A.I. AKHIEZER’s research while affiliated with New York State and other places

This chapter discusses the flow of liquid or gas in which the velocity of flow is different at different points. This is not an equilibrium state and processes will occur that tend to equalize the velocities of flow. Such processes are called internal friction or viscosity. Just as there is a heat flux from the hotter to the colder parts of a medium in thermal conduction, so in internal friction, the thermal motion of the molecules causes a transfer of momentum from the faster to the slower regions of the flow. Thus, the three phenomena of diffusion, thermal conduction, and viscosity have analogous mechanisms. The viscosity determines the rate of transport of momentum from one point in the flow to another. The chapter explains kinematic viscosity and dynamic viscosity. The kinematic viscosity is a kind of diffusion coefficient for velocity. The chapter then discusses the viscosity of gases and liquids. The viscosity of a gas may be estimated from the fact that internal friction, thermal conduction, and self-diffusion occur in a gas by the same molecular mechanism. The viscosity, like the thermal conductivity, is independent of the pressure of the gas. The viscosity of a liquid usually decreases with increasing temperature; this is reasonable because the relative motion of the molecules becomes easier. In the liquids of low viscosity, such as water, the decrease is appreciable but not very great.

This chapter discusses kinetic processes by means of which a state of equilibrium is reached. These are essentially irreversible processes because they bring a body closer to equilibrium. If a solution has different concentrations at different points, the thermal motion of the molecules causes mixing of the solution in the course of time; the solute moves from regions of higher to regions of lower concentration until the composition of the solution becomes uniform throughout its volume. This process is called diffusion. This chapter explains the properties of diffusion. It is implied that diffusion occurs in a medium at rest so that the equalizing of the concentration occurs only because of the random thermal motion of the individual molecules. Gravity may cause the composition of a medium to be equalized by movement. This is called convection; it equalizes the concentration much more rapidly than diffusion. The chapter further reviews thermal conductivity. The process of thermal conduction is akin to diffusion. If the temperature is different at different points in a body, a heat flux occurs from hotter to colder regions and continues until the temperature is the same throughout the body. The mechanism of this process is based on the random thermal motion of the molecules; molecules belonging to the hotter parts of the body collide with molecules in adjoining colder parts and transmit to them a part of their energy. The thermal conductivity determines the rate of flow of heat from hotter to colder regions.

This chapter describes some of the basic facts concerning the structure of matter. All bodies are made up of a fairly small number of simple substances, the chemical elements. The smallest particle of each element is an atom of that element. The masses of the atoms are extremely small. It is, therefore, more convenient to measure them in special units and not in grams. It would be natural to take as the unit the mass of the lightest atom, that of hydrogen. However, the precise standard of atomic weights is customarily taken not as the atom of hydrogen but as that of oxygen, which is more convenient for chemical purposes. The oxygen atom is approximately 16 times heavier than the hydrogen atom and the unit of atomic weight is taken as one-sixteenth of the mass of the oxygen atom. The mass of the atom of any element expressed in these units is called the atomic weight of the element and is denoted by A. The mass of an atom in grams is proportional to its atomic weight. It is, therefore, clear that the number of atoms in a quantity of any element whose mass in grams is numerically equal to the atomic weight of that element, which is called a gram-atom of the element, is the same for every element. This is called Avogadro's number.

This chapter discusses chemical reactions from the physical point of view with respect to the properties that are common to all reactions, whatever the chemical nature of the reacting substances. Any chemical reaction is accompanied by the absorption or evolution of heat. In the former case, the reaction is said to be endothermic and in the latter case, the reaction is exothermic. It is clear that if a reaction is exothermic, the reverse reaction is endothermic and vice versa. The heat involved in a reaction depends in general on the conditions under which it occurs. Hence, the quantity of heat is distinguished accordingly as the reaction occurs at constant pressure or at constant volume. In practice, however, the difference is usually very slight. The heat of reaction is written in the reaction equation with a positive sign on the side where heat is evolved or with a negative sign where it is absorbed. As a chemical reaction proceeds, the quantities of the original substances decrease and reaction products accumulate. Ultimately, the reaction leads to a state in which the quantities of all the substances no longer vary. This is called a state of chemical equilibrium, a particular case of thermal equilibrium. The chapter explains chemical equilibrium. It also discusses strong and weak electrolytes, activations energy, the molecularity of reactions, and chain reactions.

The fundamental concept of mechanics is that of motion of a body with respect to other bodies. The relativity of motion arises from the relativity of the concept of space itself. This chapter discusses the principle of the relativity of motion. It is reasonable to begin the study of the laws of motion by considering the motion of a body of small dimensions. The motion of such a body is especially simple because there is no need to take into account the rotation of the body or the relative movement of different parts of the body. A body whose size may be neglected in considering its motion is called a particle and is a fundamental object of study in mechanics. The possibility of treating the motion of a given body as that of a particle depends not only on its absolute size but also on the conditions of the physical problem concerned. The position of a particle in space is defined by specifying three coordinates, for instance, the three Cartesian coordinates x, y, z. For this reason, a particle is said to have three degrees of freedom. The motion of a particle is described by its velocity. The chapter also discusses momentum, motion under reactive forces, centre of mass, acceleration, force, dimensions of physical quantities, motion in a uniform field, work and potential energy, the law of conservation of energy, internal energy, boundaries of the motion, elastic collisions, and angular momentum. Besides energy and momentum, another vector quantity called angular momentum is conserved for any closed system. This quantity is the sum of the angular momenta of the individual particles. The law of conservation of angular momentum is valid for a closed system and not, in general, for the individual particles forming the system; however, it may be valid for a single particle moving in a force field.

This chapter discusses some thermal process called adiabatic processes and Joule–Kelvin processes. A very simple adiabatic process is the expansion of a gas into a vacuum; the gas is initially in a part of a vessel separated from the rest of the vessel by a partition and then, an opening is made in the partition and the gas fills the whole vessel. As the gas does not do any work in such an expansion, its energy remains constant, that is, the energy of the gas before the expansion is equal to its energy E2 after the expansion. The chapter also describes a process called Carnot cycle, which shows that, in principle, work can be done reversibly by means of two bodies at different temperatures. Being the maximum possible amount, this work is independent of the properties of the working medium. All thermal phenomena reduce ultimately to the mechanical movement of the atoms and molecules in a body. The irreversibility of thermal processes is, therefore, at first sight, in conflict with the reversibility of all mechanical motions. This contradiction is only apparent. The irreversibility of thermal processes is probabilistic. The spontaneous passage of a body from an equilibrium state to a nonequilibrium state is not impossible but only very much less probable than that from a non-equilibrium state to an equilibrium state. The irreversibility of thermal processes is ultimately because of the very large number of molecules of which bodies are composed.

Solutions are mixtures of two or more substances in which the substances are mixed on the molecular scale. The relative amounts of the various substances in the mixture may vary over a more or less wide range. If one substance is present in greater quantity than the others, it is called the solvent and the other substances are called solutes. The composition of a solution is described by its concentration that gives the relation between the quantities of the substances in the mixture —the components of the mixture as they are called. The concentration can be defined in various ways. Physically, the most informative is the molar concentration, that is, the ratio of the numbers of molecules or the ratio of the quantities expressed in moles. Alternatively, one may use concentrations by weight, volume, and so on. The mutual solubility of two substances usually has definite limits; no more than a certain amount of solute can dissolve in a given quantity of solvent. A solution containing the maximum possible quantity of solute is said to be saturated. If further solute is added to such a solution, it will not dissolve. Therefore, it can be said that a saturated solution is one that is in thermal equilibrium with the pure solute. The concentration of the saturated solution is a measure of the ability of a given substance to dissolve in the solvent concerned and is simply called the solubility of the substance. The solubility in general depends on the temperature.

Unlike liquids, solids resist both change in volume and change in shape; solids resist, therefore, any deformation. Work must be done even to change the shape alone of a solid, without altering its volume. It may be said that the internal energy of a solid depends on its shape and on its volume. In consequence, Pascal's law does not apply to solids; the pressure transmitted by a solid is different in different directions. The pressures that occur in a solid when it is deformed are called elastic stresses. Unlike the pressure in a liquid, the elastic-stress force in a solid may be in any direction relative to the area on which it acts. The simplest type of deformation of a solid is extension. An extension is a uniform deformation, that is, one in which each volume element in the body is deformed in the same way. The formulae for a simple extension are easily generalized to any uniform deformations. This chapter reviews some particular cases of uniform deformation. It also discusses uniform compression. Under uniform compression, the shape of a body remains the same and only its volume changes. In the opposite kind of deformation, that is, shear deformation, only the shape of the body changes and not its volume. There is a fundamental difference between compression or extension and shear deformations. The chapter explains these differences and describes plasticity.