36 THE THERMODYNAMICAL PROPERTIES OF SUPERHEATED STEAM. 



It may be remarked here that the formula (a), viz. 



^(K P )= - s - (CK P ) 



furnishes us with the direct consequence that in any gas or vapour in which the 

 specific heat K P is independent of the pressure the product of K P and the cooling 



effect C must be independent of the temperature, and, as applied to the present case 



-\ \ 



of superheated steam, we have here that ~ (CK P ) = and g- (K P ) = directly from 



the experimental results, and, hence, satisfying relation (a) identically. 



Further, in any gas or vapour in which the specific heat K P is independent of the 

 pressure, and REGNAULT has proved this to be the case for many important gases, it 

 follows from equation (a) that the product CK P shall also be independent of the 

 temperature in that particular gas or vapour, and hence the equation (/S) for the cooling 

 effect, viz. 



dv 



is immediately integrable in the form 



g + CKp 

 T 



where f denotes some at present undetermined function. If we assume that at very 

 high temperatures all gases become approximately " perfect " ones, as was done by 

 RANKINE for steam, though the point is at present open to question, the form of the 

 function f is easily determined by comparison with the equation for perfect gases 



pv = RT, 



R being a constant for each particular gas, and we get for the actual equation 

 connecting the pressure, volume, and temperature in any gas 



p (v + CK P ) = RT. 



The form of this equation is identical with one deduced by JOULE and THOMSON,* 

 but it is here noticed in its connection with the actual condition of things in a gas in 

 which K P is independent of the pressure, and which approximates under high 

 temperatures to a perfect gas. We have, however, no evidence to show whether the 

 latter condition is true for superheated steam or not, but the last equation is certainly 

 not true for steam, as, from the data already found, simple calculations may be made 

 showing that R is not a constant but a function of the pressure. 



* Phil. Trans.,' 1862, p. 588, " On the Thermal Effects of Fluids in Motion." 





