A— MATHEMATICAL AND PHYSICAL SCIENCES. 27 



Group IV.— Electric condensers, 



rfH=C,rfT-T|^ dq. dW=-Ydq. 

 di-9 

 In neither Group III nor Group IV is dH. = dW. 



These equations are all derived in the same way as for Group I — or 

 alternatively they can be written down at once by analogy. Work can 

 take various forms, but heat and work are always related in the same 

 way thermodynamically. 



Surely a contemplation of these cases should act as a deterrent against 

 assuming the equality of heat entry and external work done. 



Only in a particular case of Group I is the heat entry a measure of the 

 isothermal work. Hence those who claim that in the thermoelectric 

 case 7C is a measure of V must show that the conditions are analogous to 

 those of a perfect gas, or at least of a fluid whose characteristic equation 

 isp=T/(i'). 



In all the literature on this subject I find no realisation by the 

 combatants that both sides might be asserting the same thing. 



Now does electricity behave as a perfect gas when it flows through a 

 conductor — through a copper wire, for example ? 



Attempts have been made to calculate the conductivity of a wire by 

 assuming that the electrons constitute a perfect gas ; but, as is well 

 known, all these attempts have broken down. The answer to the question 

 can, however, be found in another way. When Kelvin, in conjunction 

 with Joule, wished to find the difference between real gases and the ideal 

 gas he passed the gas through a porous plug. If the gas became warmer 

 or cooler in passing through (although no heat was admitted) he knew 

 that the gas was not perfect. Experimentally, air became cooler and 

 hydrogen hotter. The difference of behaviour depends entirely upon the 



value of T^— r for the gas. No heating or cooling would be obtained 



if this expression is zero ; or, writing it in an integral form, if v=Tf{p). 



Now every time that you pass electrons through a conductor you are 

 conducting a porous plug experiment. The electrons pass through the 

 mesh of atoms like molecules of fluid through a porous solid, and in every 

 case warming takes place (the Joulean heat). It is true that in the 

 electrical case when conducted adiobatically the temperature goes on 

 rising ; i.e. it is never possible to reach the stationary state for which easy 

 calculation becomes possible. But in principle the same thermodynamics 

 applies to all these phenomena, and the fact that warming occurs is 

 sufficient to prove that the electrons do not flow as a perfect gas. 



This being so we are obliged to conclude that the isothermal heat 

 entry at a junction between two metals is not equal to the external work 

 done at the same junction, i.e. that the Peltier coefficient is not a measure 

 of the voltage drop at that junction. 



The Electron considered as a Solute. 



The developments in our knowledge of the electron since 1895 have 

 placed the subject on a new footing. When Sir William Thomson (Kelvin) 

 first gave an explanation of thermoelectric phenomena he spoke of a as 



