Joule- Thomson Thermal Effect. Ill 



probably do not know tbe value of 6 for any single case 

 within 10 per cent., seems to be a good deal wide of the 

 mark. 



Our discussion further supplies an answer to the critique 

 on Clausius's formula expressed by Natanson*" in his able 

 memoir on the Joule-Thomson effect. He affirms that the 

 results of the experiments render the existence of any physical 

 quantity corresponding to Clausius's /3 — styled C in this 

 paper — improbable. As a matter of fact, the experiments 

 give no evidence at all on this point ; for the disputed con- 

 stant enters only into terms which involve the second order 

 of small quantities, terms which would be insensible in any 

 " porous plug " experiments hitherto performed. 



(4) Some Thermodynamical Consequences of Joule and 

 Thomson s Experiments. 



(a) The Relation beticeen the Intrinsic Energy of ordinary 

 Gases and their Volume. — If a substance — whether gaseous 

 or not — be allowed to expand infinitesimally without doing 

 work or gaining heat, as in a " porous plug " experiment, we 

 know that 



d(U+pv)=0; 



if at the same time its temperature falls through a range dT, 

 we must communicate to it an amount of heat (reckoned in 

 ergs) = J . K c . dT if we desire to restore the substance to its 

 initial temperature without gaining or expending work. 



Hence any infinitesimal isothermal change in the intrinsic 

 energy may be calculated as follows : — 



1st. Let the substance expand through a porous plug till 

 its final volume is attained ; the gain of internal energy is 

 — (pdv + vdp) and the fall of temperature dT. 



2nd. Heat the substance at constant volume till its initial 

 temperature is regained ; this increases the intrinsic energy 

 by an amount J . K v . dT. Hence 



c7 T U= — pdv — vdp-\- J . K„ . dT. 



This is true for all substances ; to apply it to gases we 

 proceed as follows : — 



Writing T 6 



n lh 



as is done by Joule and Lord Kelvin, we obtain 

 c/ T U= -pdv- ( r+ jj . J . Kv)dp; 



* TViecl. Ann. xxxi. p. 502. 



