Question

Deduce Boyle’s law based on kinetic theory.

Answer 1

Boyle’s law: From PV = `2/3` U

But the internal energy of an ideal gas is equal to N times the average kinetic energy (ε) of each molecule. U = Nε.

For a fixed temperature, the average translational kinetic energy ε will remain constant. It implies that

PV = `2/3 "N"ε`

Thus PV = constant, Therefore, the pressure of a given gas is inversely proportional to its volume provided the temperature remains constant. This is Boyle’s law.