14 TONS OF EXPLOSIVE TO BRING DOWN EACH WTC TOWER (CHECK IT)
TheTruth
Cloud
[size=14:1442fe43ff] Analysis of Energy Requirements for the Expansion
of the
Dust Cloud following the Collapse of 1 World Trade
Center[/size:1442fe43ff]
[size=14:1442fe43ff]by Jim Hoffman, October 16th, 2003 (Version 3.0)
[/size:1442fe43ff]
[size=16:1442fe43ff][color=blue:1442fe43ff]Abstract[/color:1442fe43ff][/size:1442fe43ff]
This paper uses photographic evidence -- primarily a reference
photograph taken from FEMAs report -- to estimate the volume of the
dust cloud that grew from the collapse of the North Tower at about 30
seconds after the commencement of the collapse. The paper then
estimates the thermal energy required to produce the observed
expansion in the volume of the dust cloud, based on the assumption
that most of the gasses and suspended solids in the cloud originated
from within the building.
The most recent version of the paper identifies two major mechanisms
for the expansion -- thermodynamic expansion of gasses due to
increases in temperature, and expansion due to the vaporization of
water. Both represent vast energy sinks. Whatever the relative
contributions of these mechanisms to the expansion, the required
energy inputs far exceeds the energy available in the form of the
gravitational potential energy due to the towers elevated mass.
Previous versions of the paper did not consider expansion due to water
vaporization, and considered only thermodynamic expansion of gasses
present in the building at the time of collapse. That required
average dust cloud temperatures of around 1000 K, a feature several
people found implausible. The addition of the heat of water
vaporization to the analysis changes the picture dramatically. The
heat energy requirements are similar, but the temperatures need not
have been anywhere near 1000 K, since the phase change of water to
steam occurs at 100 C.
The paper shows a large disparity between the energy required to
produce the observed expansion of the dust cloud and that available
from the conversion of all the towers gravitational potential energy
to heat. It does not consider the possible energy source of the
unlikely rapid combustion of the towers contents during its collapse,
but even the energy available from consuming all of the oxygen in the
tower to burn hydrocarbons is far short of the estimated size of the
energy sink of dust cloud expansion.
On September 11th, both of the Twin Towers disintegrated into vast
clouds of concrete and other materials, which blanketed Lower
Manhattan. This paper shows that the energy required to produce the
expansion of the dust cloud observed immediately following the
collapse of 1 World Trade Center (the North Tower) was much greater
than the gravitational energy available from its elevated mass. It
uses only basic physics.
[size=16:1442fe43ff][color=blue:1442fe43ff]Introduction[/color:1442fe43ff][/size:1442fe43ff]
Vast amounts of energy were released during the collapse of each of
the Twin Towers in Lower Manhattan on September 11th, 2001. The
accepted source of this energy was the gravitational potential energy
of the towers, which was far greater than the energy released by the
fires that preceded the collapses. The magnitude of that source
cannot be determined with much precision thanks to the secrecy
surrounding details of the towers construction. However, FEMAs
Building Performance Assessment Report gives an estimate
(Ref.
(1)): "Construction of WTC 1 resulted in the storage of more
than 4 x 10^11 joules of potential energy over the 1,368-foot height
of the structure. "That is equal to about 111,000 KWH (kilowatt
hours) per tower.
Of the many identifiable energy sinks in the collapses, one of the
only ones that has been subjected to quantitative analysis is the
thorough pulverization of the concrete in the towers. It is well
documented that nearly all of the non-metallic constituents of the
towers were pulverized into fine powder. The largest of these
constituents by weight was the concrete that constituted the floor
slabs of the towers. Jerry Russell estimated that the amount of
energy required to crush concrete to 60 micron powder is about 1.5
KWH/ton. (Ref. (2)).
That paper incorrectly assumes there were 600,000 tons of concrete in
each tower, but Russell later provided a more accurate estimate of
90,000 tons of concrete per tower, based on FEMAs description of the
towers construction. That estimate implies the energy sink of
concrete pulverization was on the order of 135,000 KWH per tower,
which is already larger than the energy source of gravitational
energy. However, the size of this sink is critically dependent on the
fineness of the concrete powder, and on mechanical characteristics of
the lightweight concrete thought to have been used in the towers.
Available statistics about particle sizes of the dust, such as the
study by Paul J. Lioy, et al
([url=http://ehpnet1.niehs.nih.gov/docs/2002/110p703-714lioy/abstract.html]Ref.
(3)[/url]), characterize particle sizes of aggregate dust samples, not
of its constituents, such as concrete, fiberglass, hydrocarbon soot,
etc. Based on diverse evidence, 60 microns would appear to be a high
estimate for average concrete particle size, suggesting 135,000 KWH
is a conservative estimate for the magnitude of the sink.
A second energy sink, that has apparently been overlooked, was many
times the magnitude of the gravitational energy: the energy needed to
expand the dust clouds to several times the volume of each tower
within 30 seconds of the onset of their collapses. Note that the
contents of the dust clouds had to come from building constituents --
gases and materials inside of or intrinsic to the building -- modulo
any mixing with outside air. Given that the Twin Towers dust clouds
behaved like pyroclastic flows, with distinct boundaries and rapidly
expanding frontiers (averaging perhaps 35 feet/second on the ground
for the first 30 seconds), it is doubtful that mixing with ambient
air accounted for a significant fraction of their volume. Therefore
the dust clouds expansion must have been primarily due to an
expansion of building constituents. Possible sources of expansion
include:
[*:1442fe43ff]thermodynamic expansion of gases
[*:1442fe43ff]vaporization of liquids and solids
[*:1442fe43ff]chemical reactions resulting in a net increase in
gaseous phase molecules [color=red:1442fe43ff]That is
explosives.[/color:1442fe43ff]
The evidence does not support the idea that chemical reactions in the
dust cloud liberated vast quantities of gases.
[color=red:1442fe43ff]Actually, the evidence does support the use of
explosives to collapse the towers
([url=http://members.fortunecity.com/911/wtc/tower-explosions.htm]Ref.
(4)[/url]).[/color:1442fe43ff]
That leaves increases in gas temperatures and vaporization of solids
and liquids, primarily water, to drive the expansion.
How much heat energy was involved in expanding the dust clouds? To
calculate the energy we need to answer three questions:
[list:1442fe43ff]
[*:1442fe43ff]What was the volume of the dust clouds from a collapse
at some time soon after it started (before the clouds began to
diffuse)?
[*:1442fe43ff]How did the mixing of the dust cloud with ambient air
contribute to its size, and how can this be factored out to obtain
the volume occupied by gases and suspended materials originally
inside the building?
[*:1442fe43ff]What is the ratio of that volume to the volume of the
intact building?
[*:1442fe43ff]How much heat energy was required to produce that ratio
of expansion?
[/list:u:1442fe43ff]
Since I have better photographs for North Tower dust, I did the
calculation for it.
[size=16:1442fe43ff][color=blue:1442fe43ff]1. Quantifying Dust Cloud
Volume[/color:1442fe43ff][/size:1442fe43ff]
To answer question 1, I made estimates based on photographs taken at
approximately 30 seconds after the onset of the collapse. The photo
in Figure 1 appears to have been taken around 30 seconds after the
initiation of the collapse of the North Tower. The fact that the
spire is visible directly behind Building 7 indicates the photo was
not taken later than the 30 seconds, since video records show that
the spire started to collapse at the around 29 seconds. In this
photograph, as in other ones taken around that time, the dust clouds
still have distinct boundaries.
http://thunderbay.indymedia.org/uploads/wtc-1-dust.jpg
Figure 1. Photograph from Chapter 5 of FEMAs Building
Performance Assessment Report
I used landmarks in this photo to make several approximate
measurements of the frontier of the dust cloud. The following table
lists some of them. Measurements are in feet. The first column lists
heights above the street, and the second lists distances from the
vertical axis of the North Tower.
[b:1442fe43ff]Label[/b:1442fe43ff]
[color=blue:1442fe43ff][b:1442fe43ff]Height[/b:1442fe43ff][/color:1442fe43ff]
[b:1442fe43ff]Distance[/b:1442fe43ff]
[color=red:1442fe43ff][b:1442fe43ff]Description[/b:1442fe43ff][/color:1442fe43ff]
3 [color=blue:1442fe43ff]230[/color:1442fe43ff] 1011
[color=red:1442fe43ff]West corner of 45 Park
Place[/color:1442fe43ff]
5 [color=blue:1442fe43ff]228[/color:1442fe43ff] 729
[color=red:1442fe43ff]Top of south corner of building with stepped
roof[/color:1442fe43ff]
6 [color=blue:1442fe43ff]204[/color:1442fe43ff] 658
[color=red:1442fe43ff]East corner of Building 7, 30 stories below
top[/color:1442fe43ff]
7 [color=blue:1442fe43ff]600[/color:1442fe43ff] 776
[color=red:1442fe43ff]Upwell towering over southeast end of Post
Office[/color:1442fe43ff]
8 [color=blue:1442fe43ff]700[/color:1442fe43ff] ?
[color=red:1442fe43ff]Upwell slightly higher than the top of Building
7[/color:1442fe43ff]
11 [color=blue:1442fe43ff]190[/color:1442fe43ff] 870
[color=red:1442fe43ff]Top of west corner of 22 Cortland St
tower[/color:1442fe43ff]
12 [color=blue:1442fe43ff]508[/color:1442fe43ff] 588
[color=red:1442fe43ff]8 stories below top of face of WFC
3[/color:1442fe43ff]
13 [color=blue:1442fe43ff]498[/color:1442fe43ff] 517
[color=red:1442fe43ff]3 stories below top of upper face of WFC
2[/color:1442fe43ff]
To approximate the volume I used a cylinder, coaxial with the vertical
axis of the North Tower, with a radius of 800 feet, and a height of
200 feet. All the above reference points lie outside of this volume.
Although the cylinder does not lie entirely within the dust cloud,
there are large parts of the cloud outside of it, such as the 700
foot high upwelling column south of Building 7. The cylinder has a
volume of:
pi x (800 feet)^2 x 200 feet = 402,000,000 feet^3.
I subtract about a quarter for volume occupied by other buildings,
giving 300,000,000 feet^3.
[size=16:1442fe43ff][color=blue:1442fe43ff]2. Factoring out Mixing and
Diffusion[/color:1442fe43ff][/size:1442fe43ff]
To accurately answer question 2 would require detailed knowledge of
the fluid dynamics involved. However it does appear that for at least
a minute, the dust cloud behaved as a separate fluid from the ambient
air, maintaining a distinct boundary. There are several pieces of
evidence that support this:
[list:1442fe43ff]
[*:1442fe43ff]The WTC dust clouds inexorably advanced down streets at
around 25 MPH. This is far faster than can be explained by mixing and
diffusion.
[*:1442fe43ff]As the dust clouds advanced outward, features on their
frontiers evolved relatively slowly compared to the clouds rates of
advance. This indicates that that clouds were expanding from within
and that if surface turbulence was incorporating ambient air, its
contribution to expansion was minor.
[*:1442fe43ff]The top surface of the clouds looked like the surface of
a boiling viscous liquid - churning but not mixing with the air above.
Sinking portions of the clouds were replaced by clear air, not a
mixture of the cloud and air.
[*:1442fe43ff]The dust clouds maintained distinct interfaces for well
over a minute. Mixing and diffusion would have produced diffuse
interfaces.
[*:1442fe43ff]There are reports of people being picked up and carried
distances by the South Tower dust cloud, which felt solid. New York
Daily News photographer David Handschuh recalled:
Instinctively I lifted the camera up, and something took over that
probably saved my life. And that was (an urge) to run rather than
take pictures. I got down to the end of the block and turned the
corner when a wave -- a hot, solid, black wave of heat threw me down
the block. It literally picked me up off my feet and I wound up about
a block away.
[/list:u:1442fe43ff]
Initially the dust clouds must have been much heavier than air, given
the mass of the concrete they carried and the distances they
transported it. As time went on the cloud became more diffuse, but
all of the photographs that can be verified as being within the first
minute show opaque clouds with distinct boundaries, indicating the
dominant mode of growth was expansion, not mixing or diffusion. It
seems reasonable to assume that mixing with ambient air did not
account for a significant fraction of the expansion in the volume of
the dust cloud by 30 seconds of the start of the North Tower
collapse. Nevertheless, I reduce the estimate of the dust cloud
volume of building origin to 200,000,000 feet^3, imagining that a
third of the growth may have been due to assimilation of ambient
air.
[size=16:1442fe43ff][color=blue:1442fe43ff]3. Computing the Expansion
Ratio[/color:1442fe43ff][/size:1442fe43ff]
The answer to question 3 is easy. The volume of a tower, with its 207
foot width and 1368 foot height, is:
1368 feet x 207 feet x 207 feet = 58,617,432 feet^3.
So the ratio of the expanded gasses and suspended materials from the
tower to the original volume of the tower is:
200,000,000 feet^3 / 58,617,432 feet^3 = 3.41.
[size=16:1442fe43ff][color=blue:1442fe43ff]4. Computing the Required
Heat Input[/color:1442fe43ff][/size:1442fe43ff]
Above I identified two energy sinks that could have driven expansion
of the dust cloud: thermodynamic expansion of gases, and vaporization
of liquids and solids. Since most constituents and contents of the
building other than water would require very high temperatures to
vaporize, I consider only the vaporization of water in evaluating the
second sink.
It is clearly not possible to determine with any precision the
relative contributions of these two sinks to the expansion of the
dust cloud. If the cloud remained uniform in temperature and density
for the first 30 seconds, then the expansion would consist of three
distinct phases:
[list:1442fe43ff][*:1442fe43ff]The temperature would increase to 100
C, accompanied by thermodynamic expansion.
[*:1442fe43ff]The temperature would remain at 100 C until all of the
water was vaporized.
[*:1442fe43ff]The temperature would increase above 100 C, again
accompanied by thermodynamic expansion.
[/list:u:1442fe43ff]
Since such uniform conditions were not present, I will first treat the
two energy sinks separately, and will compute the energy requirements
for each if it alone were responsible for the expansion.
[size=14:1442fe43ff][color=#7519FF:1442fe43ff]4.1. The Thermodynamic
Expansion Sink[/color:1442fe43ff][/size:1442fe43ff]
The ideal gas law can be used to compute a lower bound for the amount
of heat energy required to induce the observed expansion of the dust
cloud, assuming that the expansion was entirely due to thermodynamic
expansion. That law states that the product of the volume and
pressure of a parcel of a gas is proportional to absolute
temperature. It is written [b:1442fe43ff]PV = nRT[/b:1442fe43ff],
where:
[b:1442fe43ff]P[/b:1442fe43ff] = pressure
[b:1442fe43ff]V[/b:1442fe43ff] = volume
[b:1442fe43ff]T[/b:1442fe43ff] = absolute temperature
[b:1442fe43ff]n[/b:1442fe43ff] = molar quantity
[b:1442fe43ff]R[/b:1442fe43ff] = constant
Absolute temperature is expressed in Kelvin (K), which is Celsius +
273. Applied to the tower collapse, the equation holds that the ratio
of volumes of gasses from the building before and after expansion is
roughly equal to the ratio of temperatures of the gasses before and
after heating. That allows us to compute the minimum energy needed to
achieve a given expansion ratio knowing only the thermal mass of the
gasses and their average temperature before the collapse.
I say that the ideal gas law allows the computation of only the lower
bound of the required energy input due to the following four
factors.
[list:1442fe43ff][*:1442fe43ff]The finite size of molecules leads to a
slight departure from the ideal gas law wherein the expansion of a
parcel of gas leads to a decrease in its temperature. This means that
slightly more heat energy is needed to achieve a given expansion ratio
than is predicted by the ideal gas law.
[*:1442fe43ff]The dust cloud at the time of the photograph used to
estimate its volume had not finished expanding. Videos show that it
continued to expand well after the 1 minute mark.
[*:1442fe43ff]The suspended dust in the cloud had many times the mass
of the gasses. This increased the energy needed to expand the dust
cloud since it takes energy to lift and accelerate mass.
[*:1442fe43ff]The suspended dust in the cloud had many times the
thermal mass of the gasses. Increasing in temperature of the dust
cloud to a level needed to induce the observed expansion entailed
raising the temperature of the gasses and suspended solids by similar
amounts. Since the solids had many times the thermal capacity of the
gasses, this multiplied the energy requirements.
[/list:u:1442fe43ff]
In this paper I examine only the fourth factor. Before considering its
effect on energy requirements, I first consider the energy
requirements of heating only the gasses in the clouds to the level
needed to achieve the observed expansion.
According to the ideal gas law, expanding the gasses 3.4-fold requires
raising their absolute temperature by the same ratio. If we assume the
tower was at 300 degrees K before the collapse, then the target
temperature would be 1020 degrees K, an increase of 720 degrees.
[color=red:1442fe43ff]Of course, this begs the question: What was the
source of energy that heated the debris cloud from 298 K (25 C) to
1020 degrees K? [/color:1442fe43ff]
Given a density of 36 g/foot^3 for air, the tower held about
2,000,000,000 g of air. Air has a specific heat of 0.24 (relative to
1 for water), so one calorie will raise one g of air 1 / 0.24 = 4.16
degrees. To raise 2,000,000,000 g by 720 degrees requires:
2,000,000,000 g x 720 degrees x 0.24 = 345,600,000,000 calories =
399,500 KWH
To evaluate the energy requirements of the fourth factor, it is
necessary to consider the composition of the dust cloud. The cloud
was a suspension of fine particles of concrete and other solids in
gasses consisting mostly of air. Since concrete was the dominant
solid, I will ignore the others, which included glass, gypsum,
asbestos, and various hydrocarbons. The small size of the particles,
being in the 10-60 micron range, would assure rapid equalization
between their temperature and that of the embedding air. Therefore
any heat source acting to raise the temperature of the air would have
to raise the temperature of the suspended concrete by the same amount.
Assuming all 90,000,000,000 g of concrete was raised 720 degrees (300
K to 1020 K), the necessary heat, given a specific heat of concrete
of 0.15 is:
90,000,000,000 g x 720 degrees x 0.15 = 9,720,000,000,000 calories =
11,300,000 KWH.
If we assume that the water vaporization sink absorbed all available
energy once temperatures reached waters boiling point, we can compute
the size of the heat sink of thermodynamic expansion that was in play
up to 100 C, or 373 K:
2,000,000,000 g x 73 degrees x 0.24 = 35,040,000,000 calories = 40,744
KWH
The associated sink of heating the suspended solids to this
temperature would be:
90,000,000,000 g x 73 degrees x 0.15 = 985,500,000,000 calories =
1,145,000 KWH.
[size=14:1442fe43ff][color=#7519FF:1442fe43ff]4.2. The Water
Vaporization Sink[/color:1442fe43ff][/size:1442fe43ff]
At 100 C at sea-level, water expands by a factor of 1680 when
converted to steam.
[color=red:1442fe43ff]Of course, this begs many questions, prominent
being:[/color:1442fe43ff]
[list:1442fe43ff]
[*:1442fe43ff]What was the source of energy that heated the building
to 100 degrees C?
[*:1442fe43ff]Was there enough time for the building to reach 100
degrees C before the collapses?
[*:1442fe43ff]How much of the water in the concrete slab is able to
escape as the slab is heated to 100 degrees C?
[/list:u:1442fe43ff]
Hence it is reasonable to expect that water in the building accounted
for a significant part of the expansion.
[color=red:1442fe43ff]This is only reasonable if the concrete has
already been pulverized, and if this is so, begs the question: What
pulverized it?[/color:1442fe43ff]
How much energy would be required to expand the volume of the cloud by
the 3.41 ratio if water vaporization were entirely responsible for the
expansion? Since water vaporization involves the introduction of
volumes of steam from comparatively negligible volumes of water, I
assume that all the incremental volume was occupied by steam. The
estimated 3.41 expansion ratio means that the incremental volume
was:
200,000,000 feet^3 - 58,617,000 feet^3 = 141,383,000 feet^3 =
4,003,542,000 liters
Given the 1680 to 1 ratio between the volume steam and water,
2,383,000 liters of water would have been required. The heat of
vaporization of water is 540 calories/gram at 100 C. Therefore the
heat energy required to produce the expansion is:
2,383,000,000 g x 540 = 1,286,820,000,000 calories = 1,496,000 KWH
Was there enough water in the building for this sink to be anywhere
near this large? That is a matter of great uncertainty. Even
well-cured concrete has a significant moisture content. Assuming that
the estimated 90,000 tons of concrete in the tower was 1 percent water
by weight, that would have provided 900 tons of water or about 900,000
liters -- well short of the 2,383,000 liter estimate above.
[color=red:1442fe43ff]This is somewhat misleading. Well-cured concrete
is indeed about 1 percent FREE water, but concrete is also about 7-20
percent chemically bound water. The free water evaporates from
concrete at 100 - 150 C, whilst chemically bound water remains until
temperatures of 450 C
([url=http://members.fortunecity.com/911/fire/SLamont.htm]Ref.
(5)[/url]).
So it turns out that there is more than enough water to account for
the expansion (as long as the concrete reaches temperatures of about
450 C).[/color:1442fe43ff]
However, there is a large amount of uncertainty in the water content
of the concrete, which, like the rest of the remains of the disaster
was apparently disposed of with little or no examination. Moreover
there were other sources of water in the building, such as the
plumbing system, which could have accounted for tens of thousands of
liters, and, gruesomely, people. The thousand victims never
identified could have accounted for about 30,000 liters of water.
[size=14:1442fe43ff][color=#7519FF:1442fe43ff]4.3. Which Energy Sink
Was Dominant?[/color:1442fe43ff][/size:1442fe43ff]
Both thermodynamic expansion and water vaporization have the capacity
to produce vast expansion in gas volume given sufficient heat.
[color=red:1442fe43ff]Explosives would produce vast expansions of gas
on detonation.
Explosives would produce vast quantities of concrete particles.
Explosives would also produce vast quantities of heat.
Vast quantities of heat applied to the concrete particles might cause
the release of some of the chemically bound water, which would
contribute to a breakup the particles, reducing them to a fine
dust.[/color:1442fe43ff]
Two major difference in the features of these sinks may help in
understanding the relative contributions of each. First,
thermodynamic expansion to the observed ratio requires very high
temperatures, whereas vaporization-driven expansion occurs at a
constant temperature of 100 C. Second, vaporization-driven expansion
would be limited by the available supply of water.
If all the expansion was due to thermodynamic expansion, it would
require that the dust cloud was heated to an average temperature of
about 1020 K. Certainly the temperatures of the cloud near the ground
were no-where near that high. Eyewitness reports show that the clouds
ground-level temperatures more than a few hundred feet away from its
center were humanly survivable. Most of these reports are from the
South Tower collapse, and it is unclear how similar the dust cloud
temperatures following the two collapses were. Although serious fires
raged in Buildings 4, 5, and 6, other nearby buildings that suffered
extensive window breakage from the tower collapses, such as the
Bankers Trust Building, and Word Financial Center Buildings 1, 2, and
3, did not experience fires. Digital photographs and videos show a
bright afterglow with a locus near the center of the cloud,
commencing around 17 seconds after the onset of the North Towers
collapse. Once the afterglow started, the cloud developed large
upwelling columns towering to over 600 feet, and the previously gray
cloud appeared to glow with a reddish hue. This suggests that at
least the upper and central regions of the North Tower cloud reached
very high temperatures, but the evidence is insufficient to draw even
general quantitative conclusions about the ranges and distributions of
temperatures.
If enough water was present for vaporization to drive most of the
expansion, temperatures in much of the cloud would have remained
around 100 C until most of the water had vaporized. Thermodynamic
expansion would occur in regions with liquid phase water until 100 C
was reached, and again after the water was vaporized.
To the extent that thermodynamic expansion was the dominant factor
driving the expansion, the distribution of concrete dust in the
cloud, and its relationship to the temperature distribution in the
cloud, would greatly affect the total energy requirements. Less
energy would be required if the hotter portions of the cloud had a
lower density of dust. The density was probably greater toward the
central portions of the cloud, which also seem to have experienced
the most heating. On the other hand, much of the dust may have
settled out by the 30 second mark. The violent churning of the cloud,
and the opaque appearance of its frontier, suggest that most of the
dust had not settled that early.
[size=16:1442fe43ff][color=blue:1442fe43ff]The Unexplored Option --
Explosives.[/color:1442fe43ff][/size:1442fe43ff]
[color=red:1442fe43ff]We will consider the explosive amatol which is a
mixture of trinitrotoluene (TNT) and ammonium nitrate (AN).
Trinitrotoluene (left) has the chemical composition C7H5(NO2)3 and
ammonium nitrate (right) has the chemical composition NH4NO3.
We choose the TNT to AN molar ratio in the amatol mixture to be 4 :
42.
This translates to a 4 x 227 : 42 x 80 = 908 : 3360 = 21 : 79 ratio by
weight.
In this case the explosion proceeds according to the equation:
4 C7H5(NO2)3 + 42 NH4NO3 ==> 28 CO2 + 94 H2O + 48 N2
From the equation we see that 4 moles of TNT and 42 moles of AN
produces 28 + 94 + 48 = 170 moles of gaseous product.
At standard temperature and pressure, 170 moles of gas occupies 170 x
22.4 = 3,808 liters. This is the volume that the explosion products
would occupy if, after the explosion, they were cooled to 25 C (with
the assumption that the water remains a vapor). In order to calculate
the volume of the hot gaseous products generated by the explosion, we
initially need to know the amount of heat released by the explosion
of 4 moles of TNT and 42 moles of AN. We also need to know the amount
of heat required to raise each of the gases, by one degree K. That is,
we need to know the enthalpy of explosion
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_explosion and the heat capacities C_p (also known as specific heats)
of each of the gases.
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_explosion = - (4
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_solid(TNT) + 21
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_solid(AN)) + (28
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_gas(CO_2) + 94
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_gas(H_2O) + 48
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_gas(N_2))
= - (4(-60) + 21(-365.5)) + (28(-393.5) + 94(-242) + 48(0.00))
= 240 + 7,675.5 - 11,018 - 22,748
= - 25,850 kJ per 4 moles of TNT and 42 moles of AN.
Here we have used the following facts:
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_gas(H2O) = -242 kJ/mol
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_gas(CO) = -110.5 kJ/mol
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_gas(CO2) = -393.5 kJ/mol
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_solid(TNT) = -60 kJ/mol
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]
H_solid(AN) = -365.5 kJ/mol
The heat capacities C_p for the gases involved are:
C_p^gas (N2) = 28.87 J/mol*K
C_p^gas (O2) = 28.91 J/mol*K
C_p^gas (H2O) = 30.43 J/mol*K
C_p^gas (CO2) = 37.12 J/mol*K
Since the heat capacities are all approximately 30 J/mol*K, we will
assume this value for all the gases, i.e., we assume:
C_p^gas (all relevant gases) = 30 J/mol*K
So, by assumption, 30 joules of energy will raise the temperature of
one mole of the gaseous product (of the explosion) by 1 degree K.
Summarizing from earlier, we have that 4 moles of TNT and 42 moles of
AN,
[list:1442fe43ff]
[*:1442fe43ff]produces 170 moles of gaseous product and
[*:1442fe43ff]liberates 25,850 kJ of energy.
[/list:u:1442fe43ff]
We will assume that the original 170 moles of explosion products mix
with N moles of air.
This 170 + N mole mixture of gases is initially assumed to be at the
temperature T_0 = 298 degrees K (25 C).
This 170 + N mole mixture of gases has an initial volume of V_0 = 22.4
(170 + N) liters.
We calculate the increase in temperature
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]T
of this 170 + N moles of gases after being heated by the 25,850 kJ of
energy released by the explosion of the 4 moles of TNT and 42 moles
of AN.
Now 30 joules raises the temperature of one mole of the gases by 1
degree K.
Hence, 25,850,000 joules raises the temperature of the 170 + N moles
by
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]T
= 25,850,000/(30 x (170 + N)).
We now calculate the volume V_1 of this 170 + N moles of gas after
being heated by the explosion to the temperature
T_1 = T_0 +
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]T
From the ideal gas law we have that V_1 / V_0 = T_1 / T_0.
Rearranging we obtain
V_1 = V_0 (T_1 / T_0) = V_0 (T_0 +
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]T)
/ T_0 = V_0 + V_0
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]T
/ T_0. On substituting we obtain
V_1 = V_0 + 22.4 x (170 + N) x 25,850,000 / (30 x (170 + N) x 298) =
V_0 + 22.4 x 25,850,000 / (30 x 298) = V_0 + 64,770 liters.
Hence, the increase in volume of the mixture of gases
[img:1442fe43ff]http://thunderbay.indymedia.org/uploads/delta-red.gif[/img:1442fe43ff]V
= V_1 - V_0 = 64,770 liters.
So, summing up, the explosion of 4 moles of TNT and 42 moles of AN
produce 64,770 + 22.4 x 170 = 64,770 + 3,808 = 68,578 liters of hot
gases.
That is, the explosion of 4,268 grams of amatol produces 68,578 liters
of hot gases.
That is, the explosion of one kilogram of amatol produces 68,578 x
1,000 / 4,268 = 16,068 liters of hot gaseous product.
Hence the 200,000,000 liter expansion calculated by Hoffman can be
explained by the detonation of
200,000,000/16,068 = 12,447 kg = 12.5 tonnes (14 tons) of the high
explosive amatol.[/color:1442fe43ff]
[size=16:1442fe43ff][color=blue:1442fe43ff]Summary[/color:1442fe43ff][/size:1442fe43ff]
[color=red:1442fe43ff]The 200,000,000 liter expansion calculated by
Hoffman can be explained by the detonation of 12.5 tonnes (14 tons)
of the high explosive amatol.[/color:1442fe43ff]
The dominant energy source assumed to be in play during the leveling
of each of the Twin Towers was the gravitational energy due to its
elevated mass, whereas the energy sinks included the pulverization of
it's concrete, the vaporization of water, and the heating of the
concrete and air in the ensuing dust cloud. Estimates for these
energies are:
[color=red:1442fe43ff][b:1442fe43ff]Energy,
KWH[/b:1442fe43ff][/color:1442fe43ff]
[color=blue:1442fe43ff][b:1442fe43ff]Source or
Sink[/b:1442fe43ff][/color:1442fe43ff]
[color=red:1442fe43ff] + 111,000 [/color:1442fe43ff]falling of mass
(1.97 x 10^11 g falling average of 207 m)[/color]
[color=red:1442fe43ff] - 135,000 [/color:1442fe43ff]crushing of
concrete (9 x 10^10 g to 60 micron powder)[/color]
[color=blue:1442fe43ff][b:1442fe43ff]Ignoring Water
Vaporization[/b:1442fe43ff][/color:1442fe43ff]
[color=red:1442fe43ff] - 400,000[/color:1442fe43ff] heating of gasses
(2 x 10^9 g air from 300 to 1020 K)
[color=red:1442fe43ff] - 11,300,000[/color:1442fe43ff] heating of
suspended concrete (9 x 10^10 g from 300 to 1020 K)
[color=blue:1442fe43ff][b:1442fe43ff]Assuming Water Vaporization Sink
was not Supply-Limited[/b:1442fe43ff][/color:1442fe43ff]
[color=red:1442fe43ff] - 1,496,000 [/color:1442fe43ff]vaporization of
water (2.389 g water)
[color=red:1442fe43ff] - 41,000 [/color:1442fe43ff]heating of gasses
(2 x 10^9 g air from 300 to 373 K)
[color=red:1442fe43ff] - 1,145,000 [/color:1442fe43ff]heating of
suspended concrete (9 x 10^10 g from 300 to 373 K)
The imbalance between sources and sinks is striking, no matter the
relative shares of the thermodynamic and water vaporization sinks in
accounting for the expansion. Moreover, it is very difficult to
imagine how the gravitational energy released by falling mass could
have contributed much to any of the sinks, since the vast majority of
the towers mass landed outside its footprint. The quantity for the
crushing of concrete appears to be conservative since some reports
indicate the average particle size was closer to 10 microns. The
quantity for the heating of suspended concrete has a large amount of
uncertainty, but the energy imbalances remain huge even when it is
ignored entirely. All of these energy sink estimates are conservative
in several respects.
[list:1442fe43ff]
[*:1442fe43ff]It is based on an estimate of dust cloud volume at a
time long before the cloud stopped growing.
[*:1442fe43ff]It uses a liberal estimate of the contribution of mixing
to the volume.
[*:1442fe43ff]It ignores thermal losses due to radiation.
[/list:u:1442fe43ff]
The calculation also ignores the role the mass of the suspended
materials in impeding the expansion of cloud and thereby increasing
the required energy.
[size=16:1442fe43ff][color=blue:1442fe43ff]Conclusion[/color:1442fe43ff][/size:1442fe43ff]
The amount of energy required to expand the North Towers dust cloud
was many times the entire potential energy of the towers elevated
mass due to gravity. The over 10-fold disparity between the most
conservative estimate and the gravitational energy is not easily
dismissed as reflecting uncertainties in quantitative assessments.
The official explanation that the Twin Tower collapses were
gravity-driven events appears insufficient to account for the
documented energy flows.
[color=red:1442fe43ff]However, the use of explosives explains all the
observed facts, and is thus probably the correct
explanation.[/color:1442fe43ff]
[size=16:1442fe43ff][color=blue:1442fe43ff]References[/color:1442fe43ff][/size:1442fe43ff]
[list:1442fe43ff]
[*:1442fe43ff][url=http://members.fortunecity.com/911/wtc/WTC_ch1.htm]http://members.fortunecity.com/911/wtc/WTC_ch1.htm[/url]
[*:1442fe43ff][url=http://www.911-strike.com/powder.htm]http://www.911-strike.com/powder.htm[/url]
[*:1442fe43ff][url=http://ehpnet1.niehs.nih.gov/docs/2002/110p703-714lioy/abstract.html]http://ehpnet1.niehs.nih.gov/docs/2002/110p703-714lioy/abstract.html[/url]
[*:1442fe43ff][url=http://members.fortunecity.com/911/wtc/tower-explosions.htm]http://members.fortunecity.com/911/wtc/tower-explosions.htm[/url]
[*:1442fe43ff][url=http://members.fortunecity.com/911/fire/SLamont.htm#3.12.2]http://members.fortunecity.com/911/fire/SLamont.htm[/url]
[/list:u:1442fe43ff]
[size=16:1442fe43ff][color=blue:1442fe43ff]Revision
History[/color:1442fe43ff][/size:1442fe43ff]
The paper is now in its third version. A complete version history is
archived here.
[list:1442fe43ff]
[*:1442fe43ff][url=http://911research.wtc7.net/papers/dustvolume/volumev1.html]Version
1[/url] - released June 13, 2003
[*:1442fe43ff][url=http://911research.wtc7.net/papers/dustvolume/volumev2.html]Version
2[/url] - released July 23, 2003
[*:1442fe43ff][url=http://911research.wtc7.net/papers/dustvolume/volumev3.html]Version
3[/url] - released October 16, 2003
[/list:u:1442fe43ff]
Version 2 adopts much smaller estimates of concrete and total building
mass, and refines the argument that mixing could not have accounted
for much of the expansion. Version 3 considers a source of expansion
ignored in the earlier versions -- the vaporization of water.
[size=16:1442fe43ff][color=blue:1442fe43ff]Acknowledgements[/color:1442fe43ff][/size:1442fe43ff]
I wish to thank Jerry Russell, proprietor of
[url=http://www.911-strike.com]www.911-strike.com[/url], for his work
on the physics of the World Trade Center collapses, work which was
invaluable in the development of my thermodynamics analysis.
[color=red:1442fe43ff]This article by J. Hoffman is a deliberate
attempt to divert your attention from the fact that explosives were
used to bring down the WTC towers. By presenting a possible
explanation for the debris cloud without considering explosives, he
is implicitly stating that he, as an expert in the field, does not
consider explosives an option, so why should you? He is deliberately
pointing you in the wrong direction.
As for the web-site http://physics911.org. It is generally of poor
quality, is full of misinformation, and has very few contributors. It
is clearly a site designed to miss-direct and cover-up for the
official media/government conspiracy theory.[/color:1442fe43ff]
[color=blue:1442fe43ff]"The best way to control the opposition is to
lead it ourselves."[/color:1442fe43ff] V. I. Lenin.
[color=red:1442fe43ff]The comment in red has been added to the
original article.[/color:1442fe43ff]
[url=http://physics911.org/net/modules/news/article.php?storyid=12]http://physics911.org/net/modules/news/article.php?storyid=12[/url]
[url]http://members.fortunecity.com/911/[/url]
[url]http://911review.org/Wget/members.fortunecity.com/911/[/url]
[url]http://guardian.150m.com[/url]
[url]http://guardian.250free.com[/url]
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