Download The Four Laws of Thermodynamics

The Four Laws of Thermodynamics
James D Emery
3/2/2012 Edition
Contents
1 Introduction
1.1 The Zeroth Law .
1.2 The First Law .
1.3 The Second Law
1.4 The Third Law .
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1
2
2
3
3
2 Some Strange Modern Conclusions About the Laws
4
3 A Brief Review of Atkins Book
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4 References
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1
Introduction
The famous Physical Chemist Peter Atkins has written a small book called
The Four Laws That Drive the Universe, which is well worth reading.
This book is at the Linda Hall Library of Science in Kansas City Missouri.
Each of the four laws of thermodynamics define a principle. The concept of
temperature springs from the Zeroth Law, and the concept of internal
energy of a system from the First Law. The Second Law implies the
property Entropy specified with symbol S, the Third Law implies that the
absolute entropy of statistical mechanics, and the classical entropy
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defined by the differential change of classical thermodynamics, namely
dS =
dQ
,
T
are the same ideas.
1.1
The Zeroth Law
If a body A is in thermal equilibrium with a body B, and body B is in thermal
equilibrium with body C, then body A is in thermal equilibrium with body C.
Informally if two bodies are in thermal equilibrium they are at the same
temperature. Temperature is defined in Statistical Mechanics in terms of a
distribution or population of energy states, the Boltzman Distribution. The
population of a state of energy E relative to the lowest energy state 0, given
by
Population of energy state E
= e−βE ,
Population of energy state 0
where
1
.
kT
T is temperature and k is Boltzman’s constant.
β=
k = 1.38 × 10−23 joules per kelvin.
1.2
The First Law
The conservation of Energy. The change in internal energy of a system dU
is equal to the heat added to the system dQ minus the work done by the
system dW
dU = dQ − dW.
For a classical system at constant pressure P where work is mechanical work,
and where there are no exotic forms of work such as work done by electric
or magnetic fields, or radiation energy, no fusion in a jar etc, then
dU = dQ − P dV,
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where dV is the change in volume of the system.
The internal energy of an isolated system is constant
Note. It is now common in physical chemistry and chemistry, as
opposed to physics, to consider the work dw to be that done on the
system, rather than that done by the system, so in chemistry the
first law is usually written as
dU = dQ + dW.
1.3
The Second Law
The following statements are equivalent:
(1) Heat can not be completly converted to work (Statement of the law by
Kelvin in terms of work).
(2) Heat will not spontaneously go from a cold object to a warm object
(Statement of the law by Clausius in terms of heat flow).
(3) Entropy of an isolated system increases.
The statistical mechanics definition of absolute entropy (Boltzman) is
S = k ln(W ),
where W is the thermodynamic probability of an energy state of enrgy E,
where W is roughly the number of different arrangements of a system that
lead to this energy.
1.4
The Third Law
In classical thermodynamics the difference of entropy is defined, but there is
not necessarily an absolute measure of entropy. The third Law says there is
an absolute scale of entropy. The entropy of a perfect crystal, the entropy of a
perfectly ordered system at absolute zero, is zero, and this corresponds to the
classical entropy of an ideal gas at absolute zero. Classical Thermodynamics
and Statistical Thermodynamics agree on an absolute measure of entropy.
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2
Some Strange Modern Conclusions About
the Laws
(1) The third law makes the existence of an ideal gas at absolute zero impossible. Hence one of the fundamental components of classical thermodynamics
is banished.
(2) Certain exotic states of matter lead to the idea of temperatures below
absolute zero.
3
A Brief Review of Atkins Book
”The laws of thermodynamics drive everything that happens in the universe.
From the sudden expansion of a cloud of gas to the cooling of hot metal, and
from the unfurling of a leaf to the course of life itself–everything is moved or
restrained by four simple laws. They establish fundamental concepts such as
temperature and heat, and reveal the arrow of time and even the nature of energy itself. Written by Peter Atkins, one of the worlds leading authorities on
thermodynamics, this powerful and compact introduction explains what these
four laws are and how they work, using accessible language and virtually no
mathematics. Guiding the reader a step at a time, Atkins begins with Zeroth
(so named because the first two laws were well established before scientists
realized that a third law, relating to temperature, should precede them–hence
the jocular name zeroth), and proceeds through the First, Second, and Third
Laws, offering a clear account of concepts such as the availability of work
and the conservation of energy. Atkins ranges from the fascinating theory
of entropy (revealing how its unstoppable rise constitutes the engine of the
universe), through the concept of free energy, and to the brink, and then
beyond the brink, of absolute zero. C.P. Snow once remarked that not knowing the second law of thermodynamics is like never having read a work by
Shakespeare. This brief but brilliant book introduces general readers to one
of the cornerstones of modern science, four laws that are as integral to the
well-educated mind as such great dramatic works as Hamlet or Macbeth.”
It is well known that thermodynamics, like quantum mechanics, is a very
difficult subject to fully understand. So Snow’s remark equating knowledge
of the Second Law, with knowledge of Shakespeare, is rather strange. In fact
in his book, Atkins says he seriously questions whether Snow himself actually
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understood the Second Law.
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References
[1]Peter Atkins, The Four Laws That Drive the Universe, Oxford University Press, 2007.
[2]Peter Atkins, The Second Law. New York: W. H. Freeman. 1987.
[3]Peter Atkins, Physical Chemistry (with Julio de Paula) 9th ed. Oxford University Press. 2010. ISBN 0199543373
[4] C. Truesdell, The Tragicomical History of Thermodynamics, 18221854. Studies in the History of Mathematics and Physical Sciences, Volume
4, Springer-Verlag, New York, Heidelberg and Berlin, 1980, xiii + 372 pages.
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