How Math Explains the World.pdf

(Marcin) #1

tion. The man was James Prescott Joule, the woman his wife, and they
were in the Alps on their honeymoon. Joule had devoted a substantial
portion of his life to establishing the fact that, when water fell 778 feet,
its temperature rose 1 degree Fahrenheit. Britain, however, is notoriously
deficient in waterfalls, and now that Joule was in the Alps, he certainly
did not intend to let a little thing like a honeymoon stand between him
and scientific truth.
A new viewpoint had arisen in physics during the early portion of the
nineteenth century: the idea that all forms of energy were convertible into
one another. Mechanical energy, chemical energy, and heat energy were
not different entities, but different manifestations of the phenomenon of
energy. James Joule, a brewer by trade, devoted himself to the establish-
ment of the equivalence between mechanical work and heat energy. These
experiments involved very small temperature differences and were not
spectacular, and Joule’s results were originally rejected, both by journals
and the Royal Society. He finally managed to get them published in a
Manchester newspaper for which his brother was the music critic. Joule’s
results led to the first law of thermodynamics, which states that energy
cannot be created nor destroyed, but only changed from one form to an-
other.
Some twenty years before Joule, a French military engineer named Nico-
las Carnot had been interested in improving the efficiency of steam en-
gines. The steam engine developed by James Watt was efficient, as steam
engines went, but nonetheless still wasted about 95 percent of the heat
used in running the engine. Carnot investigated this phenomenon and
discovered a truly unexpected result: it would be impossible to devise a
perfectly efficient engine, and the maximum efficiency was a simple
mathematical expression of the temperatures involved in running the en-
gine. This was Carnot’s only publication, and it remained buried until it
was resurrected a quarter of a century later by William Thomson (Lord
Kelvin), just one year after his chance meeting with Joule in the Swiss
Alps.
Carnot’s work was the foundation of the second law of thermodynamics.
This law exists in several forms, one of which is Carnot’s statement con-
cerning the maximum theoretical efficiency of engines. Another formu-
lation of the second law, due to Rudolf Clausius, can be understood in
terms of entropy, a thermodynamic concept that involves a natural direc-
tion of thermodynamic processes: a cube of ice placed in a glass of hot
water will melt and lower the temperature of the water, but a glass of
warm water will never spontaneously separate into hot water and ice.
The Austrian physicist Ludwig Boltzmann discovered an altogether dif-
ferent formulation of the second law of thermodynamics in terms of


The Raw Materials 187
Free download pdf