BRIDGMAN. 



THERMODYNAMIC PROPERTI KS OF WATKR. 



351 



g " LOO .90 .80 



U Volume, cm.^ per gm. 



Figure 10. The pr(>ss(ire coeffi- 

 cient of water as a function of the 

 volume. 



ties of thermotlynamic interest involve the specific heats, and these 

 in turn involve the second temperature derivative of the volume. 

 The first of these quantities is the specific heat at constant pressure. 



This is given by the thermodvnamic equation ( -~ ] = — tI .-^] . It 



\OpJr \PV/P 



will be seen that only the derivative of the specific heat is given by 

 the data as directly determined. In 

 order to obtain the specific heat itself, 

 the derivative, obtained from the ta- 

 bles in a manner already described, 

 must be integrated. This integration 

 was performed mechanically, in the 

 same manner as the integration for 

 the mechanical work of compression. 

 The results are shown in Figure 11. 

 The values for the specific heat as a 

 function of temperature at atmos- 

 pheric pressure were taken from the 

 steam tables of Marks and Davis. ^ 

 These values seem to be open to some slight question at the present 

 time due to experimental work done by Bousfield ^ since the publica- 

 tion of the tables, but in any event the possible error is slight, too 

 slight to be visible on the scale of the figure. The curves show the 

 now expected abnormalities at 0° and 20°. The striking feature 

 about the curves for the higher temperatures is the very rapid increase 

 of the specific heat with rising temperature at the higher pressures. 

 The specific heat at first decreases on all the curves except at 0°, 

 but passes through a minimum, and then increases. The pressure of 

 the minimum rapidly becomes less with rising temperature, and is 

 situated at 6500 kgm. for 40°, 5500 kgni. for 60°, and at 1100 kgm. 

 for 80°. At 80° the specific heat rises rapidly beyond the minimum, 

 reaching the value 1.17 at 12000 kgm. 



Any valid characteristic equation should predict the behavior of 

 the specific heat at high pressures as well as giving the volume in terms 

 of pressure and temperature, since from the equation the second tem- 

 perature derivative of the volume may be found. The equation of 

 Tumlirz ^° has been mentioned in the preceding paper as gi^^ng per- 

 haps as good agreement as any with the previously known facts over 



8 Marks and Davis, Steam Tables. (Longmans, Green, and Co.) 



9 W. R. and W. E. Bousfield, Trans. Roy. Soc. (A), 211, 199-251 (1911). 



10 Tumlirz, Sitzber. Wien, Bd. 68, .\bt. Ila (Feb., 1909), pp. 39. 



