Physics: The First Science

Chapter 7 - Materials and Models

CHAPTER 7 Materials and Models Ideal systems and models: the ideal gas Bouncing molecules: the microscopic point of view The macroscopic point of view Pressure Archimedes’ principle Bernoulli’s equation Absolute temperature The surprising bridge to temperature Internal energy and heat capacity Heating Work The first law of thermodynamics Other systems: adding pieces from reality Molecules Phase changes Condensed matter Metals Chemical energy Quantum theory Back to heat capacities Diatomic gases We have applied Newton’s laws of motion to the objects they were meant for: objects that are large enough to see or feel. In this chapter we use them to describe the mechanics of atoms and molecules. As we do that we have to keep in mind that Newton’s laws and classical mechanics apply in the microscopic realm only to a limited extent, and that the ideas and methods of quantum mechanics may be necessary. So far we have applied Newton’s laws to “objects” without considering the material that they are made of or their internal structure.To treat them in terms of their atoms and molecules takes us from a few simple particles and unchanging objects to composite objects that consist of very large numbers of particles.The real systems are so complex that we approximate them with models, invented, imagined systems that, however, retain the essential properties of the systems that we seek to understand. 136 / Materials and Models We begin this chapter by introducing the model called the ideal gas. It is an enormously fruitful model, which describes some of the most important properties of real gases, and, to some extent, also those of other materials. It also provides a bridge to a seemingly entirely different subject, that of heat and temperature. In addition, it shows the correspondence between two very different aspects of the world around us. On the one hand there are the large-scale objects of our direct sensory experience. Our instruments show us that underlying this macroscopic world is a microscopic world that we are normally not aware of, the world of moving, vibrating, rotating, colliding atoms and molecules, absorbing, emitting, and exchanging energy. 7.1 Ideal systems and models: the ideal gas How can we get started talking about the vastly complex real world? We know that we need to talk about one that is simpler, a model system, sometimes called an ideal system. Let’s review the rules of the game. We decide what the model is and how it works. It is an invented system that shares some of the characteristics of the corresponding system in the real world. The words ideal and model describe a system with properties that we make up and laws that we prescribe. We set the rules that we need to calculate the properties and behavior of our model system. We can then compare the model and the real material to see to what extent their properties overlap. We can also ask what the model predicts for behavior under conditions that were not originally considered, and to see how the ideal and the actual systems then compare. Here is the model that we will look at in some detail: it’s a gas whose constituents (its atoms or molecules) are particles, i.e., they have no size or internal structure. They exert forces and experience forces only when they touch each other or the walls of their container. They move in accord with the laws of Newtonian mechanics. This model is called the ideal gas. A real gas is very different. Its smallest units may be molecules, composed of two or more atoms, or single atoms, consisting of nuclei and electrons. They are not zero-size particles, and they exert forces on each other even when they don’t touch. Nevertheless, the ideal-gas model describes and predicts the behavior of real gases very well under many circumstances. Bouncing molecules: the microscopic point of view The basic feature of the model that we call the ideal gas is that its components are always in motion and have only kinetic energy. They have no internal structure, no internal motion, and no internal energy. They exert no forces on each other except when they touch, so that there is no mutual potential energy. Since the model requires that these elementary components are point particles with no internal structure, it doesn’t matter whether we call them atoms or molecules. (We’ll call them molecules.) The figure shows a portion of a gas with...