The paper The North Tower's Dust Cloud: Analysis of Energy Requirements for the Expansion of the Dust Cloud Following the Collapse of 1 World Trade Center uses photographic evidence -- primarily a reference photograph taken from FEMA's 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 exceeding the energy available in the form of the gravitational potential energy due to the tower's 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 tower's gravitational potential energy to heat. It does not consider the possible energy source of the unlikely rapid combustion of the tower's 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.
The paper is now in its third version. A complete version history is archived here.
I wish to thank Jerry Russell, proprietor of www.911-strike.com, for his work on the physics of the World Trade Center collapses, work which was invaluable in the development of this analysis.