Kinetic Interpretation Of Temperature

Temperature in kinetic theory is a direct measure of molecular motion, and the average translational kinetic energy of one molecule is $\overline{KE}=\frac{3}{2}{k}_{B}T$, where $k_B=1.38\times 10^{-23}$ J/K is the Boltzmann constant. This relation arises because each of the three translational directions contributes $\frac{1}{2}{k}_{B}T$, and it shows the energy is independent of the gas's identity and mass, depending solely on absolute temperature. Two different gases at the same temperature therefore have molecules with identical average translational energies even though their individual speeds differ. Substituting $T=300$ K gives $\overline{KE}=\frac{3}{2}\times 1.38\times 10^{-23}\times 300=6.21\times 10^{-21}$ J. The option $4.14\times 10^{-21}$ J wrongly uses $k_{B}T$ without the factor $3/2$. The option $2.07\times 10^{-21}$ J corresponds to only one degree of freedom, $\frac{1}{2}{k}_{B}T$, not the full translational energy. The option $9.0\times 10^{-21}$ J overestimates by assuming an incorrect temperature near 435 K. This is the standard NCERT result linking the kinetic interpretation of temperature to the equipartition of energy, and it underlies the definition of absolute zero as the state where molecular motion ceases. As a plausibility check, molecular energies at room temperature are of order $10^{-21}$ J, fully consistent with our answer.