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(C) According to the kinetic theory of gases, the average kinetic energy of a gas molecule is given by $K.E. = \frac{3}{2} k_B T$. This shows that the

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$a$ and $c$ are true

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(C) According to the kinetic theory of gases, the average kinetic energy of a gas molecule is given by $K.E. = \frac{3}{2} k_B T$. This shows that the temperature $T$ is a direct measure of the average kinetic energy of the molecules. Thus, statement $(a)$ is true.Temperature is a state function that depends only on the average kinetic energy of the particles and is independent of the nature of the gas. Thus, statement $(b)$ is false.The average speed of gas molecules is given by $v_{avg} = \sqrt{\frac{8RT}{\pi M}}$, where $M$ is the molar mass. Since $v_{avg} \propto \frac{1}{\sqrt{M}}$, heavier molecules (larger $M$) have a lower average speed. Thus, statement $(c)$ is true and statement $(d)$ is false.Therefore, statements $(a)$ and $(c)$ are true.

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