11%20-%20Kinetic%20Theory%20of%20Gases

# 11%20-%20Kinetic%20Theory%20of%20Gases - 11 KINETIC THEORY...

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11 - KINETIC THEORY OF GASES Page 1 Introduction The constituent particles of the matter like atoms, molecules or ions are in continuous motion. In solids, the particles are very close and oscillate about their mean positions. In gases, at low density, the particles are far away from each other and perform random motion in all directions. Also, the interactions among them are negligible. In liquids, the particles are slightly more away than in solids and their motion is less free than in gases. Pressure, temperature, volume, internal energy associated with gas are known as macroscopic physical quantities which are manifested as an average combined effect of the microscopic processes. Macroscopic quantities like, pressure, temperature, volume can be measured while internal energy can be calculated from them. Description of a system using these quantities is known as macroscopic description. Macroscopic quantities and their interrelationships can be understood from the processes occurring between the constituent particles at microscopic level, e.g., pressure of a gas can be understood from the transfer of momenta to the walls of the container by the collisions of the molecules making random motion. Thus, description of the system in relation to the speed, momentum and kinetic energy of its constituent particles is known as microscopic description. Kinetic theory of gases is an approach wherein the laws of mechanics are applied ( statistically ) to the constituent particles of the system ( i.e., gas ) and macroscopic quantities are obtained in terms of its microscopic quantities with the help of a mathematical scheme. 11.1 Laws of ideal gas Boyle’s law: “At constant temperature, volume of a fixed amount of gas, having sufficiently low density, is inversely proportional to its pressure.” V P 1 ( for fixed amount and fixed temperature ) PV = constant Figure shows P V curves for some real gas at three different temperatures obtained experimentally ( shown by continuous lines ) and theoretically using Boyle’s law ( shown by broken lines ). From the graphs, it can be seen that real gas follows Boyle’s law at high temperature and low pressure.

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11 - KINETIC THEORY OF GASES Page 2 Charles’ and Gay-Lussac’s law: “At constant pressure, the volume of a given amount of gas, having low density, is proportional to its absolute temperature.” V T ( for fixed amount and fixed pressure of gas) T V = constant Equation of state for an ideal gas: Combining Boyle’s and Charles’ laws, T PV = constant ( for a given amount of gas ). Also, the volume of gas is proportional to its amount at constant temperature and pressure. T
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11%20-%20Kinetic%20Theory%20of%20Gases - 11 KINETIC THEORY...

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