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Chapter 5 - Chapter 5 The rst law of thermodynamics Read BS...

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Chapter 5 The first law of thermodynamics Read BS, Chapter 5 Recall in the first example problem of Chapter 1, we saw that mechanical energy was con- served for a mass falling under the influence of a gravitational force. We took the mechanical energy to be the sum of the kinetic and potential energy of the system. But when we included a drag force, we found that mechanical energy was no longer conserved, but in fact dissipated with time. There was considerable discussion in the 17th and 18th centuries which pitted advocates of a so-called vis viva (“force of life,” a type of kinetic energy) against those who argued for the primacy of momentum conservation. Leibniz led the vis viva camp, and New- ton and Descartes led the momentum camp. Both ultimately are equivalent formulations when analyzed carefully. In this chapter, we will expand our notion of energy and insodoing recover a new conserva- tion principle. This new principle, not known to Newton, is the first law of thermodynamics. It takes many equivalent forms, and relies at a minimum on the introduction of a new type of energy, thermal energy, which is necessary to conserve the total energy. Thermal energy is actually a macro-scale representation of micro-scale mechanical energy. Recall that at the micro-scale, molecules are in random motion. This random motion has kinetic energy associated with it. But we cannot hope to keep track of it all for each individual particle. So we surrender knowledge of the micro-scale motions, and allow the temperature to be a measure of the average micro-scale kinetic energy. We can also take the historical approach and develop the principle of energy conservation without further appeal to micro-scale arguments. Let us begin that approach here. 5.1 Representations of the first law There are a variety of ways to represent the first law of thermodynamics, also known as the principle of conservation of energy . Some of them are not obvious, but have withstood the scrutiny of detailed experiment. Perhaps the simplest, but also the most obtuse, is the following 101
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102 CHAPTER 5. THE FIRST LAW OF THERMODYNAMICS 5.1.1 Cycle First law of thermodynamics : During any cycle, the cyclic integral of heat added to a system is proportional to the cyclic integral of work done by the system. If we denote a cyclic integral by contintegraltext , the mathematical representation of this law is J contintegraldisplay δQ = contintegraldisplay δW, ( Q in cal , W in J ). (5.1) Now during the development of thermodynamics, Q was measured in cal , where 1 cal rep- resented the energy necessary to raise 1 g of water 1 C , and W was measured in J which represented the work done in moving a 1 kg mass against a force of 1 N . In the now-discredited caloric theory, heat was thought to be a fluid and not explicitly related to work. This theory began to lose credibility with the experiments conducted in Bavaria by the colorful American scientist Sir Benjamin Thompson 1 (Count Rumford). By
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