Starkweather — Thermodynamic Relations for Steam. 135 



increasing function of the temperature. Thiesen* in a recent 

 paper has shown that the total energy, expressed as a function 

 of v and T, is not linear in T, but it has never before been 

 shown, so far as the present writer can discover, that the 

 kinetic energy is not linear, although Massieuf has given a 

 complicated proof that the specific heat at constant pressure 

 increases with the temperature ; this, indeed, was contempo- 

 raneously done by Weyrauch.f Kegnault§ has found experi- 

 mentally the same fact for carbonic acid gas. 



This iact that f'(T) is an increasing function of T is so 

 important that it is well to speak of the proof more in detail. 

 We have from page 133 



/(T) — e s — tt s 



e 8 and tt s denoting respectively the values of the total and 

 potential energies on the saturation line. At 100° C, 150° C. 

 and 200° C. the values of e s are 254757, 259571 and 264336 

 respectively, and if the last number were increased by 49, e s 

 would be linear in T. On the other hand the corresponding 

 values of — 7r s are 1183, 3257 and 6441, the zero of potential 

 energy being that of indefinitely rare gas, and the last exceeds 

 a linear formula for ir s by 1110. Now it is impossible that by 

 any change of p-v-T equation, hence a change of the form 

 of 7r, the number 1110 can be reduced to 49. 



We have next a remarkable corroboration of our formulae, in 



particular of the factor — in the last term of the jp-v-T 



equation, by means of Kegnault's experimental determination 

 of the specific heat at constant pressure. At temperature 

 403°*7, pressure 760 mm , the volume is found by the p-v-T 

 formula to be 1*8018 cubic meters per kilogram. We have 

 then, if Q 1 is the quantity of heat necessary to turn one kilo- 

 gram of water at 0° C. into this state at constant pressure, 

 € = jQ^pfv—w) = JQ i - 18609 . 



But from the formula for e on page 133, since we know (page 

 134)/(403*7) = 259932, we have e = 258909, hence JQ X =277518. 

 Similarly at temperature 473°*7, pressure 760 mm , we find the 

 volume to be 2*1314. We thus obtain in the same way 



JQ 2 = 292035, 



Q 2 being the supply of heat necessary to turn one kilogram of 

 water at 0° C. into steam of this second state, at constant 

 pressure. 



*Wied. Ann., 1897, No. 13, p. 329. 

 f Mem. des Savants Etrangers, vol. xxii, p. 58, 1876. 

 i Zeitschr. des Ver. Deutsch. Ing., xx, pp. 1, 71, 1876. 

 § Mem. of the Institute of France, vol. xxvi, pp. 128, 129. 



