The letter by M. N. Berberan-Santos in the October 2000 issue of J. Chem. Educ., concerning the temperatures of heaven and hell according to Biblical evidence, brought to mind a similar conundrum that occurred to me some years ago and which, so far as I know, has not been discussed in a forum such as this Journal.

In the Old Testament book of Daniel (Dan. 3:12-23) it is recorded that three men--Shadrach, Meschach, and Abed-Nego--were ordered to be cast into a blazing furnace. They had so incurred the wrath of King Nebuchadnezzar that instructions were given that the furnace was to be made "seven times hotter" than usual. Nebuchadnezzar clearly did not know his combustion science, otherwise he'd have realized that this was a waste of fuel and effort.

The maximum temperature that any fuel-air system can attain is the stoichiometric adiabatic value: that which is reached when there is sufficient oxygen for total oxidation of the fuel and all of the heat is retained in the combustion products. Excess air or excess fuel will lower the adiabatic flame temperature because of the effect on the total heat capacity of the post-combustion products.

It is of course true that this value is for reactants (fuel and air) initially at room temperature, and that higher temperatures are obtainable by pre-heating one or both of these. This is common in fuel technology, in such techniques as regenerative burning. However, if in the case under discussion making the furnace "seven times hotter" consisted of throwing in seven times as much fuel without any modification to the air supply, this might even have had the effect of lowering the flame temperature. The adiabatic flame temperature is always in the neighborhood of 2000 °C. Even this is only an "upper bound" for most practical purposes because of heat transfer to the surroundings. On the basis of the simple adiabatic flame temperature idea, there would be no question that excess fuel would lower the flame temperature. Pre-heating of reactants can occur naturally if fuel and air at incipient ignition receive heat from a neighboring assembly that has already ignited. We shall never know to what extent, if at all, Nebuchadnezzar made provision for this!

What then are we to make of the statement (Dan. 3:22) that the men charged with the barbarous task of casting Shadrach, Meschach, and Abed-Nego into the furnace were themselves killed by the excessive heat? Possibly the furnace walls failed through the overloading, but otherwise this might simply be literary license. I am trespassing here into an area in which I am by no means an expert, but I am given to understand that even in New Testament times writers of repute would sometimes embellish a narrative to give it greater thrust. To do so was not, by the standards of those times, unprofessional.