136 Starkweather — Thermodynamic Relations for Steam. 



Accordingly, we find for the mean specific heat at atmo- 

 spheric pressure from 403°'7 to 473°*7 



n = ^~ Q \ = 0-4846 



p 473-7 — 403-7 



or only 0*9 per cent greater than Regnault's mean specific 

 heat at atmospheric pressure from about 401 o, 7 to 490 o, 7, 

 namely 0-4805. When one considers that this deviation could 

 be cancelled by a diminution of less than 0*05 per cent in the 

 latent heat at 200° C, which is far within the limits of error, 

 the essential corroboration of the formulae is evident. 



Gray * has attempted to show that Regnault's experiments 

 on the specific heat of superheated steam give a value of 

 0-3787. He does this by comparing the total heat at 100° C. 

 with the quantities of heat obtained in the experiments on 

 superheated steam. But this is not allowable, as Regnaultf 

 himself distinctly states, and he would not even compare the 

 heats in different series of experiments. In fact if the latter 

 be compared some absurd results are obtained. 



We have now to express /(T) by a formula. To get as high 

 a determination as possible the writer has taken Regnault's 

 second determination of the mean specific heat at constant 

 pressure, namely that from 138° C. to 226° C. at atmospheric 

 pressure it is 0-48111. Assuming this to be true from 130° to 

 230°, we obtain the quantity of heat necessary to heat the 

 steam at atmospheric pressure between those temperatures. 

 Adding this to JQ X found on page 135 we obtain the quantity 

 of heat necessary to heat water at atmospheric pressure from 

 0° C. into steam at 230° C, JQ 3 . At the latter state the volume 

 is 2*2713, so subtracting^ (2-2703) from JQ 3 we find the energy 

 at this state. From the energy formula /'(T) is found to be 

 275278. 



It will be noticed that at low temperatures f"(T) apparently 

 changes sign. This is entirely dependent on the formula 

 chosen for total heats at those temperatures. In the preceding 

 article, in forming the expression for the total heats from 0° C. 



to 100° C. 4 it was assumed that since -jy was negative above 



at 



100°, it was probably so below. Under this assumption we see 



f"(T) to change sign. On the other hand, if we make^^T) of 



one sign throughout, namely positive, -=-5 must change sign. 



Now it is far more probable that the latter does so, for it 

 concerns only a particular set of states, namely those on the 



* Phil. Mag., xiii, p. 337, 1882. 



f Mem. of the Institute of France, vol. xxvi, pp. 165, 166. 



