Physics

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The Second Law of Thermodynamics

While the first law indicates that energy must be conserved in any interactions between a system and its surroundings, it gives no indication whether all forms of mechanical and thermal energy exchange are possible. That overall changes in energy proceed in one direction was first formulated by the French physicist and military engineer Nicolas Léonard Sadi Carnot, who in 1824 pointed out that a heat engine (a device that can produce work continuously while only exchanging heat with its surroundings) requires both a hot body as a source of heat and a cold body to absorb heat that must be discharged. When the engine performs work, heat must be transferred from the hotter to the colder body; to have the inverse take place requires the expenditure of mechanical (or electrical) work. Thus, in a continuously working refrigerator, the absorption of heat from the low temperature source (the cold space) requires the addition of work (usually as electrical power), and the discharge of heat (usually via fanned coils in the rear) to the surroundings (see Refrigeration). These ideas, based on Carnot's concepts, were eventually formulated rigorously as the second law of thermodynamics by the German mathematical physicist Rudolf Julius Emanuel Clausius and by Lord Kelvin in various alternate, although equivalent, ways. One such formulation is that heat cannot flow from a colder to a hotter body without the expenditure of work.

From the second law, it follows that in an isolated system (one that has no interactions with the surroundings) internal portions at different temperatures will always adjust to a single uniform temperature and thus produce equilibrium. This can also be applied to other internal properties that may be different initially. If milk is poured into a cup of coffee, for example, the two substances will continue to mix until they are inseparable and can no longer be differentiated. Thus, an initial separate or ordered state is turned into a mixed or disordered state. These ideas can be expressed by a thermodynamic property, called the entropy (first formulated by Clausius), which serves as a measure of how close a system is to equilibrium—that is, to perfect internal disorder. The entropy of an isolated system, and of the universe as a whole, can only increase, and when equilibrium is eventually reached, no more internal change of any form is possible. Applied to the universe as a whole, this principle suggests that eventually all temperature in space becomes uniform, resulting in the so-called heat death of the universe.

Locally, the entropy can be lowered by external action. This applies to machines, such as a refrigerator, where the entropy in the cold chamber is being reduced, and to living organisms. This local increase in order is, however, only possible at the expense of an entropy increase in the surroundings; here more disorder must be created.

This continued increase in entropy is related to the observed nonreversibility of macroscopic processes. If a process were spontaneously reversible—that is, if, after undergoing a process, both it and all the surroundings could be brought back to their initial state—the entropy would remain constant in violation of the second law. While this is true for macroscopic processes, and therefore corresponds to daily experience, it does not apply to microscopic processes, which are believed to be reversible. Thus, chemical reactions between individual molecules are not governed by the second law, which applies only to macroscopic ensembles.

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From the promulgation of the second law, thermodynamics went on to other advances and applications in physics, chemistry, and engineering. Most chemical engineering, all power-plant engineering, and air-conditioning and low-temperature physics are just a few of the fields that owe their theoretical basis to thermodynamics and to the subsequent achievements of such scientists as Maxwell, the American physicist J. Willard Gibbs, the German physical chemist Walther Hermann Nernst, and the Norwegian-born American chemist Lars Onsager.

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Kinetic Theory and Statistical Mechanics

The modern concept of the atom was first proposed by the British chemist and physicist John Dalton in 1808 and was based on his studies that showed that chemical elements enter into combinations based on fixed ratios of their weights. The existence of molecules as the smallest particles of a substance that can exist in the free—that is, gaseous—state and have the properties of any larger amount of the substance, was first hypothesized by the Italian physicist and chemist Amedeo Avogadro in 1811, but did not find general acceptance until about 50 years later, when it also formed the basis of the kinetic theory of gases (see Avogadro's Law). Developed by Maxwell, the Austrian physicist Ludwig Boltzmann, and other physicists, it applied the laws of mechanics and probability to the behavior of individual molecules, and drew statistical inferences about the properties of the gas as a whole.

A typical but important problem solved in this manner was the determination of the range of speeds of molecules in the gas, and from this the average kinetic energy of the molecules. The kinetic energy of a body, as a simple consequence of Newton's second law, is ymv², where m is the mass of the body and v its velocity. One of the achievements of kinetic theory was to show that temperature, the macroscopic thermodynamic property describing the system as a whole, was directly related to the average kinetic energy of the molecules. Another was the identification of the entropy of a system with the logarithm of the statistical probability of the energy distribution. This led to the demonstration that the state of thermodynamic equilibrium corresponding to that of highest probability is also the state of maximum entropy. Following the success in the case of gases, kinetic theory and statistical mechanics were subsequently applied to other systems, a process that is still continuing.

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Early Atomic and Molecular Theories

The development of Dalton's atomic theory and Avogadro's molecular law had overriding influence on the development of chemistry, in addition to their importance in physics.

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Avogadro's Law

Avogadro's law, which was easily proved by kinetic theory, indicated that a specified volume of a gas at a given temperature and pressure always contained the same number of molecules, irrespective of the gas selected. This number, however, could not be accurately determined, and the 19th-century physicists therefore had no sound knowledge of molecular or atomic mass and size until the turn of the 20th century, when subsequent to the discovery of the electron, the American physicist Robert Andrews Millikan carefully determined its charge. This finally permitted accurate determination of the so-called Avogadro's number, which is the number of molecules in that amount of material exactly equal to its molecular weight.

Besides the mass, another quantity of interest was the size of an atom. Various and only partly successful attempts at finding the size of an atom were made during the latter part of the 19th century; the most successful applied the results of kinetic theory to nonideal gases—that is, gases the behavior of which depended on the fact that molecules were not points but had finite volumes. Only later experiments involving the scattering of X rays, alpha particles, and other atomic and subatomic particles by atoms led to more precise measurements of their size as being between 10^-8 and 10^-7 cm (4 × 10^-7 and 4 × 10^-6 in) in diameter. A precise statement about the size of an atom, however, requires some explicit definition of what is meant by size, since most atoms are not exactly spherical and can exist in various states that change the distance between the nucleus and the electrons within the atom.

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Spectroscopy

One of the most important developments leading to the exploration of the interior of the atom, and to the eventual overthrow of the classical theories of physics, was spectroscopy; the other was the discovery of the subatomic particles themselves.

In 1823 the British astronomer and chemist Sir John Frederick William Herschel suggested that a chemical substance might be identified by examining its spectrum—that is, the discrete wavelength pattern in which light from a gaseous substance is emitted. In the years that followed, the spectra of a great many substances were cataloged by two Germans, the chemist Robert Wilhelm Bunsen and the physicist Gustav Robert Kirchhoff. Helium was first discovered as a new element following the discovery of an unexplained spectral line in the sun's spectrum by the British astronomer Sir Joseph Norman Lockyer in 1868. From the standpoint of atomic theory, however, the most important contributions were made by the study of the spectra of simple atoms, such as hydrogen, which showed few spectral lines. See Chemical Analysis.

Discrete line spectra originate from gaseous substances where, in terms of modern knowledge, the electrons have been excited by heat or by bombardment with subatomic particles. In contrast, a heated solid has a continuous spectrum over the full visible range and into the infrared and ultraviolet regions. The total amount of energy emitted depends strongly on the temperature, as does the relative intensity of the different wavelength components. As a piece of iron is heated, for example, its radiation is first in the infrared spectrum and cannot be seen; it then extends into the visible spectrum where the glow shifts from red to white as the peak of its radiant spectrum shifts toward the middle of the visible range. Attempts to explain the radiation characteristics of solids, using the tools of theoretical physics available at the end of the 19th century, led to the prediction that at any given temperature the amount of radiation increased with frequency and without limit. This calculation, in which no error was found, was in disagreement with experiment and also led to an absurd conclusion: A body at a finite temperature could radiate an infinite amount of energy. This required a new way of thinking about radiation and, indirectly, about the atom. See Infrared Radiation; Ultraviolet Radiation.