Page 28 - Battery Reference Book

Relationship between electrical energy and energy content of a cell 1/13

supported by imeasurement on the Daniel1 cell. When electrical energy nFE is dissipated in the circuit as
the reaction heat.
According to the Gibbs-Helmholtz equation,
Zn + CuSOd.(aq.) = Cu + ZnS04(aq.)
is carried out in a calorimeter, an evolution of heat (1.18)
of 50.13kcal occurs, which agrees well with the value
of 50.38 kcal obtained for the electrical energy yielded putting w' = n FE and dw'ldT = n F(dEldT),
by the reactio'n. This agreement, however, has since
proved to be a coincidence. In other cell reactions, the
electrical ener,gy is sometimes less, sometimes greater, (1.19)
than the difference in heat content of the system. In the
former case, the balance must appear as heat evolved Le.
in the working of the cell; in the latter case heat must AH(J) = -nF [. - T ($)d
be absorbed by the cell from its surroundings and to
maintain the conservation of energy it is necessary to
have
(1.201
w'=-H$q (1.16)
where w' is the electrical energy yielded by the cell
reaction, -H the decrease in heat content of the system
and q the heat absorbed in the working of the cell. where dEldT is the temperature coefficient of the
It is necessary, therefore, to determine the heat electromotive force at constant pressure.
absorbed in the working of the cell before the electrical Comparing Equation 1.19 with Equation I. 16 it can
energy yield of the cell can be found. be seen that
In methods for the accurate measurement of the
electromotive force of a cell, the electromotive force of (1.21)
the cell is balanced by an applied potential difference.
If the applied potential difference is slightly decreased, corresponds with the heat absorbed in the working of
the cell reaction will go forward and the cell will do the cell. Thus
electrical work against the applied potential difference.
If the applied potential difference is slightly increased, q = w' - (-AH)
the reaction will occur in the reverse direction and = nFT (%Ip
work will be done by the external electromotive force (1.22)
on the cell. The reaction thus occurs reversibly in
the cell when its electromotive force is balanced by
an outside potential difference. When a reaction goes where q is the heat absorbed in working the cell, w' is
forward under these conditions, Le. when the tendency the electrical energy yielded by the cell reaction, and
of the reaction to go is just balanced by an external -AH is the decrease in heat content of the system.
force. the maximum work that the reaction can yield The sign of q thus depends on the sign of the
is obtained. In a reaction at constant pressure, work temperature coefficient of the electromotive force:
is necessarily done against the applied pressure if If dEldT is positive, heat is absorbed in the working
any volume change occurs anid this work cannot be of the cell, i.e. the electrical energy obtained is
obtained as electrical energy. The electrical energy greater than the decrease in the heat content in the
obtained under these conditions is: therefore, the net reaction.
work of the reaction.
For n equivalents of chemical reaction, nF w' - (-AH) is positive
coulombs are produced. If E is the electromotive force
of the cell, an applied potential difference E is required If dEldT is negative, heat is evolved in the working
to balance it. The electrical work w' done when the of the cell, i.e. the electrical energy obtained is less
reaction goes forward in a state of balance (or only than the decrease in the heat content in the reaction.
infinitesimally removed from it) is thus nFE. and this
is equal to the net work of the reaction. Thus w' - (-AH) is negative
w' = IZFE (1.17) If dEldT is zero, no heat is evolved in the working
of the cell, Le. the electrical energy obtained is
It should be observed that w' is the electrical work done equal to the decrease in the heat content in the
against the applied potential difference. If there is no reaction.
opposing potential difference in the circuit, no work is
done against an applied potential difference, and the w' - (-AH) = 0