Mr Searle, The Expansion of a Gas, etc. 247 



Thus H=[ t C p ,dt, 



it" 



II --/' C n .dt-j ' C p ,dt. 



t p 



Here we must specify that the specific heat is that at the 

 constant pressure p', for in an imperfect gas the specific heat 

 may depend upon the pressure 1 . Since the specific heat G p 

 depends only slightly upon the temperature in the case of actual 

 gases, we see that the correction to be applied to the change of 

 temperature observed in the actual determination is approxi- 

 mately equal to that which occurs in the Thomson- Joule experi- 

 ment, when the initial temperature is t and the pressure falls 

 from p to p. 



The results obtained by Thomson and Joule' 2 for air show that, 

 when p is one atmo and t is 373° on the absolute scale, there is a 

 cooling of about one-seventh of a degree for a fall of pressure of one 

 atmo, or about 1/7000 degree for a fall of pressure corresponding 

 to one centimetre of water. Thus, if the difference of pressure 

 correspond to h cms. of water, we have approximately 



t"-t = - A/7000. 



Thus, approximately, 



Hence, if the pressure of the air on entering the spiral exceed 

 its pressure on leaving the spiral by so much as corresponds to 

 10 cms. of water, the correction to be applied to the observed 

 difference of temperature is only about 7 ^ degree. The differ- 

 ence of temperature would probably never be less than 10° C. 

 in an actual experiment, so that the correction is practically 

 negligible. 



If the results of the Thomson-Joule experiment be not known 

 for any particular gas, the correction can still be calculated when 

 the characteristic equation of the gas is known. To simplify the 

 calculation in the case of a gas obeying Van der Waals' equation, 

 terms involving the product ab and squares and higher powers 



dC d 2 v 



1 Since for any substance -=-^ = - 1 -r^—^ , it follows that the characteristic 

 clp t dtp* 



equation of a substance, for which G,, is independent of the pressure, is 



{v+f(p)}(l{p) = nt, 



where /(}>) and g (j)) are any functions of p. If this equation is not satisfied, 

 C v will depend upon the pressure. 



- Lord Kelvin, 'Mathematical and Physical Papers, Vol. r. p. 419. 



