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(C) The kinetic theory of gases states that the average kinetic energy $(KE)$ of gas molecules is directly proportional to the absolute temperature.Fr

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Charles's law and Boyle's law

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(C) The kinetic theory of gases states that the average kinetic energy $(KE)$ of gas molecules is directly proportional to the absolute temperature.From the kinetic theory,the pressure $P$ and volume $V$ are related by the equation: $PV = \frac{1}{3} m n v_{	ext{rms}}^2 = \frac{2}{3} 	imes (\frac{1}{2} m n v_{	ext{rms}}^2) = \frac{2}{3} E_k$,where $E_k$ is the total kinetic energy.Boyle's law states that at a constant temperature,the average $KE$ is constant. Therefore,$v_{	ext{rms}}$ remains unchanged. If the volume increases,the pressure of the gas decreases such that $PV = 	ext{constant}$.Charles's law states that if we allow the volume to change to maintain constant pressure,the volume will increase with increasing temperature,i.e.,$V = KT$.Since the kinetic theory of gases successfully derives both laws,option $(C)$ is correct.

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