E. R. Pounder

Molecular Theory of Gases

Many physical quantities change continuously with temperature. Examples are: Volume of a solid, liquid, or gas Pressure of a gas at constant volume Electrical resistance Thermal electromotive forces (voltages developed in thermocouples) The quantity and quality of radiant heat

Kinetic Theory of Gases

Equipped with the equation of state of a perfect gas and simple relations for the molar heats of simple gases, we now develop a model gas with the same basic properties. First, we shall find that an array of elastic mass-points in random motion provides a simple mechanism that obeys PV ∝ N, gives a mechanical significance to ɵ, and explains \({C_v} = \frac{3}{2}R\) as observed for monatomic gases.

Wave Motion in One Dimension

Waves on strings lend themselves to graphical consideration. In Figure 23.01, the abscissa x is distance along a flexible string, which is under tension. At time t = 0, nothing has happened, and the string lies along the X axis. Shortly afterwards the origin end of the string is subjected to a motion parallel the Y axis. The variation of y with time, for x = 0, is indicated by the squiggle drawn along the oblique time axis.

Water Substance and the Atmosphere

Water is the working substance in so many thermal processes that its properties are of particular interest. First let us consider its density, or the reciprocal of density, which is called specific volume. Starting with ice, say at − 20C, and increasing the temperature, we find that ice expands, like most solids, until at 0C its specific volume is 1.091 17 cm3 gm−1. Liquid water at 0C has a specific volume of 1.000 16, which decreases to a minimum value of 1.000 03* at 3.98C. Then it starts to expand, reaching its zero-degree value again at about 8C and expanding more and more rapidly to achieve a specific volume of 1.0435 at 100C, as shown in Figure 21.01(a). The density or specific volume of water vapor is of a different order altogether. It can be calculated with reasonable accuracy (and usefully) from its mass per mole.

Waves in Two and Three Dimensions

The string along which the waves traveled in the examples in Chapter 23 may be referred to as the medium along which the waves were propagated. It is a one-dimensional medium, but waves are frequently propagated through two- and three-dimensional media. If we strike a block of wood, we suddenly displace and compress the wood in the immediate vicinity of the point of impact. Two sorts of waves thereupon spread out in all directions from that point: transverse waves for which the particle motion is at right angles to the direction of travel or propagation of the wave, and longitudinal waves, involving particle motions along the direction of propagation, and so involving density variations.

Magnetic Properties of Matter

The response of different types of matter — elements, compounds, alloys, and other aggregates — to the presence of a magnetic field is a matter of some complexity. Certain types of behavior such as ferromagnetism are of great engineering importance, but it is a challenge to physics to explain all magnetic properties of matter. This challenge has been substantially met. Many details have yet to be resolved, but the modern quantum theory of matter, particularly the quantum theory of solids, gives good qualitative explanations and even permits quantitative predictions in some cases. Details of the theory are beyond our scope but we shall give in this chapter some discussion of the currently accepted explanations for the magnetic properties of matter.

Solids, Liquids, and Vapors

The predominant characteristic of the gaseous state is empty space. While a single atom is a complex affair, in a gas, space is so sparsely-populated by molecules of one or two or a few atoms each that we can achieve a simple picture in which the details of the atoms are omitted, in which the atoms become mass-points, with no more by way of individual characteristics than so many black dots. When there is less open space, when the molecules spend a considerable portion of their time close enough to feel each other’s attractive forces, then our simple picture must be amended.

Sizable and Attractive Molecules

The kinetic-theory “explanation” of the experimentally found relation PV = constant was derived for particles of negligible size and having no intermolecular forces. Careful experimental study over a wide range of pressures and temperatures reveals departures from Boyle’s Law, departures that can be explained by taking into account the appreciable sizes of the molecules and the attractive forces among them.

Heat Engines and the Laws of Thermodynamics

The first law of thermodynamics states that mechanical energy and heat are mutually convertible, the total energy remaining constant. Now, we have been developing a picture of heat as that form of mechanical energy in which the energy is shared among a great many independently moving particles, indeed among the independent “degrees of freedom” of those particles. It seems reasonable, therefore, that when energy is transformed from the energy of organized mechanical motion (normally referred to by us as “mechanical energy”) to the energy of disorganized motion that we call heat, the transformation should be on the basis of a joule for a joule (or one calorie for 4.18 joules, where the calorie is a unit based on the properties of water). If one joule of mechanical energy is transformed to heat, it should become one joule of heat. If one joule of heat energy is transformed to mechanical energy, it should become one joule of mechanical energy.

Magnetic Effects of Current

The electric field produced by charges at rest having been discussed in the last chapter, we now consider what happens when charges are in motion relative to each other. First it must be emphasized that Coulomb’s Law and all the electric field concepts, such as potential, derived from it are still valid; moving charges of like sign continue to experience repulsive electric forces. This was tacitly assumed in the problems of the last chapter (numbers 25 to 28) dealing with the motion of electron beams, and all experiments bear out this assumption. In addition, however, charges in relative motion interact through a second type of force called magnetic. The best way to describe this interaction is by considering that a moving charge, i.e., a current, creates a magnetic field. This magnetic field can be calculated using Biot’s Law, which we shall set up shortly, and the force experienced by a second moving charge can be expressed in terms of the magnetic field of the first.