# What happens when an explosion can't lead to volume increase of the thermodynamic system?

What if an explosion is not able to exit the container?

Take a pipe bomb for example; assuming that the pipe bomb was hypothetically made out of such a strong material that the explosion is not able to rip the material apart, what would happen?

Asking this because I was told: NO MATTER WHAT the explosion has to and WILL "exit", but what if it just can't?

• The explosive force is caused by the production of large quantities of hot gas (often $\ce{N2}$) which expands rapidly and cools. If there is no room for expansion then the gas will remain very hot and the pressure will increase. The effects of this will depend on what is inside the box – bon Dec 27 '14 at 18:30
• If the reactor withstands the pressure, you may collect your diamonds - nanodiamonds. – Klaus-Dieter Warzecha Dec 27 '14 at 19:00
• Well, take a look at what edits I made to your posts. I assumed that was what you meant. You will be able to reach results now. The "exit", just as @bon mentioned, is the release of some kind of gas (depends on what's exploding); if it doesn't result in the increase in mass it must result in the increase in pressure. I leave it to you to find the related formulas. – M.A.R. Dec 27 '14 at 21:09

I'm not an expert in thermodynamics and gas physics so there might be some errors in this calculation but here goes:

According to several sources (wikipedia included) TNT decomposes according to this equation: $$\ce{2C7H5N3O6 -> 3N2 + 5H2O + 7CO + 7C}$$

If 100kg of TNT was placed in an indestructible $1m^3$ container containing an inert gas (we will say helium) at standard temperature and pressure here is a rough estimate of what might happen if it was detonated.

Using a Hess's Law cycle we can calculate the enthalpy of decomposition of TNT from formation enthalpy data: $$\Delta_{decomp}H = 63.2*2 - 285.8*5 - 110.5*7 = -2076.1~ kJmol^{-1}$$

Then we can calculate the energy released by the decomposition: $$M_r~of~TNT = 227.13~gmol^{-1}$$ $$n = \frac{100}{0.22713} = 440.3~mol$$ $$Energy~released = 440.3 * 2076.1 *1000 = 914.1~MJ$$

I'm not sure how to go about specific heat capacities for gas mixtures so I won't put a figure on the temperature rise that this will cause but I suspect it will be in the thousands of degrees due to the amount of energy and so the resultant pressure rise will also be very significant, probably enough to liquefy the gases. Also as @Klaus Warzecha hinted at in his comment these kind of temperatures and pressures will probably cause some interesting chemical reactions to take place.

http://courses.chem.indiana.edu/c360/documents/thermodynamicdata.pdf

• You divide by 1000 (not multiply) in the last equation. – LDC3 Dec 28 '14 at 18:26
• @LDC3 2076.1 is in $kJmol^{-1}$ so to convert to $Jmol^{-1}$ you multiply by 1000. I then prefixed the answer with mega to make it a nicer number – bon Dec 28 '14 at 18:30
• ${440.3 mol \times 2076.1 kJ/mol = 914100 kJ}$ or $914.1 MJ$ – LDC3 Dec 28 '14 at 18:33
• correct which is what I wrote – bon Dec 28 '14 at 18:35
• and I multiplied by 1 MJ/1000 kJ. – LDC3 Dec 28 '14 at 18:38

I did a calculation and came up with an increase in pressure of about 280 atm. You can see my calculations here. Most gas cylinders can handle 100 to 150 atm (one is as high as 400 atm), so getting a container to hold 300 atm should not be a problem.

• interesting. i suppose 100kg of TNT in a $1m^3$ container isn't actually that much. it has a density of $1654~kgm^{-3}$ – bon Dec 28 '14 at 21:04
• @bon Water has a density of $1000kg/m^3$. – LDC3 Dec 28 '14 at 21:23