Kinetic Interpretation Of Temperature

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The average translational kinetic energy of a single gas molecule depends only on absolute temperature; calculate this energy for a molecule at 300 K.

RankGuru · Accepted Answer

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 $k_B=1.38	imes10^{-23}$ 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 $\overline{KE}=\frac{3}{2}	imes1.38	imes10^{-23}	imes300=6.21	imes10^{-21}$ J. The option $4.14	imes10^{-21}$ J wrongly uses $k_B T$ without the factor $3/2$. The option $2.07	imes10^{-21}$ J corresponds to only one degree of freedom, $\frac{1}{2}k_B T$, not the full translational energy. The option $9.0	imes10^{-21}$ 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.

Kinetic Interpretation Of Temperature

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