244 



ilie work which must be done on 1 couh)mb of free electrons, when 

 these are transferred at a temperature T from the metal A (where 

 thev may be contained between the planes F^ and F^ to the metal 

 B (where they may then be contained between the planes F\ and 

 F\). It is clear that peculiarities in the boundary layer between 

 the two metals can be left out of consideration. This work is equal 



to ub - — ua + \ p dv, where the quantities u and v relate to 1 coulomb. 



The expression i-epresents the heat absorbed at the transfer from A 

 to B, or the heat developed at the transfer from B to A. Passing 

 to the quantities U and V, which refer to the molecular quantity, 

 the PELTiER-effect, expressed in Joules, becomes 



^B 

 n=\0-' . — \ub- Ua-\- (pdv\ (5) 



Ne 



""a 



We shall only consider what this expression leads to for the low 

 temperatures. In the first place we remark that the first term in 

 the second member of equation (20) of the former paper, the zero 

 point pressure a V~^'^, does not give a contribution for the Peltier- 

 efFect. This corresponds to the remark made in § 4 of that paper, 

 that at the adiabatic expansion of an ideal gas at 7^=0 external 

 work is done at the expense of the zero point energy. The second 

 term in the development of U and /; for low temperatures gives : 



n=.\^-' .—.^hT'^Vn'-VA') (6) 



JSe 



If attention is paid to the units in which F and TI are here 

 expressed, it is immediately seen that the Kei.vin's relation between 

 n and F is satisfied. 



It appears that the PKLTiEU-effect in approaching to J'=0 will 

 decrease to and that the decrease ^vill finally take place accord, 

 ing to 2'\ 



§ 5. The TFiOMSON-e^(?c/. Applying a reasoning similar to that 

 of the former section to the TnoMSON-efFect we find, that, as is 

 well known, the TuoMsoN-coefficient a represents the specific heat 

 for the free electrons if in healing the volume of the electrons 

 considered is changed so thai the electron gas as a "saturated vapour" 

 remains continually in equilibrium with the electrons within the metal 

 atoms (which also change in temperature). Hence it is the specific 



