are almost identical at end of discharge and beginning of charge, the resistance falls from 0·0055 to 0·0033 ohm.
While a current flows through a cell, heat is produced at the rate of C2R × 0·24 calories (water-gram-degree) per second. As a consequence the temperature tends to rise. But the change of temperature actually observed is much greater during charge, and much less during discharge, than the foregoing expression would suggest; and it is evident that, besides the heat produced according to Joule’s law, there are other actions which warm the cell during charge and cool it during discharge. Duncan and Wiegand (loc. cit.), who first observed the thermal changes, ascribe the chief influence to the electrochemical addition of H2SO4 to the liquid during charge and its removal during discharge. Fig. 18 gives some results obtained by Ayrton, Lamb, &c. This elevation of temperature (due to electrolytic strengthening of acid and local action) is a measure of the energy lost in a cycle, and ought to be minimized as much as possible.
Fig. 18.
Chemistry.—The chemical theory adopted in the foregoing pages is very simple. It declares that sulphate of lead is formed on both plates during discharge, the chemical action being reversed in charging. The following equations express the experimental results.
Condition before discharge:—
| + plate | Liquid | − plate | ||
| x. PbO2 + | y. H2SO4 | + z. Pb | ||
| n. H2O |
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After discharge:—
| + 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 they first suggested the “sulphate” theory, which was based on very numerous analyses. Confirmation was given by E. Frankland in 1883, É. 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.
Fig. 19.
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 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. Planté, 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. für 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 support 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 can 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＝H46000 +Td Ed T,
where 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 d E/d T 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+2H2SO4+Pb | ＝2PbSO4+2H2O |
| −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
