Average kinetic energy of a molecule is = (3/2)kT Avg. K.E is directly proportional to temp.(T) only. As you increase temp of gas then K.E will also increase. In my book given that, Average K.E is independent of pressure, Volume or nature of the gas. When you increase the pressure of a gas temp of gas will increase (gay lussac's law ) if temp. increase then Avg. K.E of gas also increase. Then how the K.E is independent from pressure.