Amanda Angelika wrote:

A gas cooker flame is around 800C. These flames regularly come into
contact with Steel, Copper and aluminium cookware for sustained
periods without having any adverse affect on the metal at all.

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[ ... ] Do you leave metal pots on a gas hob
empty and unattended? Do you know what happens when you do?
If left uhnattended long enough, the non-ferrous pots melt. the
cast iron, and stainless lose their temper, and can easily get
distorted.

Your analogy is flawed. when a pot is placed on a cook top, it
generally has something in it, like a liquid, or something that has
quite a bit of liquid in it, for instance, vegetables. Water absorbs
great amounts of heat, and when it begins to boil, the heat
disipates. Same with anything else being cooked. The heat is first
absorbed, then it disipates. Usually in the form of steam.

If the pots are allowed to cook themselves dry, there will be an
effect. Try it for yourself.

That's due to lack of conductivity. The steel in the WTCs would have been a
very good conductor of heat since it was attached to the ground.

The ground does not make for a very good heat sink. The thermal
conductivity of concrete or soil is very much lower (25 to 100 times)
than that of steel.

http://www.learn.londonmet.ac.uk/packages/clear/thermal/buildings/building_fabric/properties/conductivity.html

But that is hardly relevant. The heat from the fire woudn't reach the
ground at nearly high enough a rate. Computer simulations of the
WTC fire take into account all the relevant thermal properties of the
materials involved (concrete slabs, insulation, etc.) and the exact
geometry of the steel structure, and detailed fire dynamics.
Individual beams still reach 700C-800C at places.

http://wtc.nist.gov/NISTNCSTAR1-6D.pdf

Heat is conducted along beams at a rate that it proportional
to the temperature gradient (temperature differential per length
unit), to the beam's cross section, and to the thermal conductivity
of the material. So, if the same temperature differential exists
across a beam twice as long, the flow rate of heat is halved.

Consider a column with a cross section of 100cm^2 and
a thermal conductivity (typical for steel) of 50W/mK
(50Watt/(meter.Kelvin)). Let suppose that fire heats
one segment of the beam at a rate of 100W. That is,
lets put thermal energy in the beam at the rate
produced by a 100W light bulb. Let us suppose that
the beam only has to move this heat 15meter away
from the fire with a constant gradient guaranteeing
steady state (the same heat flow across the whole
length of the beam.) What must the temperature
differential be?

Temp. differential = (100W * 15m) / ((50W/mK) * 0.01m)

And that is 3000K or 3000 degree C.

This means that if the only escape for heat from the
beam is thermal conduction along its length towards
a perfect heat sink at the other end, then heating it
with a mere 100W light bulb will bring the first end
to 3000C eventually.

So, the "thermal grounding" of the WTC beams is irrelevant.
The conduction and dissipation of heat just a few meters
away from the fire is relevant, but it still allows for huge
temperature differentials in very thick beams with quite
small heat input rates.