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Transcript
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 2 3 3 2 Some Strange Modern Conclusions About the Laws 4 3 A Brief Review of Atkins Book 4 4 References 5 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 1 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, 2 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. 3 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 4 understood the Second Law. 4 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. 5