sharpening bend. With increasing load and decreasing strength over the course of an hour or more, the material became unable to rebound elastically, had the load been released. The steel entered the range of plastic deformation, it could still be stretched through a bend, but like taffy it would take on a permanent set. Eventually, it snapped.

Months later, when this section of steel would be dug out of the rubble pile, would the breaks have the fluid look of a drawn out taffy, or perhaps “melted” steel now frozen in time? Or, would these be clean breaks, as edge glass fragments; or perhaps rough, granular breaks as through concrete?

The basements of the WTC Towers included car parks. After the buildings collapsed, it is possible that gasoline fires broke out, adding to the heat of the rubble. We can imagine many of the effects already described, to have occurred in hot pockets within the rubble pile. Water percolating down from that sprayed by the Fire Department might carry air down also, and act as an oxidizing agent.

The tight packing of the debris from the building, and the randomization of its materials would produce a haphazard and porous form of ironcrete aggregate: chunks of steel mixed with broken and pulverized concrete, with dust-, moisture-, and fume-filled gaps. Like a pyramid of barbecue briquettes, the high heat capacity and low thermal conductivity of the rubble pile would efficiently retain its heat.

Did small hunks of steel melt in rubble hot spots that had just the right mix of chemicals and heat? Probably unlikely, but certainly possible.

Pulverized concrete would include that from the impact zone, which may have had part of its water driven off by the heat. If so, such dust would be a desiccating substance (as is Portland cement prior to use; concrete is mixed sand, cement and water). Part of the chronic breathing disorders experienced by many people exposed to the atmosphere at the World Trade Center during and after 9/11/01 may be due to the inhalation of desiccating dust, now lodged in lung tissue.

Did the lingering hydrocarbon vapors and fumes from burning dissolve in water and create acid pools? Did the calcium-, silicon-, aluminum-, and magnesium-oxides of pulverized concrete form salts in pools of water? Did the sulfate from the gypsum wall panels also acidify standing water? Did acids work on metal surfaces over months, to alter their appearance?

In the enormity of each rubble pile, with its massive quantity of stored heat, many effects were possible in small quantities, given time to incubate. It is even possible that in some little puddle buried deep in the rubble, warmed for months in an oven-like enclosure of concrete rocks, bathed in an atmosphere of methane, carbon monoxide, carbon dioxide, and perhaps a touch of oxygen, that DNA was formed.

Endnotes

[1] MANUEL GARCIA, Jr., “The Physics of 9/11,” Nov. 28, 2006, [search in the Counterpunch archives of November, 2006 for this report and its two companions; one on the mechanics of building collapse, and the other an early and not-too-inaccurate speculative analysis of the fire-induced collapse of WTC 7.]

[2] “Executive Summary, Reconstruction of the Fires in the World Trade Center Towers,” NIST NCSTAR 1-5, , (28 September 2006). NIST = National Institute of Standards and Technology, NCSTAR = National Construction Safety Team Advisory Committee. https://www.nist.gov/topics/disaster-failure-studies/world-trade-center-disaster-study

[3] “Fire Structure Interface and Thermal Response of the World Trade Center Towers,” NIST NCSTAR1-5G, (draft supporting technical report G), http://wtc.nist.gov/pubs/NISTNCSTAR1-5GDraft.pdf, (28 September 2006), Chapter 3, page 32 (page 74 of 334 of the electronic PDF file).

[4] 1 m = 3.28 ft;    1 m^2 = 10.8 ft^2;    1 m^3 = 35.3 ft^3;    1 ft = 0.31 m;    1 ft^2 = 0.93 m^2;    1 ft^3 = 0.28 m^3.

[5] “National Institute of Standards and Technology (NIST) Federal Building and Fire Safety Investigation of the World Trade Center Disaster, Answers to Frequently Asked Questions,” (11 September 2006). https://www.nist.gov/topics/disaster-failure-studies/world-trade-center-disaster-study

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This article originally appeared as:

The Thermodynamics of 9/11
28 November 2006
https://www.counterpunch.org/2006/11/28/the-thermodynamics-of-9-11/

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