20 Sir G. Greenhill on 



Take a pound of gunpowder, and explode it in a closed 

 steel vessel o£ volume C inches 3 ; and suppose the fraction (3 lb 

 was solid and non-gaseous, leaving 1 — >S lb in a state of 

 gas. 



In a rise of temperature of dT degrees Fahrenheit (F.) 

 the heat dH, in British Thermal Units (B.T.U.), given out 

 by the non-gaseous part, of S.H. \, is given by 



dR=-l3\dT (2) 



Denoting the volume of the non-gaseous part by «, the 

 gaseous part, 1 — /31b, obeys the gas-equation 



JPfo-")_ Pnfoo — «) /»\ 



T ~ T ' ■■''■/ w 



where T, T denote absolute temperature F. ; so that, taking 

 logarithmic differentials, 



dp dv dT „ . . x 



p V—OC. 1 



and then with (2), 



?--*<£+£) <*> 



Supposing^? and v to vary one at a time, 



7\TT 7^1-T 



dB. = ^— dp (v constant) + -^r— dv (p constant), ((]) 



where, when p varies while v is constant, 



and when p is constant and u varies, for 1 — yS lb of gas, 



f = WM=( 1 -^I = (1-/ 3 )C ? ^ ) • (8) 



C», C p denoting the S.H. of the one lb of gaseous product at 

 constant^volume and constant pressure ; so that (6) becomes 



f = (1-/9)0 f +(1-/8)0,^ . . (9) 



