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T Utorial Exercises

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Tutorial Exercises Answers to se/ected even-numbered exercises fol/ow. 1-1. An automobile with mass of 1250 kg travelling at the legal speed Iimit of90 km/h {55 mph) collides head on with an unyielding stone wall. a) What is the energy of the impact? b) What is its TNT equivalent? 1-2. The energy release per fission of a uranium nucleus is approximately 195 million electron volts (one electron volt equals 1.602 x 10-19 J). Of this, about 89% is released promptly and the balance of 11% appears in the course of time during radioactive decay of fission products. a) Compute the number of atoms of uranium which must undergo fission in order to provide an energy release of twenty kilotonnes TNT. b) How many moles of uranium is this? {The Avogadro number is 6.022 x 10 23 per mole). c) How many kilograms of pure uranium-235? 1-3. The standard 30-06 militaryrille fires a buHet with mass 150 g at a muzzle velocity of 884 m/s (2900 ft/s). a) What is the kinetic energy? b) What is its TNT equivalent? 1-4. The energy released in a lightning flash has been found tobe about 105 Jjm. What is the TNT equivalent of the energy release in a lightning fiash that extends 1.6 km? 1-5. A propellant "powder" based on cellulose nitrate shows an energy of explo­ sion of about 3 kJ/g. 195 196 Tutorial Exercises a) Characterize this material with regard to brisance and whether it is a deflagrating or a detonating explosive. b) Specify its explosive strength relative to TNT. 1-6. A munitions factory plans a storage facility for 7.5 tonnes explosive. a) What minimum distance should this facility be away from a public highway? b) The quality controllaboratory should be at least how far away? c) How close could sentries and guards be stationed? 1-7. A small hand-carried satchel is suspected of containing a terrorist bomb. a) What quantity of explosive might such a satchel contain? b) Out to what distance could missiles from its possible explosion be thrown? c) What distance should be corded off? d) Fire fighting foam can reduce missiledarnage distances by about one half. To what distance would missiles be expected if the area were foam protected? 1-8. Two standard igloo magazines are located twenty metresapart in an open area. a) What is the maximum amount of chemical explosivestobe stored in each if neither is earth covered? b) If both are earth covered? c) If one of these earth covered magazines exploded accidently when containing its maximum permissible contents about how far would missiles and fragments be thrown? d) What diameter crater would such an explosion create? e) Estimate the probability that there is a near simultaneaus sympathetic detonation of the second magazine. 1-9. A tank er has off-loaded 4200 steres of crude oil cargo so that the nominally empty tank contains an explosive mixture ofhydrocarbon fumes and air. The explosive strength of such fumes for surface explosions is estimated to be about 0.6 g TNT per litre. a) What would be the TNT equivalent of the explosion of this cargo tank? b) How far from explosion center would debris from deck piping, deck pumps, etc., be expected to be thrown? 1-10. Two structures used for assembly oftest munitions might house as much as 75 kg of high explosive each. a) How close to each other may these structures be ifthere is no protecting barricade between them? b) To what distance would this be reduced if a protecting barricade were erected between them? c) What are the odds against an accidental explosion in one structure being propa­ gated into the other if there is no barricade? 1-11. Assurne a one-tonne PETN "block buster" bomb hits the ground and explodes at a distance of only ten metres away from a store of explosive ammunition. What is the probability that this store of ammunition would also explode? Tutorial Exercises 197 1-12. A crater near Winslow, Arizona, has a diameter of about 1250 m and a parapet of about 40 m. Estimate the energy required to produce such a crater in terms of the TNT equivalent. 1-13. A meteor with a mass of 300 kg strikes the earth at a speed of 16,000 m/s. a) What is the TNT equivalent of its kinetic energy? b) What diameter crater would this probably produce if impact were normal to the earth's surface? 1-14. What minimum amount of demolition explosive C-4 placed in direct contact is required in order to puncture a bunker wall of concrete 350 cm thick? 1-15. What minimum thickness of reinforced concrete is needed in order to defeat a projectile from a !arge Naval rifle with a mass of210 kg and an impact velocity of 415 m/s? 2-1. The high explosive 2,4,6-trinitroaniline has the chemical formula C6 H 2 (N02}JNH 2 • a) What is its oxygen balance to carbon dioxide and to carbon monoxide? b) Characterize this explosive as oxygen rich, oxygen balanced, or oxygen deficient. c) Write chemical equations depicting its explosive d~composition into nominal prod­ ucts at the very high pressures comparable to detonation conditions, to fireball conditions, and for fully expanded products. 2-2. a) For each explosion requested in part b), compute its mass percentage oxygen balance, and then characterizc its relative oxygen content. b) Write a material balance in form of a chemical equation for explosion to nominal products for the following conventional chemical explosives: HMX, PETN, Tetryl, Nitromannite, and Cyclonite. 2-3. Amatol 80/20 is a mixture 80% by mass ammonium nitrate (AN) and 20% TNT. a) Assign this mixture an apparent chemical formula and a corresponding formula mass. b) What is the oxygen balance for Amatol 80/20 to carbon monoxide; to carbon dioxide? c) Express in form of a chemical equation the explosive decomposition of Amatol 80/20 to nominal lireball products. 2-4. Torpex is an aluminized explosive containing 42% RDX, 40% TNT, and 18% finely powdered aluminum. a) Convert these mass percentages into male percentages; find an apparent chemical formula and an apparent formula mass for Torpex. b) Write a chemical equation for explosion of Torpex into the nominal products. c) What is the mass percentagc oxygen balance for Torpcx to carbon monoxide? 198 Tutorial Exercises 2-5. The organic compound bis(2,2-dinitropropyl) fumarate has the formula C 10 H 10 N 4 0 12 . It is a relatively dense explosive developed in about 1951. a) Classify this explosive as oxygen deficient, oxygen balanced, or oxygen rieb with respect to carbon monoxide formation. b) Write balanced chemical equations that describe the combustion, the formation, and the explosion of this explosive. c) The "heat of combustion" forthismaterial is reported as 3070 calfg. Take it that this reputed value is for constant pressure conditions with water formedas a liquid, and report the corresponding thermodynamic item "enthalpy of combustion" in kilo­ joules per mole. d) What is the corresponding "internal energy of combustion" in kilojoules per mole? e) What is the corresponding "internal energy of formation"? f) Compute a theoretical value for the "heat of explosion" of bis(2,2-dinitropropyl) fumarate. g) A "heat of explosion" describes the thermal energy release as a material explodes and so could be measured in a conventional but sturdy calorimeter. What ad­ ditional information is required for augmentation so that the total "energy of explosion", and also the relative strength of this material, can be computed? 2-6. Butanetrial trinitrate (BTTN), C4 H 7 N 3 0 9 , is an explosive plasticizer for cellulose nitrate. Its formula mass is 241 g/mol and its heat of combustion (Reference 3 of Chapter 2) is 2168 cal/g. a) Convert this heat of combustion into a molar enthalpy of combustion in metric units and also into an internal energy of combustion. b) What is its internal energy of formation? c) Write a material balance in form of a chemical equation for its explosion into nominal products. Then compute the molar internal energy of explosion and the corresponding heat of explosion as might bc measurcd in a sturdy calorimeter. 2-7. Butanetrial trinitrate, C4 H 7 N 3 0 9 , the BTTN of Exercise 2-6, could be obtained on paper through a transmutation of butane by substituting three nitrate (ON02) groups for three hydrogen atoms. a) On this basis, obtain an estimated internal energy of formation for butanetriol trinitrate. b) Compare this estimated value for the internal energy of formation of BTTN with that obtained by calorimetric methods in the laboratory, -365 kJjmol. c) Estimate the entropy for solid BTTN by the transmutation method of Table V. Compare with that indicated by the approximation of equation (2-9). 2-8. a) Write a chemical equation that describes the explosion of picric acid into nominal products. b) From values for the internal energy of formation for each component of this equation find the corresponding internal energy of explosion. c) Similarly, find the entropy of explosion. d) Compute a corresponding theoretical value for the Helmholtz free energy of explo­ sion of picric acid. e) What explosive strength does this thermodynamic calculation indicate? What Tutorial Exercises 199 explosive strength is indicated by the Berthelot approximation? Campare these calculated values with measured values reported in Table I. 2-9. a) Estimate the internal energy of formation of tetranitrotoluene using the group Substitution method. What is the corresponding "heat of explosion" (nominal products)? b) Estimate the entropy of solid tetranitrotoluene and also its entropy of explosion.
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