Spoiler warning: if you haven't read Cryptonomicon, reading further could spoil the ending slightly.

Call me a nitpicker, but after digesting most of Neal Stephenson's epic I was unconvinced by the ending, wherein the protagonist causes a metric fuckton (1FT) of gold to melt and flow through a rock tunnel into a river, by detonating 1FT of diesel in the mineshaft above the chamber containing said gold. I found myself asking, "What is the melting point of gold? What is the temperature of a diesel furnace? Exactly how much heat would it take to melt 1FT of gold anyway? How much diesel would you need?"

Here are my best attempts to answer those questions...

Melting point

Melting point of gold = 1338 K = 1064°C

Furnace temp

This is more difficult to determine. The ignition temp of diesel ranges from about 180 - 380°C depending on the type of diesel. The maximum temperature of any hydrocarbon burning in pure oxygen is around 3000°C (unless it's pre-heated, in which case you could get a little higher, but you can't preheat diesel any more than a couple of hundred degrees before pouring it into a hole in the ground - otherwise it would ignite on first contact with oxygen, turning the hose into a giant flame-thrower, so let's ignore pre-heating for the moment). Within the range 180 - 3000°C there are many different flame temperatures that can be achieved. The conditions described in the book (diesel and compressed air injected into a hole in the ground, then ignited) are similar to those found inside a jet engine, which is one of the hottest ways to burn a hydrocarbon without using pure oxygen. That said, there are some environmental factors at play (such as the thermal mass of the rock walls, and any water or other crap that's inside the hole) which are all acting to keep the flame cool. A reasonable first guess would be somewhere in the 1000 - 2000°C range.

At one point, Stephenson talks about a "jet of white hot flame" coming out of the drain hole. I'm not sure what he means by "white hot flame" - a flame is generally yellow or blue. White-hotness (eg. in metals) however, occurs at about 1200°C. Perhaps he's describing a 1200°C jet plume, which incidentally would be a light yellow colour. In any case, the flame could easily be hot enough to melt the gold.

How much heat is required?

The heat capacity of gold is approximately 25 Joules per mole per unit Kelvin. If it was a typical stinking hot day in the Philippines (say 35°C) we need to multiply by 1064 - 35 = 1029 (the required increase in temp) which gives us approx 26,000 J/mol. Now to convert moles to fucktons... there are about 5 moles of gold in a kilogram, 5000 in a metric tonne. Hmmm, let's say there are one million moles in 1FT (we can "balance" this approximation later with a reverse approximation on the energy side)... So we require about 26,000 MJ plus the latent heat of melting.

The latent heat of melting (for gold) is quite low because of its high atomic mass - 64 kJ/kg. Using the same conversion factor for FT we get 64 * 200,000 = 12,800,000 kJ (approx 13,000 MJ).

Overall we're looking at 26,000 + 13,000 = about 40,000 MJ - or in other words, balancing the prior approximation, we need one metric fuckjoule (1FJ) of heat.

How much diesel do you need?

Finally to calculate the amount of diesel required, we need to know its combustion energy. Cue the drumroll... and, it's 40.9 MJ/L! This is kind of neat - it looks like 1000 litres would give us the 1FJ we need - but let's take into consideration that a fair whack of that energy is going to go into the surroundings rather than into the gold. Say we lose 90% of it, in fact. We still only need 10,000 litres of diesel to melt the gold. In the book, a figure of "a few thousand gallons" is quoted, which should be more than enough.

It's a little unnerving that the aforementioned protagonist is able to pull this figure out of thin air at the crucial moment... but then again, he is a pretty hardcore geek.

http://www.chemicool.com/elements/gold.html - melting point
http://hypertextbook.com/facts/2005/EileenTang.shtml - ignition temp
http://www.mrsharkey.com/lpg.htm - ignition temp
http://www.tms.org/pubs/journals/JOM/0112/Eagar/Eagar-0112.html - WTC fire facts
http://hypertextbook.com/facts/2001/CarineFang.shtml - white hotness
http://www.junkyardjet.com/primitive.html - how hard it is to make a primitive jet engine
http://en.wikipedia.org/wiki/Gold - heat capacity etc
http://www.engineeringtoolbox.com/latent-heat-melting-solids-d_96.html - latent heat of melting
http://www.answers.com/diesel - combustion energy