Equivalences

The theme that dominated Joule’s research from beginning to end, and served as
his guiding theoretical inspiration, was the belief that quantitative equivalences
could be found among thermal, chemical, electrical, and mechanical effects. He
was convinced that the extent of any one of these effects could be assessed with
the units of any one of the other effects. He studied such quantitative connections
in no less than eight different ways: in investigations of chemical effects converted
to thermal, electrical, and mechanical effects; of electrical effects converted
to thermal, chemical, and mechanical effects; and of mechanical effects
converted to thermal and electrical effects.
At first, Joule did not fully appreciate the importance of mechanical effects in
this scheme of equivalences. His earliest workcentered on chemical, electrical,and thermal effects. In 1840, when he was twenty-two, he started a series of five
investigations that was prompted by his interest in electrochemistry. (Joule was
an electrochemist before he was a physicist.) First, he demonstrated accurately
that the heating produced by an electrical current in a wire is proportional to the
square of the current I and to the electrical resistance R—the “I2R-heating law.”
His experimental proof required temperature measurements in a “calorimeter” (a
well-insulated, well-stirred vessel containing water or some other liquid), electrical
current measurements with an instrument of his own design, and the invention
of a system of absolute electrical units.
Joule then invested considerable effort in various studies of the role played
by his heating law in the chemical processes produced in electric cells. He
worked with “voltaic cells,” which supply an electrical output (the modern flashlight
battery is an example), and “electrolysis cells,” which consume an electrical
input (for example, a cell that decomposes water into hydrogen gas and oxygen
gas). In these experiments, Joule operated an electrolysis cell with a battery of
voltaic cells. He eventually arrived at the idea that the electrical currents generated
by the chemical reaction in the voltaic cell carried the reaction’s “calorific
effect” or “chemical heat” away from the primary reaction site either to an external
resistance where it could be converted to “free heat,” according to the I 2Rheating
law, or to an electrolysis cell where it could be invested, all or partly, as
“latent heat” in the electrolysis reaction.
To determine the total chemical heat delivered to the electrolysis cell from the
voltaic cells, call it Qe, Joule found the resistance Re of a wire that could replace
the electrolysis cell without causing other electrical changes, measured the current
I in the wire, and calculated Qe with the heating law as I2Re. He also measured
the temperature rise in the electrolysis cell doubling as a calorimeter, and
from it calculated the free heat Qt generated in the cell. He always found that
Qe substantially exceeded Qt; in extreme cases, there was no heating in the cell
and Qt was equal to zero. The difference Qe Qt represented what Joule wanted
to calculate: chemical heat converted to the latent heat of the electrolysis reaction.
Representing the electrolysis reaction’s latent heat with Qr, Joule’s calculation
was
Qr Qe Qt.
This is the statement Joule used in 1846 to determine several latent heats of
electrolysis reactions with impressive accuracy. It is a complicated and exact
application of the first law of thermodynamics, which Joule seems to have understood
in terms of inputs and outputs to the electrolysis cell. That is evident
in the last equation rearranged to
Qt Qe Qr,
with Qe an input to the cell, Qr an output because it is lost to the reaction, and
Qt the difference between the input and output (see fig. 5.1). This was a balancing
or bookkeeping kind of calculation, and it implied a conservation assumption:
the balanced entity could not be created or destroyed within the cell. Joule did
not have a name for the conserved entity. It would be identified six years later
by Rudolf Clausius and William Thomson, and called “energy” by Thomson.
Although he had not arrived at the energy concept, Joule clearly did have, wellahead of his contemporaries, a working knowledge of the first law of
thermodynamics.
Joule’s electrochemistry papers aroused little interest when they were first
published, neither rejection nor acceptance, just silence. One reason for the indifference
must have been the extraordinary nature of Joule’s approach. The
input-output calculation was difficult enough to comprehend at the time, but in
addition to that, Joule used his measured heats of electrolysis reactions to calculate
heats of combustion reactions (that is, reactions with oxygen gas). For
example, he obtained an accurate heat for the hydrogen combustion reaction,
2 H2 O2 2 H2O,
which is just the reverse of the water electrolysis reaction,
2 H2O 2 H2 O2,
and therefore, Joule assumed, its heat had the same magnitude as that of the
electrolysis reaction.
This was an exotic way to study a combustion reaction. Joule’s first biographer,
Osborne Reynolds, remarks that “the views they [the electrochemistry papers and
others of Joule’s early papers] contained were so much in advance of anything
accepted at the time that no one had sufficient confidence in his own opinion or
was sufficiently sure of apprehending the full significance of the discoveries on
which these views were based, to venture an expression of acceptance or rejection.”
We can imagine a contemporary reader puzzling over the papers and finally
deciding that the author was either a genius or a crank.
But for Joule—apparently unconcerned about the accessibility or inaccessibility
of his papers for readers—the complicated method was natural. His primary
interest at the time was the accurate determination of equivalences among thermal,
electrical, and chemical effects. He could imagine no better way to tackle
this problem than to use electrical and calorimetric measurements to calculate
the thermal effect of a chemical effect.