128 Mr Bevan, On the Joule-Thomson Effect. 



We have therefore 



%\- V = G *fW (1 >' 



where f(0) represents the cooling effect. 



Differentiating equation (1) with respect to we obtain 



Now we have, if u is the total energy of the gas, </> the entropy 

 and dq the heat added in any process which is only an infinite- 

 simal change 



dq = 0d<f> = du + pdv, 



and therefore G p = 6 ~^ ) , 



oa/p 



and by Maxwell's fourth thermodynamical relation 



dj>\ _dv y 



dpj e dd 

 ., , d*<j> d*v\ 1 dC p \ 



sothat w9 ss -dfi), =s e'dpJ. t 



a &v\ dC p \ 

 We have therefore 



r JQ 



multiplying this equation by f{&) and writing I -7jW\ =z > we ^ ave 



^{o P f(e)}+l{G p /(d)} = o, 



and therefore 



G p f{6) = F(p-z). 



We thus obtain from equation (1) 

 Integrating this equation we obtain 



Ir+W+J^^tf (2). 



where <£ (jp) is a function of p only. 



