CHAPTER IV. 



ON THE PRESSURE VARIATION OF SPECIFIC HEAT IN LIQUIDS. 



21. Introductory. The measurement of the specific heat of a liquid in its 

 relation to pressure is surrounded by so many difficulties that any method 

 which gives a fair promise of success deserves to be carefully scrutinized. 

 During the course of my recent work on interferometry I have had this in 

 view, and the plan which the present paper proposes is particularly interesting, 

 as it seems to be quite self-contained. 



22. Equations. If $, p, P, c denote the absolute temperature, the pressure, 

 the density, and the specific heat of constant pressure, respectively, of the 

 liquid, and if a' (dv/v}/dd is its coefficient of volume expansion, the relation 

 of these quantities may be expressed by the well-known thermodynamic 

 equation 



(i) 



where J is the mechanical equivalent of heat, and the transformation is along 

 an adiabatic. The main difficulty involved would therefore be the measure- 

 ment of the temperature increment ; for dp could be read off with facility on a 

 Bourdon gage after a partial stroke of the lever of my screw compressor. 

 It is my purpose to find dd by the displacement interferometer. To fix the 

 ideas, suppose the liquid in question is introduced into a long steel tube TT, 

 figure 40, and that the tubulure p conveys the increments of pressure dp. 





c 



& 



FIG. 40. 



This end p is rigidly fixed. The other end q of the tube is free to move. By 

 aid of the stylus e, the elongation is registered on the plate n of a contact 

 lever d, read by interferometry, the lever being identical in construction with 

 that in the apparatus (fig. 29) described in the preceding paper on magnetic 

 elongation. Thus the interferometer will indicate the elongations due both 

 to the pressure increment and to the corresponding temperature increment 

 of the suddenly compressed liquid, and it becomes a question to what degree 

 the two may be adequately separated. If A/, Ap, A$ are corresponding 

 increments of the length / of the tube and the pressure and temperature of its 

 liquid content, we may write successively, if Al = Al'+Al", etc., 



(2) A/Y/=(ri 2 /3&02 2 -n 2 )) A = /3A, (say), 



(3) Al"/l = aM 



37 



