M. R. Clausius on the Deportment of Vapour. 399 



by the last condition ; namely, that in which the vapour is sepa- 

 rated from water and left to itself to expand, and that in which 

 the vessel which contains the vapour contains water also, which 

 by its evaporation always replaces the quantity of vapour which 

 escapes. 



First, then, suppose a unit of weight of vapour at its maxi- 

 mum density to be contained in a vessel separated from water*, 

 and let the vapour expand itself by pushing back a piston for 

 instance. Let us suppose that the vapour in each stage of its 

 expansion exerts against the piston the entire expansive force due 

 to that stage. To eifect this, it is only necessary that the piston 

 should recede so slowly, that the vapour which follows it can 

 always adjust its expansive force to that of the vapour in the 

 remaining portion of the vessel. During the expansion so much 

 heat is to be communicated to the vapour, or abstracted from it, 

 as is necessary to its preservation in the saturated gaseous state. 

 The question is, what quantity of heat is here necessary. 



To this case the proposition expressed by Mr. Rankine and 

 myself applies. The work executed by the vapour in this in- 

 stance, and the quantity of heat consumed in its pi'oduction, are 

 so considerable, that, were this heat supplied from the vapour 

 itself, the latter would be cooled to an extent that would render 

 the retention of the gaseous condition impossible. It will there- 

 fore be necessary to communicate heat to it from without. 



The quantity of heat to be communicated, which corresponds 

 to an alteration of temperature dt, I have expressed in my former 

 memoir by hdt, where /* is a negative quantity ; so that the pro- 

 duct hdt for increasing temperatures is negative, and for de- 

 creasing temperatures is positive. The value of h in the case of 

 water I have expressed as a function of the temperature t in 

 equation (33.) ■\, thus : 



. ^on" 606-5-0-695^-000002^^-0-0000003/3 



273 + ^ 



If, therefore, the quantity of heat necessary to be communicated 

 to the unit of steam when its temperature changes from t^ to t^ 

 be called Q,, we have 



Q,= T'hdt, (1.) 



and from this we can readily calculate the value of Qj for each 

 particular case. For example, let the tension of the vapour at 

 the beginning be 5 or 10 atmospheres, and let the expansion be 



* For the sake of brevity I will always speak of water, although the same 

 hoUls Hubstantially true for all other fluids, 

 t lu the place cited, p. 621 . 



