Saturday, 17 September 2011

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 (. 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 1mv2, 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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