lecture-ch20 - Contents 20 Entropy and the Second law of...

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Unformatted text preview: Contents 20 Entropy and the Second law of Thermodynamics 1 20.1 Reversible and Irreversible Processes . . . . . . . . . . . . . . 2 20.2 Heat Engines and the Second Law . . . . . . . . . . . . . . . . 5 20.2.1 Efficiency of a Heat Engine . . . . . . . . . . . . . . . 6 20.2.2 Kelvin-Planck form for the second law: . . . . . . . . . 6 20.3 Refrigerators and the Second Law . . . . . . . . . . . . . . . . 6 20.3.1 The Coefficient of Performance . . . . . . . . . . . . . 7 20.3.2 Clausius form for the second law: . . . . . . . . . . . . 7 20.3.3 Equivalence of Clausius and Kelvin-Planck Statements 8 20.4 The Carnot engine . . . . . . . . . . . . . . . . . . . . . . . . 9 20.4.1 Efficiency of a Carnot engine . . . . . . . . . . . . . . . 10 20.4.2 Coefficient of Performance of a Carnot Refrigerator . . 11 20.4.3 Carnot’s Theorem and the Second Law . . . . . . . . . 11 20.5 Entropy: Reversible Processes . . . . . . . . . . . . . . . . . . 13 20.5.1 Carnot engine in T − S diagram . . . . . . . . . . . . . 16 20.6 Entropy: Irreversible Processes . . . . . . . . . . . . . . . . . 17 20.7 Entropy and The Second Law of Thermodynamics . . . . . . . 19 20.7.1 Free Compression . . . . . . . . . . . . . . . . . . . . . 19 20.7.2 The Kelvin-Planck Form of the Second Law . . . . . . 20 20.7.3 The Clausius Form of the Second Law . . . . . . . . . 20 20.7.4 The Arrow of Time . . . . . . . . . . . . . . . . . . . . 20 20.8 A Statistical View of Entropy . . . . . . . . . . . . . . . . . . 20 20.8.1 Probability and Entropy . . . . . . . . . . . . . . . . . 22 20 Entropy and the Second law of Thermo- dynamics In this chapter we will introduce the second law of thermodynamics. The following topics will be covered: Reversible processes. Entropy. The Carnot Engine. Refrigerators. Real engines. 1 20.1 Reversible and Irreversible Processes Consider a typical system in thermodynamic equilibrium, say n moles of a (real) gas confined in a cylinder-piston arrangement of volume V , the gas having a pressure p and a temperature T . In an equilibrium state, these ther- modynamic variables remain constant with time. Suppose that the cylinder, whose walls are insulating but whose base conducts heat, is placed on a large reservoir maintained at this same temperature T . Now let us take the system to another equilibrium state in which the temperature T is the same but the volume V is reduced by one-half. Of the many ways in which we could do this, we discuss two extreme cases. 1. We depress the piston very rapidly, we then wait for equilibrium with the reservoir to be re-established. During this process, the gas is turbulent, and its pressure and temperature are not well defined. We cannot plot the process as a continuous line on a p − V diagram because we would not know what value of pressure (or temperature) to associate with a given volume....
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lecture-ch20 - Contents 20 Entropy and the Second law of...

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