Deduce Boyle's law based on kinetic theory.

Explanation

Boyle's law:
From equation `P=(2)/(3)(U)/(V)=(2)/(3)u`, we know that `PV=(2)/(3)U`
But the internal energy of an ideal gas is equal to N times the average kinetic energy `(in)` of each molecule
`U=Nin`
For a fixed temperature, the average translational kinetic energy `in` will remain constant. It implies that `PV=(2)/(3)Nin` Thus PV = constant
Therefore, pressure of a given gas is inversely proportional to its volume provided the temperature remains constant. This is Boyle's law.