ch4 - Chapter 4 Introduction to Thermodynamics In this...

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Unformatted text preview: Chapter 4 Introduction to Thermodynamics In this chapter we introduce the topic of thermodynamics which are needed to develop governing equations (specifically constitutive equations) for a continuous medium. The development of constitutive equations will be done in the next chapter. 4.1 Fundamental Laws of Thermodynamics Of course we only label them as laws because we have encountered no contradiction to these laws; they are based entirely on observation and experiments [2]. First Law of Thermodynamics: Conservation of Energy In an isolated system (where no heat, mass, etc. may enter in or go out), there is a scalar quantity, called energy , which remains unchanged as the system evolves. Energy exists in different forms, including gravitational energy, kinetic energy, heat energy, elastic energy, electrical energy, chemical energy, radiant energy, etc., and the energy of each of these forms are not conserved, and in fact may vary depending upon the way in which the system evolves (path dependent). But when the total energy is calculated, it is found to remain unchanged. Second Law of Thermodynamics: Entropy Must Increase This law tells us how an isolated system evolves - a room full of air does not evolve so that all the oxygen ends up in one corner; it evolves in such a way that the oxygen will end up as uniformly distributed as possible. The measure of this “randomness” is termed entropy, and if energy is constant, then the system will evolve so as to increase entropy. Entropy is an abstract concept and difficult to conceptualize. Third Law of Thermodynamics: Absolute Zero Temperature This law was only appreciated after the establishment of quantum mechanics and states that the entropy of a pure crystalline substance at absolute zero thermody- namic temperature (0 o K) may be taken to be zero. In other words, absolute zero cannot be achieved. 1 1 As a side remark, experimentally negative temperatures have been obtained but were reached not by 79 80 CHAPTER 4. INTRODUCTION TO THERMODYNAMICS Resnick and Halliday [10] humorously refer to these three laws as: (1) You can’t win, (2) You can’t break even, and (3) You can’t get out of the game. 4.2 Entropy Entropy is a measure of randomness, and is quantified exactly for a gas at equilibrium in term of the number of permutations which give the same distribution. It is not a quantity which is directly measurable, which makes it a difficult quantity to get an intuitive idea of what entropy is. STILL NEED TO TYPE IN 4.3 Thermodynamic Equilibrium This section is based on material from [2]. For a simple system (e.g. neglecting radiation, electro-magnetic effects, but not me- chanical work or heat), we assume that the total energy is a function of entropy, volume, and the number of (moles of) molecules, i.e....
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This note was uploaded on 11/11/2009 for the course MATH 6735 taught by Professor Bennethum during the Fall '06 term at University of Colombo.

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ch4 - Chapter 4 Introduction to Thermodynamics In this...

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