120 Mr. W. J. M. Rankiue on the Mechanical Action of Heat. 



at the higher temperature : let the vapour then be allowed to 

 expand, being maintained always at the temperature of saturation 

 for its density, until it is restored to the original temperature, at 

 which temperature let it be liquefied : — then the excess of the heat 

 absorbed by the fluid above the heat given out, ivill be equal to 

 the expansive 'power generated. 



To represent those operations algebraically, let the lower 

 absolute temperature be Tq : the volume of unity of weight of 

 liquid at that temperature, t-Q, and that of vapour at saturation, Vf,: 

 let the pressure of that vapour be Pq : the latent heat of evapo- 

 ration of unity of weight, L^ : and let the corresponding quan- 

 tities for the higher absolute temperature t,, be v,, Vj, P,, L,. 

 Let Kl represent the mean apparent specific heat of the sub- 

 stance in the liquid form between the temperatures Tq and Tp 

 Then,— 



First. Unity of weight of liquid being raised from the tempe- 

 ratui'e Tq to the temperature t,, absorbs the heat 



Kl(ti-To), 



and produces the expansive power. 



J ■Of, 



dv . P. 



Secondly. It is evaporated at the temperature Tj, absorbing 

 the heat 



and producing the expansive power, 



p,(V,-^0- 



Thirdly. The vapour expands, at saturation, until it is restored 

 to the original temperature Tq. In this process it absorbs the heat 



f'dr . Ks, 



and produces the expansive power, 



■»v„ 



A 



dV.T. 



Fourthly. It is liquefied at the original temperature, giving 

 out the heat 



and consuming the compressive power, 



Po(Vo-^^o)- 

 The equation between the heat which has disappeared, and 

 the expansive power which has been produced, is as follows : — 



