174 Mr. W. J. M. Rankine on the Mechanical Action of Heat. 



"WTien Frencli measures are used in the calculation, the following 



is the result : — 



v=l cubic centimetre per gramme, 

 '57=1033"3 grammes per square centimetre, 



_, ,, = 46' 78 metres per Centigrade degree, ] 



= 153-48 feet > ' ^^ 



or 85*27 feet per degree of Fahrenheit. J 



The difference, which is of no practical importance in calcu- 

 lating the power of the steam-engine, arises in the estimation of 

 the density of liquid water. 



(22.) Unit of weight of steam at saturation, of the elasticity 

 Pj and volume V, corresponding to the absolute temperature Tj, 

 being cut off from external sources of heat, it is now to be inves- 

 tigated what amount of power it will produce in expanding to a 

 lower pressure Pg and temperature Tg. 



It has already been shown at the end of the second section, 

 that if vapour at saturation is allowed to expand, it requires a 

 supply of heat from without to maintain it at the temperature 

 of saturation, otherwise a portion of it must be liquefied to sup- 

 ply the heat required to expand the rest. Hence, when unity of 

 weight of steam at saturation, at the pressure Pj and volume Vj, 

 expands to a lower pressure P, being cut off from external sources 

 of heat, it will not occupy the entire volume V corresponding to 

 that pressure, according to equation (38), but a less volume 

 S = mV, 



where m represents the weight of water remaining in the gaseous 

 state, the portion 1—m having been liquefied during the expan- 

 sion of the remainder. The expansive action of the steam will 

 therefore be represented by 



y^'^^S.P (43) 



The law of variation of the fraction m flows from the following 

 considerations : — 



Let Bm represent the indefinitely small variation of m corre- 

 sponding to the indefinitely small change of temperature Br; 

 L, the latent heat of evaporation of unity of weight ; Ks, as in 

 equation (30), the specific heat of vapour at saturation, which is 

 a negative coefficient varying with the temperature; then we 

 must have 



— liBm = mKs St, or — = — ^p- St, 

 m L 



in order that the heat produced by the liquefaction oiBm may be 



