248 



Mr Searle, The Expansion of a Gas, etc. 



of a and b may be neglected. The equation then takes the 

 modified form 



pv—pb + - = Rt 



.(12). 



Let the points A, B in the figure represent, on the pv diagram, 

 the state of the gas on entering and leaving the spiral. Then, in 

 finding the difference between V, the energy of one gramme of 



l 



\ {p,v,t) 



e \^ 



D(j!»"') E 





d 



j [p' t V 



f 







h 





Fig. 1. 



gas at B, and U the energy at A, we may take the gas by any 

 path we please. The most convenient path is A CB, which is 

 made up of the isothermal AC passing through A and the 

 isopiestic CB passing through B. Let the areas into which the 

 diagram is divided by lines of constant pressure and constant 

 volume be indicated by the letters placed in them. If C p > be the 

 specific heat at the constant pressure p' and if Q be the heat 

 absorbed by one gramme of gas as it expands, at constant tem- 

 perature, from A to C, we have 



work done in path A CB 



U'-U=Q+ C p ,dt 

 = Q+j C p ,dt- 



(e + g + h). 



But 



J P dp t 



p' . dv 



dt r 



dp, 



the temperature having the constant value t in the last two 

 integrals. 



Now, if H ergs of heat be absorbed from the calorimeter by 

 each gramme of gas as it passes through the spiral, 



pv-p'v' + H=U'-U. 



