Diane Greco, Ph.D., Massachusetts
Institute of Technology
It is possible to identify the development of the idea of energy
conservation in the nineteenth century with the confluence of three
traditions: a medieval tradition linking motion and mechanics; a tradition
of correlated forces with roots in the Enlightenment; and an engineering
tradition, unique to the nineteenth century, that linked heat and
mechanical work. Of these three, only the last two are particularly
relevant to the nineteenth century.
The tradition of correlated forces was founded on a belief that it was possible to reduce imponderable phenomena (heat, light, electricity, magnetism) to the workings of a single universal fluid. Because many preferred the more easily quantifable notion of different fluids for different imponderables, this scheme fell out of favor in the late eighteenth century; however, the Voltaic pile (1800) changed that view dramatically. Working after Volta during the first half of the century, H. C. Ørsted and Michael Faraday's establishment of connections between electric and magnetic forces provided a foundation for the interchangability of natural forces. The electric current generated heat and light; in 1820, Ørsted showed that it also induced magnetic force. In 1831, Faraday inverted the induction, demonstrating that electric current can be produced by moving magnets. Others, especially in physiology (Liebig, Helmholtz, Müller), established connections between heat, chemical activity, and muscular work in studies of animal physiology. By 1840, several different physicists had announced the equivalence and convertability of all forms of "force."
After Laplace, the everyday use of differential equations to describe the behavior of imponderables allowed researchers to dispense with speculations about the nature of particular imponderables and to explain their behavior using similar models for all types of imponderables in order to better achieve the goal of formal unity. In this way, it was hoped that all imponderables could be described by a single set of equations. By 1850, the formulation of the law of conservation of energy allowed researchers to reject the supposition of anomalous or diverse forms of matter (as separate imponderables) in favor of an even more reductive concept of matter, composed of nothing but particles in motion.
Others, such as Sadi Carnot (1796-1832) and J. P. Joule, worked in an engineering tradition, thereby establishing the equivalence of heat and mechanical work. The science of thermodynamics, a branch of physical science concerned with the direction of heat flow in the production of work, emerged from this area of research. Until Joule demonstrated in the 1840s that heat and mechanical work were equivalent, physicists considered mechanical and non-mechanical processes as separate physical systems. In 1824, Sadi Carnot's theory of heat engines, a study of steam and the efficiency of steam engines, identified the temperature difference in an engine as the crucial factor in the generation of work; work was generated by the passage of heat from a warmer to a cooler body, heat being conserved in the process.
At mid-century, Rudolf Clausius and William Thomson independently developed the first two laws of thermodynamics from Carnot and Joule:
- The amount of energy in a system always remains constant.
- Entropy, or the state of internal organization of a gas, is almost always increasing.
(In 1905, Walther Nernst proposed a third law, that the entropy of a system vanishes as it cools to absolute zero. Quantum physics later rendered this law inadequate, maintaining that a zero-point energy exists for molecular oscillations even at absolute zero.)
For both Clausius and Thomson, heat consisted of the motion of particles comprising the bodies under investigation, rather than some quality inherent in the microstructure of molecules, such as caloric. This new, kinetic theory of heat interpreted macroscopic properties of a gas (such as pressure and temperature) as functions of the average values of the momentum and energy of its constituent particles. Computing these averages proved a formidable task, for which Maxwell introduced a statistical distribution function in 1859. Maxwell's treatment left one fundamental question unanswered: if entropy almost always increases, its growth is irreversible, yet the laws of mechanics are reversible. How can entropy be a mechanical quantity?
Addressing this problem in 1877, Ludwig Boltzmann provided the fundamental statement of statistical mechanics: the second law of thermodynamics does not hold absolutely, but is rather a statement of relative probabilities. Specifically, Boltzmann showed that if molecules in a gas have many equally likely microstates, the vast number of molecules with states at equilibrium overwhelms the very few at any other condition. Boltzmann thus defined the entropy of a gas as proportional to the logarithm of the number of microstates that define its macroscopic condition. (This constant of proportion, k, is known as Boltzmann's Constant.) When a system is not at equilibrium, its entropy is almost always increasing; equilibrium states have a tremendously high entropy.
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