- ? ) =0, 



130 Mr Bevan, On the Joule-Thomson Effect 



Consider again the original equation for the cooling effect 



the actual cooling effect -r— being f{&). 



To integrate this equation we are not justified in regarding 

 C p as independent of 6 and p and using any empirical formula 

 for f{6) which fits the observations more or less accurately. The 

 change of C p with temperature is considerable when p is large 

 and 6 small. For example at 10 atmospheric pressures the value 

 of C p for air at - 50° 0. is -254 and at - 140° C. it is - -408*. 



The dependence of C p on the pressure is however of not so 

 much account as that on the temperature. Regnault assumed 

 that C p was independent of the pressure. This is only an approxi- 

 mation, but it leads to results not very far from expressing the 

 experimental data. If we make this assumption we have 



dCp 

 dp 

 and therefore by the relation we have already used 



and integrating this 



dv\ 



dd) p 



is a function of p only, and 



v = $4>(p) + ^ (p). 



This equation has a fairly wide range of applicability, but is 

 of course not generally true, as is at once shewn by the experi- 

 mental numbers for the expansion coefficients for gases at constant 



pressure. However, for a wide range the variation of ^) , owing 



oojp 



to changes in 6, is small ; and so the quantity -^) is at any rate 



very small, and for an approximation we may assume that in 

 the small term, representing the cooling effect, C p is independent 

 of p. 



Equation (2) with this assumption becomes 



£=<M*>) + <M0) (3), 



* Rapports, Gongres de Physique (Paris, 1900) i. p. 686, 



