EXPLOSIVES 81J means adopted may be summed up under the two headings of (1) experiment alons, and (2) calculation and experiment combined. In the first category may be placed the experi ments of Roux and Sarrau, already noticed. By the second method, Berthelot (Force de la Poudre et Matieres Explosives, 1872) calculates the volume of gases which would be produced, and having ascertained the quantity of heat generated by the explosion, considers that their pro duct affords a term of comparison according fairly well with the results of experiment. Sarrau (E/ets de la poudre et des substances explosives, 1874), from a train of reasoning somewhat similar to that here followed, arrives at the con clusion that the explosive force is nearly proportional to the product of the heat of combustion by the weight of perma nent gases produced ; he obtains both these data by experiments carried out at the Depot central des Manufac tures de 1 Etat. The following table shows the results of the two methods: Explosive Substance. Relative Force. Sarrau. Berthelot. Gunpowder 1-00 * 3-06 4 - 55 1-98 1-49 1-82 1-08 i-oo 3-42 6-80 2-44 2-07 3-46 0-85 Gun-cotton Nitro-gl vcerin Picrate of potash Picrate of potasli and saltpetre Picrate and chlorate of potasli Chloride of nitrogen The plan pursued by Sarrau appears the more reliable of the two, in that he obtains by experiment the quantity of permanent gases evolved; the relative proportions he gives agree fairly well with those experimentally determined by him, in conjunction with Roux, for simple explosion. With reference to Berthelot s figures, it is a well known fact that nitre-glycerin, when not detonated, is very un certain in its action, so that in all probability it would never give its full theoretic force ; Sarrau seems nearer- its correct value. On the other hand, chlorine gas, liberated by the explosion of chlorate of potash and chloride of nitrogen, is very heavy, so that considerable variation may arise from estimating it by weight instead of volume. The mean of the results given by five descrip tions of gunpowder was adopted by Sarrau as his standard, and he estimates the pressure at about 5290 atmospheres, Noble and Abel have proved these figures to be consider ably too low ; and we shall, in all probability, be not far wrong if we multiply each of the ratios given in Sarrau s table by GOOD, in order roughly to show the pressure, in atmospheres, of equal weights of each of the substances in question exploded in about its own volume, but not detonated. Products We have considered the tension developed in a close vessel of com- O f constant volume. Let us now investigate the case of the alk>wd P r0( ^ uct3 f combustion being allowed to expand in a vessel to ex- impervious to heat, it having been conclusively proved pand. that with large charges the loss of heat by communication to the metal of a gun is relatively very small, and may practically be neglected. If V, P, and T be respectively the initial volume occupied by the substance, the maximum pressure, and the temperature of explosion, we shall deduce expressions for the pressure and temperature corresponding to any volume v, and the work done by the expansion of the permanent gases in the space v - V. It will simplify the calculation if we suppose that the gravimetric density of the substance is unity, that it fills the volume in which it is exploded, and that the charge is burnt before it commences to do work, either upon a projectile or otherwise ; even with gunpowder the correction due to this last assumption is not great, and the action of the more violent explosives may practically be considered instantaneous, especially when detonated. It has already been stated that, with most explosives, there is an ultimately solid or liquid residue, the products not being wholly gaseous ; with gun powder this residue is very considerable. As before, let p lie the ratio of the volume of the non-gaseous products at the instant of explosion ; then the original volume of gas and vapour will be V(l - p), and the expanded volume v-pV; for the sake of brevity these corrections will be made at the end of the calculations. As already stated, for gunpowder the value of p is about 6 ; it is relatively inconsiderable for the more violent explosive compounds. Starting with the fundamental relation for permanent gases, PV=KI. . " ....... (r), if we suppose the pressure to remain constant while the volume varies by an infinitesimal amount dv, the temperature will undergo pdv a corresponding variation ~^n~, and the gases gain or lose an amount of heat -^ , CP being the specific heat for constant pres sure ; similarly, if the volume be supposed to remain constant. while the pressure varies by dp, we have a gain or loss of heat c vd?) , c v being the specific heat for constant volume ; consequently, when both pressure and volume vary simultaneously, the gain or loss of heat is c,.vdp)=d/i ...... (2); and differentiating (1), pdv+vdp-Kdt ........ (3). Eliminating vdp between these equations, we get c ^ .pdv+ci dt = dh ...... (4) Again, if c be the specific heat of the solid residue, assumed to be constant, and a the ratio of its weight to that of tire gas and vapour, it is evident that the residue will part with an amount of heat, ac .dt, during an instant of the expansion while the temperature is lowered by an amount dt ; but, by our hypothesis, the heat given off by the residue is acquired by the gases ; therefore, dh = ffc .dt, ..... . . . (5); and (4) becomes, for the expansion from V to v, c )/ dt=-^ f V p J T K J V (6). Substituting for_p its value derived from (1), dividing both sides by t, and integrating, we have whence fpfv <=T /yc,i<r c ....... (3); making the correction for the volume of the solid or liquid residue
(9).
In a precisely similar manner, or more briefly by remembering
thatPV = UT, we find
C + ffc
?. . , . . do).
( V (TV)
But the definite integral f jidi; represents the work done by the y rk
^ V done by
expansion of the gas and vapour from the volume V to any volume the ex-
v, and from equation (6), pausioa
/ R(f + rc ) /"
pdv = - ( _ f V dt ..... (11).
^ * */ T
Integrating, and remembering that fp--c, = y, where J is Joule s
mechanical equivalent of heat, we get
W=J(c+<rc ){r-<} .... . (12);
or the work done is directly proportional to the loss of temperature
during the expansion.
Substituting the value above found for t, we have
but T(f, + <rc ) = H, the whole amount of heat generated by the
