Question

derive boyl's law from kinetic molecular theory of gases?

Answer 1

According to Boyle's Law, at constant temperature, the pressure exerted by a fixed mass of a gas is inversely proportional to the volume occupied by the gas.
P ∝ 1 / V
⇛PV = constant, where
P = pressure of an enclosed gas
V = volume of an enclosed gas

This relation can be derived on the basis of the kinetic theory of gases. Consider a gas of volume Vwith N molecules, each of mass m. Mass of the gas, M = N m.
According to the kinetic theory of gases, the expression for pressure is given by the following equation:
$$\begin{gathered} P=\frac{1}{3}\mathrm{\rho }{C^2}_{Rms} \\ P=\frac{1}{3}\frac{M}{V}{C^2}_{Rms} \\ PV=\frac{1}{3}Nm{C^2}_{Rms} \\ PV=\frac{2}{3}N\left(\frac{1}{2}m{C^2}_{Rms}\right) \end{gathered}$$
Since N is constant, the quantity $\frac{1}{2}mN{C^2}_{Rms}$ , which is the average kinetic energy of the gas molecules, remains constant at constant temperature. Therefore,
PV = constant or
P ∝ 1/ V
This equation is known as Boyle's Law.