32 SECTIONAL ADDRESSES. 



The actual measured value for a for copper at 150° C. is about 

 2-5 micro-joules per deg. C. per coulomb. Since the electric charge of 

 an electron is about 1-57 X 10~''' coulombs, the value of a for an electron 

 in copper would be 2-5 X 1-57 X 10"-'' X 10 ergs per deg. C, or 3-9x10-" 

 ergs per deg., while the corresponding quantity for a gas molecule is about 

 2 X lO""' ergs per deg. The measured value is considerably less than the 

 usual molecular value. We know, however, that for some metals it is 

 actually negative. This is no doubt due to the fact that, being a negative 

 charge, it gives up energy as it goes up potential at constant temperature, 

 and consequently less heat is needed to raise it one degree at any given 

 temperature. If only the Thomson effect could be reliably measured 

 important information could be obtained of clY'dT in each metal. 



Electrolytic Regions. 



I must now pass on to consider electrolytic regions, i.e. voltaic cells. 

 Volta's own theory was that the driving force was situated at the metal- 

 metal junction. His view was afterwards adopted by Lord Kelvin. 

 This is a sjiecially interesting fact because Kelvin was one of the first to 

 show that the energy of the current was supplied by the chemical actions 

 in the cell. This was afterwards slightly corrected by Helmholtz, who 

 showed that strictly E was a measure of the free energy per unit charge 

 and not of the total energy.'^ 



We can in fact no more ignore the heat taken in in this case than we 

 had a right to ignore the internal work done when dealing with the thermo- 

 electric circuit. 



We must be prepared to find that the osmotic conditions in voltaic 

 cells are different from those in metals. Consider the circuit of a Daniel) 

 cell : Zn—ZnSo^sol"— Membrane— CuSojSol"—Cu— outside circuit— Zn. 



The first difference is that it is not merely electrons that move. What 

 happens at the Zinc-Liquid junction ? We are not certain. Physical 

 chemists under the influence of Debye are revising their conceptions in 

 regard to solutions. The old dissociation theory assumed that positive 

 and negative ions moved about quite freely unless appropriate collisions 

 occurred, when combination might take place, the amount of combination 

 being calculable from the law of mass action. The theory was exceedingly 

 useful, but there was an outstanding difficulty in regard to ' strong ' 



■"' For a reversible action d\J = rfH — dW 



= T(/9 - Xrfa; 

 or (f{U - Tcp) = - 9rfT - X^dx. 



The quantity U — T9 is the free-energy, F, 9 = entropy, U = internal energy, X a 

 ' force ' doing work in the ' displacement ' x. 



Hence — dF = X.dx or the work done at constant temperature = decrease of F. 

 Now F depends onl\- on the state of the system, hence dY is a perfect differential, 

 and we have y^ = — 9, so that 



F = U+ Tl^l 

 ,)T la; 



or -U = T34(? 



Mt 



The expression for the internal latent heat on p. 31 is an example of this relation. 



