The Physics of Explosives

It’s my understanding (corrections welcome) that explosives work by very quickly converting a relatively small volume of explosive into a much larger volume of gas. (Please ignore things like fuel-air explosives in this discussion. I’m thinking of solid high-explosives like TNT, etc.)

I’m trying to get a handle on the ratio of volumes before and after the explosion.

Imagine this thought experiment: I have a very large vessel. Inside it is 1 kg of TNT and nothing else (i.e, the vessel is air-tight and I’ve pumped out all of the gas inside).

I detonate the TNT.

1. What was the volume of the original 1 kg of TNT?
2. How big does the vessel have to be so that the maximum pressure inside it is 1 atmosphere after the explosion?

(My assumption is that the pressure spikes up after the TNT is detonated and then slowly drops down after the gas produced by the explosion cools off. Does it work this way?)

I don’t think it works that way. Detonation of explosives releases a large quantity of energy which is (partially) dissipated by a blast or pressure wave propagating through the medium that the explosive is in (air, water, the ground, etc). This blast is what causes the destruction. The conversion of solid explosive to gaseous or tiny particulate material would be incidental compared to that.

If you set off an explosive in the middle of an evacuated chamber, there would be no blast other than the waste materials of the explosion flying around. Detonating 1 Kg of solid explosive would result in 1 Kg of gaseous (or very tiny particulate) waste. The resulting pressure of this gas would depend on what it’s made of and its temperature (as you already noted).

Let’s start with a balanced chemical equation.

I’ll have to look at my old text books, but we’re talking bout

Tri-nitro toluene --> Nitrogen + Carbon dioxide + water + what else? anything?

C[sub]7[/sub]N[sub]3[/sub]O[sub]9[/sub]H[sub]3[/sub] --> N[sub]2[/sub] + CO[sub]2[/sub] + H[sub]2[/sub]O

Hmmm… not enough oxygen in the reactants. Some CO will be produced. Must balance… Hmmm if still not enough Oxygen in the TNT formula, elemental Carbon is formed.

Now, we can just use the balanced equation and the molar ratio from that to determine relative volumes of gases.

WAIT!!! the products are very HOT! We have to calculate new pressure or volume with the gas law. (let’s make it simple and use the ideal gas law.)

PV = nRT

Temp… How hot will it get? Hmmm… gotta get all sort of H[sub]f[/sub] information.

…losing interest…

Density of trinitrotoluene is 1.654 g/cm[sup]3[/sup]
Mw = 227.13
So 1 kg takes up 604 cm[sup]3[/sup], and contains 4.4 moles TNT.
Assuming the explosion breaks each molecule into ~10 gas molecules, that gives ~44moles X 22.4 L/mol = 985 liters of gas at 1 atmosphere pressure and RT.
The number of pieces I used for the calculation (10) is an estimate based on the number of C,H,N,O atoms in the molecule, times a kludge factor for incomplete reaction. Someone who has actually studied TNT reactions can probably give a better estimate.

Volume expansion. Specifically, the rate at which it expands. A good explosive must expand quickly lest it blow itself apart before the entire bunch of it gets to ignite. Not that the heat given off is unimportant to us, but the explosion part of detonation is rapid volume expansion pure and simple.