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For now, however, we may regard Tas simply what one gets by adding A brief history of this empirical gas law runs as follows.
In the years 1. Gay-Lussac used literally mercury thermometers and the Celsius scale. By , Gay-Lussac had found that reacting gases combine in a numerically simple fashion.
For example, one volume of oxygen requires two volumes of hydrogen for complete combustion and yields two volumes of water vapor all volumes being measured at a fixed pressure and temperature. This information led Amadeo Avogadro to suggest in that equal volumes of different gases contain the same number of molecules again at given pressure and temperature.
The empirical gas law, as displayed in 1. All the functional dependences were known and well-established before the first quarter of the nineteenth century was over. Our version of the empirical law is microscopic in the sense that the number TV of individual molecules appears. Although data for a microscopic evaluation of the proportionality constant were available before the end of the nineteenth century, we owe to Max Planck the notation k and the first evaluation.
To determine their numerical values, he compared his theory with existing data on radiation as will be described in section 6.
Then, incorporating some work on gases by Ludwig Boltzmann, Planck showed that his radiation constant k was also the proportionality constant in the microscopic version of the empirical gas law.
Equation 1. Thus far, I have chosen to use the phrase "empirical gas law" to emphasize that equation 1.
Although the relationship is accurate only for dilute gases, it is thoroughly grounded in experiment. As it enters our development, there is nothing hypothetical about it.
II. Problem Sets and Exams
So long as the gas is dilute, we can rely on the empirical gas law and can build on it. Nevertheless, from here on I will conform to common usage and will refer to equation 1. Those expressions must be numerically equal, and so comparison implies 1. In working out the kinetic theory's expression for pressure, we assumed that the gas may be treated by classical Newtonian physics, that is, that neither quantum theory nor relativity theory is required.
Moreover, the ideal gas law fails at low temperatures and high densities. Some of these criteria will be made more specific later, in chapters 5 and 8.
There can also be energies associated with the motion and location of the center of mass CM of the entire gas: translational kinetic energy of the CM, kinetic energy of bulk rotation about the CM, and gravitational potential energy of the CM, for example. Usually the energies associated with the center of mass do not change in the processes we consider; so we may omit them from the discussion.
Rather, we focus on the items in the displayed list and others like them , which-collectively—constitute the internal energy of the system. The internal energy, denoted by E9 can change in fundamentally two ways: 1.
If particles are permitted to enter and leave what one calls "the system," then their passage may also change the system's energy. In the first five chapters, all systems have a fixed number of particles, and so—for now—no change in energy with particle passage need be included. For sound historical reasons, equation 1.
The word thermodynamics itself comes from "therme," the Greek word for "heat," and from "dynamics," the Greek word for "powerful" or "forceful. Indeed, a year-old William Thomson, later to become Lord Kelvin, coined the adjective "thermodynamic" in in a paper on the efficiency of steam engines.
We need a way to write the word equation 1. The lower case letter q will denote a small or infinitesimal amount of energy transferred by heating; the capital letter Q will denote a large or finite amount of energy so transferred. Thus the First Law becomes Figure 1. Donald M.
Eigler and Erhard K. Schweizer moved the 35 atoms into position on a nickel surface with a scanning tunneling microscope and then "took the picture" with that instrument.
The work was reported in Nature in April When thermodynamics was developed in the nineteenth century, the very existence of atoms was uncertain, and so thermodynamics was constructed as a macroscopic, phenomenological theory. If you put a can of warm soda into the tub of water and crushed ice, the soda cools, that is to say, energy passes by conduction from the soda through the can's aluminum wall and into the ice water.
In the course of an hour or so, the process pretty much runs its course: energy transfer ceases, and the soda now has the same temperature as the ice water. One says that the soda has come to "thermal equilibrium" with the ice water. More generally, the phrase thermal equilibrium means that a system has settled down to the point where its macroscopic properties are constant in time.
Surely the microscopic motion of indivi- dual atoms remains, and tiny fluctuations persist, but no macroscopic change with time is discernible. We will have more to say about temperature later in this chapter and in other chapters.
The essence of the temperature notion, however, is contained in the first paragraph of this subsection. The paragraph is so short that one can easily under- estimate its importance; I encourage you, before you go on, to read it again.
The molecules of diatomic nitrogen and oxygen are in irregular motion. The molecules collide with one another as well as with the walls of the room, but most of the time they are out of the range of one another's forces, so that—in some computations—we may neglect those inter- molecular forces.
Whenever we do indeed neglect the intermolecular forces, we will speak of an ideal gas. We will need several relationships that pertain to a dilute gas such as air under typical room conditions. They are presented here. Pressure according to kinetic theory Consider an ideal gas consisting of only one molecular species, say, pure diatomic nitrogen. There are N such molecules in a total volume V.
In their collisions with the container walls, the molecules exert a pressure. How does that pressure depend on the typical speed of the molecules? Because pressure is force exerted perpendicular to the surface per unit area, our first step is to compute the force exerted by the molecules on a patch of wall area A.
The reasoning is based on Newton's second law of motion, 1.
When the molecule strikes the wall, its initial x-component of momentum mvx will first be reduced to zero and will then be changed to —mvx in the opposite direction.
The letter m denotes the molecule's rest mass. Only the velocity component vx transports molecules toward the wall; it carries them a distance vxAt toward the wall in time At. To hit the wall in that time interval, a molecule must be within the distance vxAt to start with.
In a moment, we will correct for that temporary assumption. The product v2x appears, and we must average over its possible values. We can usefully relate that average to v2 , the average of the square of the speed. Angular brackets, , denote an average. Another, analogous meaning will be explained later, when it is first used. Thus, denoting the pressure by P, we emerge with the relationship The pressure is proportional to the average translational kinetic energy and to the number density.
The temperature T is the absolute temperature, whose unit is the kelvin, for which the abbreviation is merely K. Precisely how the absolute temperature is defined will be a major point in later chapters.
You may know a good deal about that topic already. For now, however, we may regard Tas simply what one gets by adding A brief history of this empirical gas law runs as follows.
In the years 1.
Thermal Physics: Newtonian Dynamics, and Newton to Einstein: The Trail of Light
Gay-Lussac used literally mercury thermometers and the Celsius scale. By , Gay-Lussac had found that reacting gases combine in a numerically simple fashion. For example, one volume of oxygen requires two volumes of hydrogen for complete combustion and yields two volumes of water vapor all volumes being measured at a fixed pressure and temperature. This information led Amadeo Avogadro to suggest in that equal volumes of different gases contain the same number of molecules again at given pressure and temperature.
The empirical gas law, as displayed in 1.Surely the microscopic motion of indivi- dual atoms remains, and tiny fluctuations persist, but no macroscopic change with time is discernible.
Ralph Baierlein- Thermal Physics
In a moment, we will correct for that temporary assumption. The steam loses energy and also drops in temperature.
There are no discussion topics on this book yet. To bring the Second Law to bear on this issue, we need to compare multiplicities. Marcello Lappa. The entire "world" is returned to its original state. Thus equation 2. The book is well written, uses plenty of descriptive material to establish the basic fundamentals, and is supplemented with useful applications.