1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gas Problem Dealing with Explosives

  1. Jul 12, 2005 #1
    This is the problem i am trying to solve. It is forensic in nature.

    I have a video of two floors of a burning building collapsing from explosives. The explosives created overpressure. I am trying to infer how much explosives might have been used. I figured out the air volume of the two floors. I can visually estimate the volume of ejected smoke clouds at a few places during collapse. It appears that equal amounts of clouds ejected on all sides of the buildings as it collapsed. Problem, the clouds continue to expand significantly a few moments after the collapse and the video does not give me a full picture.

    Question #1: How can i infer the air volume of the overpressure?

    Once i know this, i can determine the quantity of explosives. My ability is basic newtonian physics. This gas stuff is starting to get above my head. I appreciate the guidance!

  2. jcsd
  3. Jul 12, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hi Hank, welcome to the board. Interesting question, no easy answer I suspect. I have to believe there are a number of expert government agencies around the world that do this kind of thing all the time. Have you Googled forensics? Have you tried contacting the local state police? I'd suspect they have contacts at those agencies that could help. Can you explain why you're doing this?

    If you're going alone on this for some reason, you might want to tell us a bit more about what information you have. Is the camera on the outside or inside of the building? What does it look like? Can you post it on the web?

    If the camera is on the outside, then one thought that comes to mind is to try and measure the velocity of the air being expelled from the windows. There may be smoke or bits of paper or other material swept up by the explosion that you could use to determine velocity. A measure of the distance something traveled divided by the time between frames would give you the velocity. Once you have velocity, it would be a simple matter to apply Bernoulli's equation to this and assume you have an overpressure that is virtually instantaneous at the time of the explosion. Bernoulli's would then give you the pressure at that time. It wouldn't be exact, but I have to believe it would get you in the ballpark. Any other values calculated from other means could also be compared. Also, you should try to make some judgements about how accurate these estimates are and how they may be affected by the basic assumptions and the accuracy of the calculations to give you a range of possible explosive mass.
  4. Jul 13, 2005 #3

    What do you mean by the 'air volume of the overpressure'?
  5. Jul 13, 2005 #4
    Thanks Q_Goest,

    Yes, i realize my question might raise a few eyebrows. I am trying to teach myself science. I might as well make it interesting, right? I saw a demolition on the Discovery channel and became curious as to how much explosives might have been used. Nothing major. But it poses an interesting challenge as i have to somehow infer it.

    I think there is enough data to do a ballpark estimate? The building is rectangle, 30 x 30 m. The building was on fire for some reason and created smoke. When the collapse happened, smoke was expelled along with debris. I can measure the diameter of the expanding clouds by comparing to the floor height. I can measure time using a stopwatch. So i can make a "Point A" and a "Point B" snapshot of what happened. Below are my estimates. Times are relative to the collapse start (0 secs).

    Cloud State
    Point A
    Time: 0.90 secs
    Cloud Diameter: 4.3 m
    Cloud Volume (4 sides): 1732 cubic meters

    Point B
    Time: 1.30 secs
    Cloud Diameter: 7.6 m
    Cloud Volume (4 sides): 5440 1732

    4 * (30 * (4.3/2)^2 * 3.14) = 4 * (30 * 4.6 * 3.14) = 4 * 433 = 1732
    4 * (30 * (7.6/2)^2 * 3.14) = 4 * (30 * 14.44 * 3.14) = 4 * 1360 = 5440

    This is the first gas problem i have done, so sorry if i need the hand holding. From the internet this is what i got for Bernoulli's equation:

    P1 + p/2 * V1^2 = P2 + p/2 * V2^2

    p - density of gas
    P1 - pressure of gas at point A
    P2 - pressure of gas at point B
    V1 - volume of gas at point A
    V2 - volume of gas at point B

    Did i get this right? Where do i go from here? I don't think i can use this formula "out of the box". Where do i get pressure values from? Bernoulli's equation may be "basic" physics but is no means friendly to those who have never seen it before.

  6. Jul 13, 2005 #5

    What do i mean by the 'air volume of the overpressure'?

    From my understanding from chemistry (i am self-teaching that too!) an explosive compond releases a lot of gas when it expodes. Example, 1 mole of TNT release 10 moles of gas. This is added to the air already inside the building and happens in an instant. This added air is the referred "overpressure". By working backwards starting with the cloud volume, i hope to infer how much TNT was used in the demolition.

    I think this is a cool problem. It definitely encourages me to learn science. But as you can see, it is a bit challenging for a newbie. I got as far as i could get.

    Sorry, i left out a measurement in an earlier post. I used a floor height of 3 m. This is necessary for calculating the original air volume of a floor.

    Last edited: Jul 13, 2005
  7. Jul 13, 2005 #6


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The model I'd suggest using here would be one used to determine what velocity of air/gas is generated from a given pressure.

    If you could imagine holding all that pressure inside the building with the windows closed, not letting anything escape, that would be the pressure you're looking for. Obviously that's not exactly what happened, but it's close in the sense that most of the pressure was inside the building when the explosive went off. You might imagine an expanding cloud of gas generated by the explosive coming up to the walls and being contained. From there it has to get out the windows, so for a moment at least, most of the pressure would be contained inside the building even if the walls were forced outwards and knocked down. The walls would contain the pressure at least momentarily as the mass of the walls would need to be accelerated. The path of least resistance is the windows, so there's where you would get your best indication of the velocity of air/gas coming out of the building from the pressure built up inside.

    Bernoulli's could be used for that, though the air/gas is compressed slightly (ie: relative to ambient pressure) so it's probably not the best thing to use. It does however give you a feel for why you might model something like this. The pressure energy inside the building is accelerating the air/gas through the windows, so per your description above, point A is a point inside the building and point B is in the streamline of the gas coming out of the window that has been accelerated to a velocity V2 (note: V1 and V2 are velocity, not volume). Even if the walls do get thrown outwards slightly from the blast, you should see higher velocity through the windows where there is no resistance.

    So point A is inside the building and point B is in air being accelerated through a window from the internal pressure. Now you can solve for P1, the pressure inside the building. Assume V1 is small (ie: V1 is zero). Assume P2 is ambient pressure. Assume density is an average density for the gas using the ideal gas equation PV=mRT where density = m/V = P/RT. Make a guess as to how hot the air might have gotten.

    You could also use other equations for flow of a compressible gas through a restriction to determine internal pressure, there are numerous equations. If the intent here is to learn a bit about how to model things then I think just using Bernoulli's is good enough. The whole point here is only that fluids are accelerated by pressure. How you calculate that gets into what equation best fits the assumptions.

    I'm sure there are other ways to estimate the overpressure inside such as some type of structural analysis, but that would be much more difficult I think. Perhaps someone else has some other ideas.
  8. Jul 13, 2005 #7

    Thanks for the explaination.
    Obviously, for what you want to calculate, you will need to assume that a particular explosive was used. We assume that it's TNT.
    It seems, from your video, you can find out the rate of formation of the gas clouds, i.e., volume of gas liberated per second. Then, you need to know the ratio of moles of explosive burnt to moles of gas produced. Using this, you can find the amount of explosive burnt per second (assuming that all the cloud comes from the explosive only; a bad assumption indeed). If you know that for how much time it kept going on, then you can find the amount of explosive used. But of course this will give a very very approximate estimate.
  9. Jul 13, 2005 #8


    User Avatar
    Science Advisor
    Gold Member

    I do not see the point of this. I don't want to discourage the OP, but I think this stuff is harder to calculate than we think. I do not know how are you going to measure the volume of a cloud visually and how you could infere it is only formed by the product gas of the explosion instead of a mixing process between it and the ambient air or dust.
  10. Jul 13, 2005 #9
    Even I don't see much point in it. I wrote this under the assumption that hankw is somehow able to find the rate of increase in the volume.
    Also, I think, that the information that is available is very less to infer anything from it. We must assume several things, the variety of the explosive being one of them. According to me, we can only arrive at a very approximate estimate which is of not much help.
    To put it in a nutshell, the full exercise doesn't seem so enlightening.
  11. Jul 14, 2005 #10

    Thanks for the suggestions.

    Is it possible to infer velocity by a change in the volume of the clouds? Trigonometry? This way i can use the equation at various times during the collapse, then average out the results.

    vinter and Clausius2,

    Keep in mind that because of fire, smoke was produced. This marks the otherwise invisible air. When the collapse occurred, well-defined clouds were ejected from the sides of the building. Would this not faithfully represent the air volume inside the building? I can measure how much clouds were ejected when the first floor collapsed. This likely represented what other floors ejected when collapsing one floor. Using this measurement i can then measure the cloud volume at each floor and infer how much cloud volume the first floor ejected. I then account for air turbulence. I have read that a rule of thumb, as long as clouds are expanding and are well defined (no noticeable diffusion with the air), that one subtracts 1/3 of the volume. So i am left with a volume of air that was inside one floor when the explosives went off. I then account for the original air volume. I calculate its size when heated by explosives and then subtract. I am left with a volume of air representing the overpressure caused by explosives. Am i oversimplifying this?

    From my understanding of TNT, in the reaction it produces three things: 1) heat; 2) gas; 3) carbon. If TNT was used then the overpressure volume was made up directly by the produced gas and indirectly by the heat. Is this right? Is there a rule of thumb that establishes "total" air volume for a certain amount of explosives? Could i then work backwards and infer how much explosives was used?


    With the measurements i have outlined, what is missing that would NOT make a credible estimate? I am confused as it seems all the information needed to solve the problem is there. I wish i could post the demolition video but i am unable to video capture my VCR.

    Last edited: Jul 14, 2005
  12. Jul 14, 2005 #11


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    For a contained volume that has a gas or air rushing out of some opening, the pressure can be determined given the velocity of the gas rushing out. If you had a container (ie: building) which stayed together and all you knew was the velocity of the air coming out of the building over time, you could fairly accurately calculate the pressure in the container. Even if the container held together for a second or two, if you could determine the velocity of the gas coming out during those few seconds you could fairly accurately determine pressure inside. The more data points on velocity you had for those few seconds the more accurate the estimate. The accuracy of the estimate obviously depends on how accurately you know all the variables, but it should be simple enough to quantify the error and therefore the accuracy of the estimate.

    If however, the container ruptures like a popped balloon, and all you see is a cloud expanding, that's a different story. The wikipedia link you mentioned talks about contained or uncontained explosions. For the uncontained explosion, you'll need a bit more information. You might do a first law analysis, but the gas/air has done work on the walls to push them out which is a big unknown. If that is closer to the type of explosion you're looking at, I'd have to give it some thought as to how best to get an estimate on it, but it would seem to lend itself to a first law analysis.
  13. Jul 15, 2005 #12

    I understand your suggestion about measuring the air velocity before the collapse initiates. The problem i have is that my technology is a thumb and a stopwatch. The expelling of the small amount of clouds right before the collapse only happens in a few frames- a split second. I have no way to frame count with my VCR. So i am looking for other ways to measure that don't need such accuracy. One possibility is to start plugging in numbers in an equation and see when the results match with what can be observed. It is trial-n-error, but one way to do it.

    Let me ask, if compressed gas does work by pressing out the building sides, then my final estimate of the quantity of explosives will be conservative? That is ok. If i get a quantity estimate of explosives that resembles what typically would be used in building demolition, then i did good. This is a type of reverse engineering not many people think is possible! Keep in mind that the collapse itself contributed to buckling of the walls, which opened them up and let air to escape. And then there is all the windows openings. So maybe compressed gas did not significantly push the walls. Let us do a ballpark estimate for now using a simpler model and see if we get a credible result.

    So to estimate the velocity of expanding clouds do i just measure the difference between two points in time? Or is cloud expansion a phenomena that cannot be measured this way? I can see that as a compressed gas expands its pressure goes down. I am starting to "sink" in all this fluid mechanics!

    I am currently working on the chemistry side of the problem, to determine how much "total" air volume explosives create.

    I think i discouraged some posters. They gave up saying the problem is not doable. I have never known a scientist to turn down an interesting problem. Can you look over my response to vinter and Clausius2 and see if there are significant faults in my methodology? I think the methodology should be checked. I am a newbie. If there is a flaw in it, then it needs to be adjusted. Getting the methodology straight will help me research the internet and prepare in advance for discussions that might start getting over my head.

  14. Jul 15, 2005 #13
    I think one important aspect of explosives is overlooked here.

    Explosives release a certain amount of gas yes but they do so at a certain speed. the so-called "VoD" or "Detonation velocity". The VoD of TNT is lower than that of PETN for instance which makes the force excerted by the expanding gas coming from a kg of TNT smaller than the force of the gas that is produced by an equimolar amount of PETN. The VoD is of great importance in the destructive power of an explosive.

    E.G. When a kg of TNT detonates it might batter away the supporting walls of a building because of the sudden increase in pressure. But when a kg of BP (black powder) deflagrates (BP does not detonate) it will not destroy the room because the gas is not released fast enough. It will shatter the winodws but the gas has enough time to cool down and dissipate so it won't batter down the walls.

    I may not be completely clear but I think my point will come across :)

    The calculations you are attempting to are quite probably very complicated and they might even be different for different kinds of explosives! I know someone in the EOD so I might ask him but quite frankly I don't think you should get your hopes up. :)
  15. Jul 16, 2005 #14
    Hi Nerro,

    That is an excellent point! Is it possible to measure the air volume created by detonation velocity?

    So far, i have to calculate the following in order to infer quantity of explosives. Any additions anyone can suggest?

    -Volume of gas produced by explosives (have formula)
    -Volume of the produced gas heated up by explosives (have formula)
    -Volume of the original air heated by explosives (working on formula)
    -Volume volume produced by velocity (have nothing)

  16. Jul 16, 2005 #15
    the fourth criterium you name is where the snag is because that will require an extremely complicated complex formula... Not only will the gasses produced by the explosion cool down at a certain rate but as they do so they will also expand less violently. Also the VoD decreases rapidly as the gas expands...
  17. Jul 16, 2005 #16


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Detonation velocity is defined as follows:

    Ref: http://www.globalsecurity.org/military/systems/munitions/explosives.htm

    Dentonation velocity is the velocity of the shock wave inside the explosive as the explosive goes off. That velocity can be increased when it is confined and pressure increases (ie: to tens of thousands of psi), but it doesn't propogate past the explosive. Detonation velocity is not the velocity of the air or byproducts of the explosion. Propellants for weapons such as the propellants in artillary shells, morter shells and bullets are a prime example. When confined inside the brass casing and fixed inside the chamber of a gun, these propellants burn violently, building up pressure and propelling the round out of the barrel. If you take these same propellants and put them on the ground and light a match to them, they're more like flash powder or black powder, they burn relatively slowly.

    An explosive can create a shock wave in the surrounding air, and that wave will propogate outwards at some supersonic velocity, but I don't believe that shock wave is affected by the detonation velocity, only the total amount of energy given off by the explosive.
  18. Jul 16, 2005 #17


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Is this building you're refering to something that was intentionally leveled by a demolition company or a building destroyed by an explosion? If it was leveled by a demolition company, then I'd assume you realize that the explosives used are carefully placed to cut the structure. They use shaped charges packed into strips that can be wrapped around girders or other steel members to cut the structure. They actually cut along a line, unlike military rounds that punch holes. So the total amount of explosive used by demolition companies is minimal.
  19. Jul 16, 2005 #18


    User Avatar
    Gold Member

    A couple of things to keep in mind here.
    One, although it's maybe not important, is that most of what you call smoke is probably dust. The rest would be from the original fire (and why on earth was it burning anyhow?) Modern demolition charges are smokeless.
    The second is that there's no way you'll ever be able to figure out how much explosive was used without knowing what kind it was. Through the aforementioned methods, you can probably figure out what the total explosive force was, but it could be a fair pile of 40% Forcite, a lesser amount of 90% Forcite, or significantly less C5. Most commercial building demolition is done with 40% Forcite or equivalent (Forcite is a CIL product, a gelatine dynamite wherein part of the nitroglycerine is replaced by ammonium nitrate) set in drill holes throughout the structure. The charges are very intricately timed to result in an orderly collapse of the building without any undo scattering of bits. It shouldn't be too difficult to find out what company did the deed and ask them what they used. Work your formulae to get your best solution, then contact the company again to find out if you got the amount right.
    Last edited: Jul 16, 2005
  20. Jul 17, 2005 #19


    User Avatar

    You might have some problems figuring out how many and what kind of explosives have been used simply because there are too many variables that you don't know. For example, the formula: PV=nRT means that the pressure in a chamber will vary with temperature. Also, you do not state what the explosives are, different explosives create different amounts of gas. Another factor is trying to find the maximum stress on the floors, and computing the pressure needed for exeeding that value by equating maximum stress per unit squared with pressure per unit squared. Another factor that would be very difficult to account for would be the temperature of the floor and finding the maximum stress under those specific conditions. You would also have to know about whether any parts of the floor were cratered by the explosion, reducing the maximum stress. finding out how much explosives were used would be easier if you knew the residue products and things like the size of the produced crater. finally as mentioned before, the pressure would be continually falling due to the cooling of the gases. Threrefore, I reccomend self-educating on more practical and easier problems.
    P.S. Why in the world do you need to know this?
  21. Jul 18, 2005 #20
    To All,

    Thanks for all the input. Since my last post i have learned how to calculate bursting pressure. Basically, one using a combination of temperature, detonation velocity, and gammas of gasses and water. From this one can determine pressure at a distance. Then one can infer air volume. I am not yet clear about all this. Here is a snippet of the email i got:

    "Similarly, remembering Cp/Cv equals gamma, and the gammas for CO2, N2 and H2O are 1.29, 1.40, and 1.30 respectively, and I guess an average of about 1.35. Assuming your initial temperature and pressure was 298K and 1 atmosphere, the bursting temperature will be as we just calculated and the bursting pressure will be (4886.6/298)^(1.35/0.35) to give 48,486 atmospheres or 712,754 psi.. If you know the burning rate of the TNT-AN mixture, and I'll guess it is maybe 7,000m/sec., you can profile the pressure gradient from the mensuration formulae of a sphere."

    Some heavy thermodynamics, i know. And my knowledge of physics and chemistry can be held in cupped hands!

    Does this bursting pressure sounds like that detonation velocity factor that Nerro mentioned? Or is this something else? Another question i have- of the four major factors i listed to calculate explosion air volume, does the bursting pressure/detonation velocity factor create its own air volume or does it include the air from factors 1 and 2?

    -Volume of gas produced by explosives
    -Volume of the produced gas heated up by explosives
    -Volume of the original air heated by explosives
    -Volume volume produced by burst pressure/denotation velocity

    So i am guessing that these above factors are the "major" contributors of explosion air volume? I am not trying to make a detailed model here, not that i would succeed anyways.

    I do realize that this demolition problem has grown a magnitude or two in difficulty. I may not be able to estimate the explosives used in the demoliton. But hey, the goal was learning. I am learning chemistry, physics, and behavior of explosives all in one problem. I am learning how bring together different science disciplines to solve things. That is a rich learning experience. I theoretically could take this knowledge and reverse engineer all sorts of explosions seen on TV- a trick i can do at parties for scooby snacks! If nothing else!

  22. Jul 18, 2005 #21


    User Avatar
    Staff Emeritus
    Science Advisor

    I'm not familiar with "bursting pressure" - it would be interesting if you could post the formula for it and some more details, - but nonetheless, I think I can give you some basic info that could be useful.

    (Note: on reflection, it seems likely to me like the point of bursting temperature, and bursting pressure is to create an initial model of the gas - i.e. you want to model an initial sphere of gas generated by the explosion as having some temperature, volume, and pressure, to start with - then model what happens next via physics. But that's sort of a guess at this point. I don't know what the "bursting volume" would be, perhaps the volume of the explosives themselves?).

    After your explosive has all burned, you will have a big ball of hot gas generated by the chemical process of burning. The manner in which this ball will expanded, _after the burning process is done_, is best approximated by adiabatic expansion.

    You might try the wikipedia on this


    The idea behind adiabatic expansion is the conservation of enregy. This is where the ratio gamma, and the expressions Cp and Cv come in (the heat capacity of the gas at constant pressure, and at constant volume).

    The adiabatic law , when you go through all the calcuations, winds up to be

    [itex]P V^\gamma=[/itex] constant, and it supplements the traditional ideal gas law PV=nRT.

    Note that adiabaitc expansion will _not_ be a perfect model of the behavior of the gas. As others have noted, the gas will be doing work in the process of disassembling a building. The adiabatic law gives the pressure-temperature relationship

    As I think about this, it seems to me that expanding of the cloud of gas against the pressure of the atmosphere itself implies that the gas is doing work, and that this work should be subtracted from the adaibatic model, creating a new, more complex model. I don't think I've ever read anything detailed about this though.
  23. Jul 19, 2005 #22
    This is the rest of the email i got. Someone contacted me anonymously to give me a nudge in the right direction- or to confuse me. Is this bogus? No specific formula was given, but a general framework. See if you can figure it out. This was dealing with the explosive compound Amatol, Trinitrotoluene-ammonium nitrate. For a mixture with a molar ratio 4 : 42 the reaction equation is 4 C7H5(NO2)3 + 42 NH4NO3 -> 28 CO2 + 94 H2O + 48 N2.

    "Hank, I just assume you have balanced your TNT-AN equations and have done the right arithmetic leading to the 25,850Kj/4 moles and that the heat capacities you looked up are right. The following may be new ground:

    The enthalphy for the reaction you propose divided by the summation of the heat capacities times the molar quantities of each will give you value of 5.286Kj/mole-deg. This number divided into the the 25,850 will give you a bursting temperature of 4886.6 degrees Kelvin on explosion.

    Similarly, remembering Cp/Cv equals gamma, and the gammas for CO2, N2 and H2O are 1.29, 1.40, and 1.30 respectively, and I guess an average of about 1.35. Assuming your initial temperature and pressure was 298K and 1 atmosphere, the bursting temperature will be as we just calculated and the bursting pressure will be (4886.6/298)^(1.35/0.35) to give 48,486 atmospheres or 712,754 psi.. If you know the burning rate of the TNT-AN mixture, and I'll guess it is maybe 7,000m/sec., you can profile the pressure gradient from the mensuration formulae of a sphere. "

    The 25,850Kj/4 moles number was derived from another set of equations. I posted them on a chemistry forum. I will post them in the next post. I know we are getting into chemistry here, but it is only to obtain physical measurements such as heat and volume.

    One note to all- i have decided to change my problem slightly. I have come to accept that to reverse engineer a demoltion is a massive undertaking. So i am going to change the problem so i just concentrate on analyzing the volume of air produced by an explosive. I still had to do this with the demolition, but in this new problem i don't have to deal with a bunch of other variables that are specific to the collapse.

  24. Jul 19, 2005 #23
    We will consider the explosive amatol which is a mixture of trinitrotoluene (TNT) and ammonium nitrate (AN).

    Trinitrotoluene (left) has the chemical composition C7H5(NO2)3 and ammonium nitrate (right) has the chemical composition NH4NO3.

    We choose the TNT to AN molar ratio in the amatol mixture to be 4 : 42.
    This translates to a 4 x 227 : 42 x 80 = 908 : 3360 = 21 : 79 ratio by weight.

    In this case the explosion proceeds according to the equation:

    4 C7H5(NO2)3 + 42 NH4NO3 28 CO2 + 94 H2O + 48 N2

    From the equation we see that 4 moles of TNT and 42 moles of AN produces 28 + 94 + 48 = 170 moles of gaseous product.

    At standard temperature and pressure, 170 moles of gas occupies 170 x 22.4 = 3,808 liters. This is the volume that the explosion products would occupy if, after the explosion, they were cooled to 25 C (with the assumption that the water remains a vapor). In order to calculate the volume of the hot gaseous products generated by the explosion, we initially need to know the amount of heat released by the explosion of 4 moles of TNT and 42 moles of AN. We also need to know the amount of heat required to raise each of the gases, by one degree K. That is, we need to know the enthalpy of explosion H_explosion and the heat capacities C_p (also known as specific heats) of each of the gases.

    H_explosion = - (4 H_solid(TNT) + 21 H_solid(AN)) + (28 H_gas(CO_2) + 94 H_gas(H_2O) + 48 H_gas(N_2))
    = - (4(-60) + 21(-365.5)) + (28(-393.5) + 94(-242) + 48(0.00))
    = 240 + 7,675.5 - 11,018 - 22,748
    = - 25,850 kJ per 4 moles of TNT and 42 moles of AN.

    Here we have used the following facts:

    H_gas(H2O) = -242 kJ/mol
    H_gas(CO) = -110.5 kJ/mol
    H_gas(CO2) = -393.5 kJ/mol
    H_solid(TNT) = -60 kJ/mol
    H_solid(AN) = -365.5 kJ/mol

    The heat capacities C_p for the gases involved are:

    C_p^gas (N2) = 28.87 J/mol*K
    C_p^gas (O2) = 28.91 J/mol*K
    C_p^gas (H2O) = 30.43 J/mol*K
    C_p^gas (CO2) = 37.12 J/mol*K

    Since the heat capacities are all approximately 30 J/mol*K, we will assume this value for all the gases, i.e., we assume:

    C_p^gas (all relevant gases) = 30 J/mol*K

    So, by assumption, 30 joules of energy will raise the temperature of one mole of the gaseous product (of the explosion) by 1 degree K.

    Summarizing from earlier, we have that 4 moles of TNT and 42 moles of AN,

    * produces 170 moles of gaseous product and
    * liberates 25,850 kJ of energy.

    We will assume that the original 170 moles of explosion products mix with N moles of air.

    This 170 + N mole mixture of gases is initially assumed to be at the temperature T_0 = 298 degrees K (25 C).
    This 170 + N mole mixture of gases has an initial volume of V_0 = 22.4 (170 + N) liters.

    We calculate the increase in temperature T of this 170 + N moles of gases after being heated by the 25,850 kJ of energy released by the explosion of the 4 moles of TNT and 42 moles of AN.

    Now 30 joules raises the temperature of one mole of the gases by 1 degree K.
    Hence, 25,850,000 joules raises the temperature of the 170 + N moles by

    T = 25,850,000/(30 x (170 + N)).

    We now calculate the volume V_1 of this 170 + N moles of gas after being heated by the explosion to the temperature

    T_1 = T_0 + T

    From the ideal gas law we have that V_1 / V_0 = T_1 / T_0. Rearranging we obtain

    V_1 = V_0 (T_1 / T_0) = V_0 (T_0 + T) / T_0 = V_0 + V_0 T / T_0. On substituting we obtain

    V_1 = V_0 + 22.4 x (170 + N) x 25,850,000 / (30 x (170 + N) x 298) = V_0 + 22.4 x 25,850,000 / (30 x 298) = V_0 + 64,770 liters.

    Hence, the increase in volume of the mixture of gases V = V_1 - V_0 = 64,770 liters.

    So, summing up, the explosion of 4 moles of TNT and 42 moles of AN produce 64,770 + 22.4 x 170 = 64,770 + 3,808 = 68,578 liters of hot gases.
    That is, the explosion of 4,268 grams of amatol produces 68,578 liters of hot gases.
    That is, the explosion of one kilogram of amatol produces 68,578 x 1,000 / 4,268 = 16,068 liters of hot gaseous product.
  25. Jul 19, 2005 #24
    Bursting Heat seems to be a known term, makes sense that there would be a bursting pressure. When the explosive reaction starts- like popcorn- bursting heat is reached near-instantaneously. A "bursting pressure" must also exist because of the gas and high heat generated. It is like the relationship between voltage and amps.

    I think the starting volume is immediately after the reaction. This would include the solid byproducts, the gas byproducts, and the generated heat. Then one expands outward from there. This appears to be what that scientist is saying. From this do i use the ideal gas law to figure volume at distance?

    When i estimate the expanding explosion i am going to have to measure change in temperature too. I am sure the behavior is like sound or gravity, where the intensity drops in magnitudes over distance, but what is the rule-of-thumb? I will need the temperature in order to calculate the expansion by heat of the surrounding air. I think for ballpark analysis i could use an asserted rule-of-thumb that for air turbulance one takes 1/3 of a gas volume. So the equivalent of 1/3 of the explosion volume would be surounding air that is heated up.

    But i could be totally way off mark on all this stuff. I am a newbie just trying to think things through logically.

    I welcome comments on all this.
  26. Jul 20, 2005 #25


    User Avatar
    Staff Emeritus
    Science Advisor

    I've only skimmed through this (I've been a bit busy recently), but it looks to me that the intent is indeed to model the state of the explosive after the explosion as a volume of gas occupying the intial volume of the explosive with a pressure and temperature of the bursting pressure and the busting temperature. These numbers are calculated to preserve energy, and the amount of matter present.

    The detailed analysis seemed to take a back-road, though - if that was indeed the intenet, I don't see why C_v was not used rather than C_p (the heat capacity at constant volume). There is a well known relationship between C_p and C_v that is closely relatied to the adiabiatic process link that I posted earlier.

    I'll look at this some more, later, if I have time, but I would encourage you to read up about adiabatic processes.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook