Heat of reaction = electrical work done latent heat or, in symbols,

Q=W-L

It is this term L-positive in the Daniell and accumulator, negative in the Clark-that we ignored in § 2, and about which we have so far no information.

According to the definition of electromotive force (E), the electrical work done by the cell is the product of this into the quantity of electricity (F) flowing. Hence

With regard to the latent heat of a voltaic cell it is to be noted (i.) that it is reversible; if taking current out of a cell (say, a lead accumulator) causes it to fall in temperature, charging it with current from an outside source will reverse the chemical reaction, and so cause heat to be evolved in the cell. In this way it is to be distinguished from the effect of resistance in the cell, which is always to cause heating (the so-called irreversible or "Joule" heating). (ii.) The heat absorbed or evolved is proportional to the amount of chemical action, and so to the current; whereas the "Joule" heating, due to resistance, is proportional to the square of the current.

In

Actual measurement of the latent heat has been accomplished in the case of the lead accumulator.1 A small cell with electrodes 9°3 × 16 cms., cut from "Tudor" plates was placed inside the working chamber of a Bunsen ice calorimeter, and charged or discharged with a small constant current. an experiment with acid of density 1153, the voltage of the cell was 199, the current used o'0678 amperes, the time of charge or discharge two hours, and it was found that during charge the heat evolved in the calorimeter was o‘0137 joules per second; during discharge, o'00159. Now, in both cases the resistance heating was the same; but during charge there was a reversible heating to be added, during discharge a cooling to be subtracted. The reversible effect is

1 Streintz, Wied. Ann., 49. 564 (1893).

This quantity, o'0061 joule, is the heat absorbed when 0'0678 coulomb flows through the cell, but the chemical equation (p. 152) refers to 2 X 96600 coulombs. Hence the latent heat, reckoned for the quantity of reagents expressed in the chemical equation is

The heat of reaction given in § 2 was for an accumulator with acid of abnormally low density; with stronger acid the heat of reaction is greater, and for 1'153 acid, such as Streintz used, about 368,600 joules (mean of Streintz and Tscheltzow's determinations).

We have therefore Q 368,600, L = 17,400, and since two faradays correspond to the chemical reaction,

in practically exact agreement with observation.

Here the latent heat is some 4 per cent. of the total energy transformed, and the approximate method of § 2 would be by so much in error.

In cells other than the accumulator the resistance is usually much greater, and the reversible heating effect is swamped by heating due to resistance, so that it would be impracticable to measure it directly. But the reversible heating effect may, of course, be deduced if the heat of reaction (Q) and electrical work (W) are known. To take the instances mentioned in § 2, we see that in the Daniell cell the latent heat is a small positive quantity, in the Clark a large negative one. In the Daniell cell, of composition used by Jahn, and at o°,

This is less than 1 per cent. of the total; the Daniell cell, then, is an arrangement which transforms into electrical energy all the chemical energy lost by its materials, and a small quantity of heat besides.

In the Clark cell, according to E. Cohen,1 at 18° Cent.

Q = 340,730 joules

W =

1'4291 × 2 × 96,540 =275,930 joules L=W - Q = −64,800 joules

or about 24 per cent. of the total.

The Clark cell, therefore only converts 76 per cent. of its chemical into electrical energy, the remainder into heat.

All that has been said so far is a simple consequence of the first law of thermodynamics, i.e. of the principle of conservation of energy, but further deductions can be made from the second law. The most important of these lies in the conception of free energy. The energy conveyed by an electric current is of a completely available kind; it can be converted into mechanical work by an electrometer, with no loss except that due to mechanical imperfections in the motor; it may be taken as a measure of the work that the chemical reaction is capable of doing. Further, the process of transformation of chemical into electrical energy is a reversible one in the sense in which that word is used in thermodynamics; that is to say, it can be carried out backwards (as in charging an accumulator) with as slight a change of circumstances as we please (by using only a small current). Now, reasoning based on the second law of thermodynamics shows that a chemical reaction, performed at a fixed temperature, is capable of doing the same amount of work, whatever form that work may take, provided only the transformation of energy takes place reversibly; and if the process is not reversible the work done is always less. Hence the electrical work done is not merely a fact of consequence to the voltaic cell considered; it is the measure of the capacity for work of a certain chemical action, under whatever circumstances. Whether that amount of possible work is realised depends only on how close an approach to

1 Zeitschr. phys. Chem., 34. 62-68 (1900).

the ideal of reversibility can be made. It is therefore appropriate to speak of this amount of "free energy" being given out by the reaction, without specifying whether it is to be spent in generating electric current, in working against an osmotic pressure, or directly in mechanical form, or otherwise; the electrical measurement affords merely the most convenient means of estimating the loss of free energy by the reacting materials.

Accordingly, the calorimetric measurement Q gives the total energy-available or not-lost by the chemical materials during reaction: the electrical measurement W gives the free or available-energy lost. The latter quantity may fall short of or exceed the former.

The extreme importance of the notion of free energy demands as complete illustration as possible; we shall therefore take in detail an instance in which there are two known ways of measuring it, and compare the results. The electromotive force of a lead accumulator increases with increase in strength of acid; consequently if two cells, one with strong acid, the other with weak, are coupled in opposition, the former will send a current through the latter. The cell with the strong acid will be discharged, that with weak acid charged. We may write the equations thus :

:

Pb+ PbO2 + 2H,SO, (concentrated) = 2PbSO, + 2H2O

2PbSO, + 2H2O = Pb+ PbO2 + 2H,SO, (dilute)

The total amount of each insoluble solid material remains the same as before, so that no change occurs in either the free or total energy possessed by these. The total amounts of acid and of water also remain the same, but their distribution is different; for in place of the original strong solution we have, in the first cell, a solution which has lost acid and gained water, and is consequently weaker; in place of the original weak solution we have in the second cell a stronger one. Now, the energy (whether free or total) of a solution depends on its composition, so that a certain change has been effected; in fact, it is as if the two acids had been partly mixed with each other. If the current were allowed to flow indefinitely it would

continue until the acid was of the same strength in each cell; this would be effectively the same as a complete mixture of the two liquids, and the electrical energy of the current that had flowed would measure the work that could be done by the acid on mixing—i.e. the loss of free energy attending mixture.

But again, if the two vessels of acid be placed side by side in an air-tight chamber, water from the weak acid (which has the higher vapour pressure) will distil over to the strong, until the same final result is obtained-viz. uniformity in strength. No work will be done thus-i.e. with no appropriate mechanism for making use of the energy; but if the evaporation and condensation be effected by the mechanism imagined on p. 162, work will be done, and according to the principles of thermodynamics, the amount of work must be the same as in the electrical method, for each amount is a measure of the loss of free energy.

Now, the electromotive force of accumulators with various strengths of acid has been measured at o° by Streintz, Heim, Dolezalek, and others; the vapour pressure of sulphuric acid of various strengths has been measured at the same temperature by Dieterici; hence all the data are at hand for comparing the two quantities of work.

The calculation is easier if, instead of following the mixture out to an extreme, we suppose it to proceed only to a very small extent (the same in both cases), or, what comes to the same thing, suppose the quantity of acid in the cells indefinitely large, so that the transfer of one mol produces only a very small effect on its composition.

As numerical example we will take

Then (1) we must suppose two faradays to flow through the

cells; the net electromotive force is 2'103

2001 = 0102

volt, and the work done (reckoned for the quantities occurring in the chemical equation)