+ plate Liquid - plate
x. PbO2 + y. H2SO4 + z. Pb
n. H2O
After
+ plate Liquid - plate
(x-p). PbO2 (y-2p). H2SO4 (z-p). Pb
{ }+{ }+{
p. PbSO4 (n+2p). H2O p. PbSO4
During charge, the substances are restored to their
original condition: the equation is therefore reversed.
An equation of this general nature was published by
Gladstone and Tribe in 1882, when Oley first suggested the
``sulphate', theory, which was based on very numerous
analyses. Confirmation was given by E. Frankland in 1883,
E. Reynier 1884, A. P. P. Crova and P. Garbe 1885, C. Heim
and W. F. Kohlrausch 1889, W. E. Ayrton, &c., with G. H.
Robertson 1890, C. H. J. B. Liebenow 1897, F. Dolezalek
1897, and M. Mugdan 1899. Yet there has been, as Dolezalek
says, an incomprehensible unwillingness to accept the
theory, though no suggested alternative could offer good
verifiable experimental foundation. Those who seek a full
discussion will find it in Dolezalek's Theory of the Lead
Accumulator. We shall take it that the sulphate theory is
proved, and apply it to the conditions of charge and discharge.
From the chemical theory it will be obvious that the
acid in the pores of both plates will be stronger
during charge than that outside. During discharge
the reverse will be the case. Fig. 19 shows a curve
Fig. 19.
of potential difference during charge, with others showing
the concurrent changes in the percentage of PbO2 and the
density of acid. These increase almost in proportion to
the duration of the current, and indicate the decomposition
of sulphate and liberation of sulphuric acid. There are
breaks in the P.D. curve at A, B, C, D where the current
was stopped to extract samples for analysis, &c. The
fall in E.M.F. in this short interval is noteworthy;
it arises from the diffusion of stronger acid out of the
pores. The final rise of pressure is due to increase
in resistance and the effect of stronger acid in the
pores, this last arising partly from reduced sulphate and
partly from the electrolytic convection of SO4 (see also
Dolezalek, Theory, p. 113) . Fig. 20 gives the data for
discharge. The percentage of PbO2 and the density here
fall almost in proportion to the duration of the current.
The special feature is the rapid fall of voltage at the end.
Several suggestions have been made about this phenomenon.
The writer holds that it is due to the exhaustion of the
acid in the pores. Plante, and afterwards Gladstone and
Tribe, found a possible cause in the formation of a film
of peroxide on the spongy lead. E. J. Wade has suggested
a sudden readjustment of the spongy mass into a complex
sulphate. To rebut these hypotheses it is only necessary
to say that the fall can be deferred for a long time by
pressing fresh acid into the pores hydrostatically (see
Liebenow, Zeits. fur Elektrochem., 1897, iv. 61),
or by working at a higher temperature. This increases the
diffusion inwards of strong acid, and like the increase due
to hydrostatic pressure maintains the E.M.F. The other
suggested causes of the fall therefore fail. Fig. 20 also
shows that when the discharge current was stopped at points
A, B, C, D to extract samples, the voltage immediately rose,
owing to inward diffusion of stronger acid. The inward
diffusion of fresh acid also accounts for the recuperation
found after a rest which follows either complete discharge or
a partial discharge at a very rapid rate. If the discharge
be complete the recuperation refers only to the electromotive
force; the pressure falls at once on closed circuit. If
discharge has been rapid, a rest will enable the cell to resume
work because it brings fresh acid into the active regions.
Fig. 20.
As to the effect of repose on a charged cell, Gladstone and
Tribe's experiments showed that peroxide of lead lying on
its lead supoort suffers from a local action, which reduces
one molecule of PbO2 to sulphate at the same time that an
atom of the grid below it is also changed to sulphate. There
is thus not only a loss of the available peroxide, but a
corrosion of the grid or plate. It is through this action
that the supports gradually give way. On the negative plate
an action arises between the finely divided lead and the
sulphuric acid, with the result that hydrogen is set free--
Pb + H2SO4 = PbSO4 + H2.
This involves a diminution of available spongy lead, or loss
of capacity, occasionally with serious consequences. The
capacity of the lead plate is reduced absolutely, of course,
but its relative value is more seriously affected. In the
discharge it gets sulphated too much, because the better
positive keeps up the E.M.F. too long. In the succeeding
charge, the positive is fully charged before the negative, and
the differences between them tend to increase in each cycle.
Kelvin and Helmholtz have shown that the E.M.F. of a voltaic
cell oan be calculated from the energy developed by the chemical
action. For a dyad gram equivalent (= 2 grams of hydrogen,
207 grams of lead, &c.), the equation connecting them is
E = H/46000 + T dE/dT,
here E is the E.M.F. in volts, H is the heat developed by a
dyad equivalent of the reacting substances, T is the absolute
temperature, and dE/dT is the temperature coefficient of the
E.M.F. If the E.M.F. does not change with temperature,
the second term is zero. The thermal values for the various
substances formed and decomposed are -For PbO2, 62400; for
PbSO4, 216210; for H2SO4, 192920; and for H2O, 68400
calories. Writing the equation in its simplest form for
strong acid, and ignoring the temperature coefficient term,
PbO2 + 2 H2SO4 + Pb = 2PbSO4 + 2 H2O
-62440 - 385840 + 432420 + 136720
leaving a balance of 120860 calories. Dividing by 46000
gives 2.627 volts. The experimental value in strong acid,
according to Gladstone and Hibbert, is 2.607 volts, a very
close approximation. For other strengths of acid, the energy
will be less by the quantity of heat evolved by dilution
of the acid, because the chemical action must take the
H2SO4 from the diluted liquid. The dotted curve in fig.
10 indicates the calculated E.M.F. at various points when
this is taken into account. The difference between it and
the continuous curve must, if the chemical theory be correct,
depend on the second term in the equation. The figure shows
that the observed E.M.F. is above the theoretical for
all strengths from 100 down to 5%. Below 5 the position is
reversed. The question remains, Can the temperature
coefficient be obtained? This is difficult, because the value
is so small, and it is not easy to secure a good cycle of
observations. Streintz has given the following values:--
E 1.9223 1.9828 2.0031 2.0084 2.0105 2.078 2.2070
dE/dT.106 140 228 335 285 255 130 73
Unpublished experiments by the writer give dE/dT. 106 =
350 for anid of density 1.156. With stronger acid, a true
cycle could not be obtained. Taking Streintz's value, 335
for 25% acid, the second term of the equation is TdE/dT =
290 X .000335 = 0.0971 volt. The first term gives 88800
calories = 1.9304 volt. Adding the second term, 1.9304 +
0.0971 = 2.2075 volts. The observed value is 2.030 volts
(see fig. 10), a remarkably good agreement. This calculation
and the general relation shown in fig. 10 render it highly
probable that, if the temperature coefficient were known
for all strengths of acid, the result would be equally
good. It is worth observing that the reversal of relationship
between the observed and calculated curves, which takes
place at 5% or 6%, suggests that the chemistry must be on
the point of altering as the acid gets weak, a conclusion
which has been already arrived at on purely chemical
grounds. The thermodynamical relations are thus seen to
confirm very strongly the chemical and physical analyses.1
Accumulators in Central Stations.---As the efficiency of
accumulators is not generally higher than 75%, and machines
must be used to charge them, it is not directly economical
to use cells alone for public supply. Yet they play an
important and an increasing part in public work, because they
help to maintain a constant voltage on the mains, and can be
used to distribute the load on the running machinery over a
much greater fraction of the day. Used in parallel with the
dynamo, they quickly yield current when the load increases,
and immediately begin to charge when the load diminishes, thus
largely reducing the fluctuating stress on dynamo and engine
for sudden variations in load. Their use is advantageous if
they can be charged and discharged at a time when the steam
plant would otherwise be working at an uneconomical load.
Fig. 21.
Regulation of the potential difference is managed in various
ways. More cells may be thrown in as the discharge proceeds,
and taken out during charge; but this method often leads to
trouble, as some cells get unduly discharged, and the unity
of the battery is disturbed. Sometimes the number of cells
is kept fixed for supply, but the P.D. they put on the mains
is reduced during charge by employing regulating cells in
opposition. Both these plans have proved unsatisfactory,
and the battery is now preferably joined across the mains
in parallel with the dynamo. The cells take the peaks
of the load and thus relieve the dynamo and engine of
sudden changes, as shown in fig. 21. Here the line current
(shown by the erratic curve) varied spasmodically from 0
to 375 amperes, yet the dynamo current varied from 100 to
150 amperes only (see line A). At the same time the line
voltage (535 volts normal) was kept nearly constant. In
the late evening the cells became exhausted and the dynamo
charged them. Extra voltage was required at the end of a
``charge,' and was provided by a ``booster.'' Originally a
booster was an auxiliary dynamo worked in series with the
chief machine, and driven in any convenient way. It has
1 For the discussion of later electrolytic theories as apolied to
accumulators, see Dolezalek, Theory of the Lead Accumulator.
developed into a machine with two or more exciting coils,
and having its armature in series with the cells (see fig.
22). The exciting coils act in opposition; the one carrying
the main current sets up an E.M.F. in the same direction
as that of the cells, and helps the cells to discharge
as the load rises. When the load is small, the voltage
on the mains is highest and the shunt exciting current
greatest. The booster E.M.F. now acts with the dynamo
and against the cells, and causes them to take a full
charge. Even this arrangement did not suffice to keep the
line voltage as constant as seemed desirable in some cases,
as where lighting and traction work were put on the same
plant. Fig. 23 is a diagram of a complex booster which
gives very good regulation. The booster B has its armature
in series with the accumulators A, and is kept running
in a given direction at a constant speed by means of a
shunt-wound motor (not shown), so that the E.M.F. induced
in the armature depends on the excitation. This is made
Fig. 22.
to vary in value and in direction by means of four
independent enciting coils, C1, C2, C3, C4. The last
is not essential, as it merely compensates for the small
voltage drop in the armature. It is obvious that the
excitation C3 will be proportionate to the difference
in voltage between the battery and the mains, and it is
