Explain the formula K.E = rac32 k_B T in the context of the kinetic theory of gases.

The formula shown, $K.E = \frac{3}{2} k_B T$, represents the average translational kinetic energy of a single molecule in an ideal gas.

• $K.E$ is the average translational kinetic energy per molecule, measured in Joules (J).
• $k_B$ is the Boltzmann constant, with an approximate value of $1.38 \times 10^{-23} \text{ J/K}$. It relates the average kinetic energy of particles to the absolute temperature.
• $T$ is the absolute temperature of the gas, measured in Kelvin (K).

This formula is a key result from the kinetic theory of gases, describing the energy associated with the translational motion of gas particles.