CHAPTER 4 THE SECOND LAW
4.3 CONCEPTSDEVELOPED WITHCARNOTENGINES 109
BIOGRAPHICAL SKETCH
Rudolf Julius Emmanuel Clausius (1822–1888)Rudolf Clausius was a German theoretical
physicist who was the first to treat thermody-
namics as a rigorous science, based on the ear-
lier writings of Carnot and Clapeyron.
He was born in Koslin, Prussia, into a large ̈
family. His father was an educator and church
minister.
Clausius was successively a professor at
universities in Berlin, Zurich, Wurzburg, and ̈
Bonn. In addition to thermodynamics, he did
work on electrodynamic theory and the kinetic
theory of gases.
Max Planck, referring to a time early in his
own career, wrote:a
One day, I happened to come across the trea-
tises of Rudolf Clausius, whose lucid style and
enlightening clarity of reasoning made an enor-
mous impression on me, and I became deeply ab-
sorbed in his articles, with an ever increasing en-
thusiasm. I appreciated especially his exact for-
mulation of the two Laws of Thermodynamics,
and the sharp distinction which he was the first
to establish between them.
Clausius based his exposition of the second
law on the following principle that he pub-
lished in 1854:b
... it appears to me preferable to deduce the gen-
eral form of the theorem immediately from the
same principle which I have already employed
in my former memoir, in order to demonstrate
the modified theorem of Carnot.
This principle, upon which the whole of the
following development rests, is as follows:—
Heat can never pass from a colder to a warmer
body without some other change, connectedtherewith, occurring at the same time. Every-
thing we know concerning the interchange of
heat between two bodies of different temperature
confirms this; for heat everywhere manifests a
tendency to equalize existing differences of tem-
perature, and therefore to pass in a contrary di-
rection,i. e.from warmer to colder bodies. With-
out further explanation, therefore, the truth of the
principle will be granted.
In an 1865 paper, he introduced the symbol
Ufor internal energy, and also coined the word
entropywith symbolS:c
We might call S thetransformational contentof
the body, just as we termed the magnitude U
itsthermal and ergonal content. But as I hold
it better to borrow terms for important magni-
tudes from the ancient languages, so that they
may be adopted unchanged in all modern lan-
guages, I propose to call the magnitude S theen-
tropyof the body, from the Greek word oJ,
transformation. I have intentionally formed the
wordentropyso as to be as similar as possible
to the wordenergy; for the two magnitudes to
be denoted by these words are so nearly allied in
their physical meanings, that a certain similarity
in designation appears to be desirable.
The 1865 paper concludes as follows, end-
ing with Clausius’s often-quoted summations
of the first and second laws:d
If for the entire universe we conceive the same
magnitude to be determined, consistently and
with due regard to all circumstances, which for
a single body I have calledentropy, and if at the
same time we introduce the other and simpler
conception of energy, we may express in the fol-
lowing manner the fundamental laws of the uni-
verse which correspond to the two fundamental
theorems of the mechanical theory of heat.
1.The energy of the universe is constant.
2.The entropy of the universe tends to a max-
imum.
Clausius was a patriotic German. During
the Franco-Prussian war of 1870–71, he un-
dertook the leadership of an ambulance corps
composed of Bonn students, was wounded in
the leg during the battles, and suffered disabil-
ity for the rest of his life.
aRef. [ 134 ], page 16. bRef. [ 32 ], page 117. cRef. [ 33 ], page 357. dRef. [ 33 ], page 365.