Statistical and Thermal Physics: With Computer Applications
Our goal is to understand the properties of macroscopic systems, that is, systems of many electrons, atoms, molecules, photons, or other constituents. Examples of familiar macroscopic objects include systems such as the air in your room, a glass of water, a copper coin, and a rubber band (examples of a gas, liquid, solid, and polymer, respectively). Less familiar macroscopic systems are superconductors, cell membranes, the brain, and the galaxies.
We will ﬁnd that the type of questions we ask about macroscopic systems diﬀer in important ways from the questions we ask about microscopic systems. An example of a question about a microscopic system is “What is the shape of the trajectory of the Earth in the solar system?” In contrast, have you ever wondered about the trajectory of a particular molecule in the air of your room? Why not? Is it relevant that these molecules are not visible to the eye? Examples of questions that we might ask about macroscopic systems include the following:
1. How does the pressure of a gas depend on the temperature and the volume of its container?
2. How does a refrigerator work? What is its maximum eﬃciency?
CHAPTER 1. FROM MICROSCOPIC TO MACROSCOPIC BEHAVIOR
3.How much energy do we need to add to a kettle of water to change it to steam?
4.Why are the properties of water diﬀerent from those of steam, even though water and steam consist of the same type of molecules?
5.How are the molecules arranged in a liquid?
6.How and why does water freeze into a particular crystalline structure?
7.Why does iron lose its magnetism above a certain temperature?
8.Why does helium condense into a superﬂuid phase at very low temperatures? Why do some materials exhibit zero resistance to electrical current at suﬃciently low temperatures?
9.How fast does a river current have to be before its ﬂow changes from laminar to turbulent?
10.What will the weather be tomorrow?
The above questions can be roughly classiﬁed into three groups. Questions 1–3 are concerned with macroscopic properties such as pressure, volume, and temperature and questions related to heating and work. These questions are relevant to thermodynamics which provides a framework for relating the macroscopic properties of a system to one another. Thermodynamics is concerned only with macroscopic quantities and ignores the microscopic variables that characterize individual molecules. For example, we will ﬁnd that understanding the maximum eﬃciency of a refrigerator does not require a knowledge of the particular liquid used as the coolant. Many of the applications of thermodynamics are to thermal engines, for example, the internal combustion engine and the steam turbine.
Questions 4–8 relate to understanding the behavior of macroscopic systems starting from the atomic nature of matter. For example, we know that water consists of molecules of hydrogen and oxygen. We also know that the laws of classical and quantum mechanics determine the behavior of molecules at the microscopic level. The goal of statistical mechanics is to begin with the microscopic laws of physics that govern the behavior of the constituents of the system and deduce the properties of the system as a whole. Statistical mechanics is the bridge between the microscopic and macroscopic worlds.
Thermodynamics and statistical mechanics assume that the macroscopic properties of the system do not change with time on the average. Thermodynamics describes the change of a macroscopic system from one equilibrium state to another. Questions 9 and 10 concern macroscopic phenomena that change with time. Related areas are nonequilibrium thermodynamics and ﬂuid mechanics from the macroscopic point of view and nonequilibrium statistical mechanics from the microscopic point of view. Although there has been progress in our understanding of nonequi-librium phenomena such as turbulent ﬂow and hurricanes, our understanding of nonequilibrium phenomena is much less advanced than our understanding of equilibrium systems. Because understanding the properties of macroscopic systems that are independent of time is easier, we will focus our attention on equilibrium systems and consider questions such as those in Questions
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