Question

Derive Boyle's law using kinetic theory of gases.

Answer 1

According to Boyle's law at constant temperature pressure & volume of gas are related as $PV=$ Constant

According to kinetic theory, pressure of gas is

$P=\frac{1}{3}r{V}^2$

Since $\frac{mv}{v}=r$

$PV=\frac{1}{3}mN{v}^2$

Multiplying & dividing by $2$ on $RHS$

$PV=\frac{2}{3}N\left(\frac{1}{2}m{V}^2\right)$

$\frac{1}{2}m{V}^2=K.E.$

$PV=\frac{2}{3}NK.E.$= constant