THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
277 
molecule of reaction without change of temperature, 8A is null as above in the equi¬ 
librium state at each temperature, so that SAq = - EJ log K'. And, with partial 
differentiation, dlclT. (SA/T) = djclT (SAq/T), hence it is equal to - R, djdT ..log K' 
~ ^{ d ^ log K, and is independent of the unknown term Aq. Now revertino* to 
the general theory, if E is the energy in a system, r/H the heat imparted to it and 
f/W the work done to it, fZE = cZW -{- r/H = c/W + T dcj) and A = E ~ T<j!) -f T^, 
where A, E, T, are all analytical functions of the state of the system. I'hus, 
employing total differentials, d{A/T)=-EdT/T~+dE/T-d(li=-EdT/T-+dW/T\ 
so that in the present case d{SA/T) = - SE.eZT/T^ + dSW/T. If the small amount 
of reaction represented by 8 occurs so that no mechanical work is done on the system, 
8W is null; hence 8E is equal to 8H the amount of heat taken into the system from 
its surroundings per molecule of the reaction when it proceeds without work. Thus 
finally 8H = - T^d/dT (8A/T) = E^T^ d/dT (logK), which is the thermal relation 
developed by van’t Hoff.* 
On the Electromotive Forces established by Finite Diffusion. 
63. The function of an osmotic partition in preventing by pure constraint the 
diffusive degradation of energy (§ 54) is illustrated by the theory of electromotive 
forces of diffusion. In the concentration-cells, of which the theory was established 
by VON Helmholtz, the solution in each cell was homogeneous, and the influence of 
concentration was determined by balancing different cells against each other : there 
being no diffusion, the process svas reversible, and thermodynamic formula were 
applicable. By forming an electrode of a metal surrounded by one of its insoluble 
salts, such as mercury surrounded by calomel, employing for the other one zinc 
immersed in zinc chloride solution, the net constitutive change at the mercuiy 
electrode when electricity passes through the cell is independent of the concentration 
of the solution, being simply the deposition of the equivalent quantity of mercury 
from undissolved calomel : hence that electrode accounts for a constant part of the 
electromotive force. On the other hand the change of free energy by dissolution of 
the equivalent of zinc is made up of a part arising from change of chemical constitu¬ 
tion and another part depending on the concentration of the solution which receives 
the resulting chloride. The part of the electromotive force depending on the 
processes at the zinc electrode is thus in the case of a reversible electrode equal to 
const.—RT log 2 ?, where p is the osmotic pressure of the zinc chloride solution and R 
* D/. WiLLARv Gibbs, loc. cit. p. 231, where the case of gaseous reactions was treated. More directly, 
we can form a reversible Carnot cycle in which the constitutive change cA is made at temperature T 
and unmade at T - dT. The work of the cycle must be . rZT/T, where ch is the heat absorbed in the 
change when the maximum amount of mechanical work is done in it by osmotic or other appliances : 
thus . dT/T = dT.d cA/dT, so that ch = Td cAjdT. When no work is done in the change, the heat 
absorbed is ^H, equal to ch - BA, which is - T^d/dT (SA/T) as above. 
