CHAPTER III. 



MOTION OF ELASTIC FLUIDS. 



128. Work of the Expansion of Air. If air expands 

 without doing any work its temperature remains constant.* 

 It follows from this that as air changes its state, the inter- 

 nal work done is proportional to the change of temperature. 

 When, in expanding, air does work against an external 

 resistance, either heat must be supplied or the temperature 

 falls. 



Suppose a given mass of air to be confined in a cylinder 

 having a piston of one square foot area. Let v^ be the 

 initial volume and p l the initial pressure of the air, and 

 suppose the piston to move so as to expand the air to any 

 other volume v with pressure p. Then if heat is supplied 

 to the air during the expansion so that the temperature 

 remains constant, we have (Art. 48), 



(I) 



Now if we represent the pressures 

 by the ordinates, and the correspond- 

 ing volumes by the abscissas of a curve 

 AB referred to the axes OX, OY, the 

 curve represents the relative changes 

 of volume and pressure. Then OM = 



v l and M?! = p l is a point P t corre- Fig. 67 



sponding to a volume v and pressure 



/;,. Similarly (v, p) is any other point P of the curve cor- 



responding to a volume v and pressure p; and since each 



member of (1) is constant, the curve is a rectangular 



hyperbola. 



* This result was first demonstrated experimentally by Joule. 



