Chapter 5: Kinetic TheoryClass 11 Physics — summary, notes, extra questions & MCQ quiz

Summary

Kinetic theory explains the behaviour of gases by treating them as large numbers of tiny molecules in rapid, random motion, with intermolecular forces negligible except during brief elastic collisions. Matter is made of atoms about an angstrom in size; in gases the molecules are far apart, so the mean free path is large. Gases at low pressure and high temperature obey the ideal-gas equation \(PV=\mu RT=k_B NT\), which embodies Boyle's law, Charles' law, Avogadro's hypothesis and Dalton's law of partial pressures. From the assumption of elastic molecular collisions with the walls, the pressure of an ideal gas is derived as \(P=\tfrac13 nm\overline{v^{2}}\), leading to the kinetic interpretation of temperature: the average translational kinetic energy of a molecule is \(\tfrac32 k_B T\), independent of the gas, and the root-mean-square speed is \(v_{rms}=\sqrt{3k_B T/m}\). The law of equipartition of energy assigns \(\tfrac12 k_B T\) to each degree of freedom, explaining the molar specific heats of monatomic, diatomic and polyatomic gases and of solids. The mean free path \(l=1/(\sqrt2\,\pi n d^{2})\) is the average distance a molecule travels between collisions and accounts for diffusion, viscosity and conduction in gases.

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