Hate of Explosion in Gases. 93 



and nitrogen obtained from this immediately after the 

 explosion. 



fi = gram-equivalent (in this case, 84 grms.). 



From (1) and the equations of motion, we obtain 



aV 2 

 i ? -i>o= f rr(«o-v) (2)* 



v o 



This formula of Riemann assumes a relation to subsist 

 between Y, p, and v at all points of the wave ; and from it 

 the work performed by the wave during explosion may be 

 calculated. • - 



Work performed by the gas 

 fiY 2 



2v< 



( v -v y+p {v-v ) 



For the purpose of testing this result, it maybe shown that 

 the external work performed by the piston (fig. 1) is equal to 

 the work performed on the gas together with the gain of 

 kinetic energy. 



The work performed on the gas 



= fp - v o) 2 +Po( v o - «0 • 

 The gain of kinetic energy 



_ (V-«)V 



it V 2 Yv 



The external work performed by the piston 

 = p(v -v) 

 _ fj,Y 2 



m {vo-v) 2 +p (v -v). 



.*. External work performed by the piston 



= gain of kinetic energy -f work performed on the gas. 



Assume that in the explosion n molecules become m mole- 

 cules. For example, in the explosion of equal volumes of 



* Rayleigh's ' Sound/ vol. ii, j Schuster's note in the Bakerian Lecture 

 on Explosions, 



