Behaviour Of Perfect Gas And Kinetic Theory

Check us out at www.tutorvista.com A theory, largely the work of Count , James Prescott Joule, and James Clerk Maxwell, that explains the physical properties of matter in terms of the motions of its constituent particles. In a gas, for example, the pressure is due to the incessant impacts of the gas molecules on the walls of the container. If it is assumed that the molecules occupy negligible space, exert negligible forces on each other except during collisions, are perfectly elastic, and make only brief collisions with each other, it can be shown that the pressure p exerted by one mole of gas containing n molecules each of mass m in a container of volume V, will be given by: p=nm¯c2/3V , where ¯c2 is the mean square speed of the molecules. As according to the gas laws for one mole of gas: pV=RT, where T is the thermodynamic temperature, and R is the molar gas constant, it follows that: RT=nm¯c2/3 Thus, the thermodynamic temperature of a gas is proportional to the mean square speed of its molecules. As the average kinetic energy of translation of the molecules is m¯c2/2, the temperature is given by: T=(m¯c2/2)(2n/3R) The number of molecules in one mole of any gas is the Avogadro constant, NA; therefore in this equation n=NA. The ratio R/NA is a constant called the Boltzmann constant (k). The average kinetic energy of translation of the molecules of one mole of any gas is therefore 3kT/2. For monatomic gases this is proportional to the internal energy (U) of the gas, ie U ...
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