How to study Boyle's law - JEE Main

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Published on February 20, 2014

Author: ednexa

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How to study Boyle's law - JEE Main by ednexa.com

Boyle’s law using the expression for pressure exerted by an ideal gas Boyle’s law : At a constant temperature, the pressure exerted by a fixed mass of gas is inversely proportional to its volume. If p and V denote the pressure and volume of a fixed mass of gas, then pV = constant at a constant temperature, for a fixed mass of gas. According to the kinetic theory of an ideal gas, the pressure exerted by the gas is given by p 2 1 Nm0crms 3 V where, N is the number of molecules of the gas, m0 is the mass of a single molecule, crms is the rms speed of the molecules and V is the volume occupied by the gas. We can write the above equation as 2 1 2  pV   m0crms   N 2  3  (KE of a gas molecule)  2 N 3 …(i)

For a fixed mass of gas, N is constant. Further, in the ideal gas model, intermolecular forces are ignored so that the potential energy of the gas molecules may be assumed to be zero. Therefore, 1 2 m0 crms is also the total 2 1 2  N  m0crms  energy of a gas molecule and  2  is the total energy of the gas molecules, which is proportional to the absolute temperature of the gas. Then, the right hand side of equation (i) will be constant if its temperature is constant. Hence, it follows that pV = constant for an isolated mass of gas at constant temperature. Keep on visiting www.ednexa.com for more study materials. - Team Ednexa

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