Why Is Kelvin Temperature a Measure of Average Kinetic Energy?

• French B
• Geography
• German A
• German A Lit
• German ab initio
• German B
• Global Politics
• History
• History (First Exam 2028)
• Mathematics Analysis and Approaches (AA)
• Mathematics Applications & Interpretation (AI)
• Philosophy
• Physics
• Psychology
• Psychology (First Exam 2027)
• Spanish A
• Spanish A Lit
• Spanish ab initio
• Spanish B
• Sports, exercise and health science (SEHS)
• Theory of Knowledge (TOK)
• World Religions

Combining this microscopic model with the ideal gas law gives

where $\overline{E_k}$ is the average translational kinetic energy per particle, $k_{\mathrm{B}}$ is the Boltzmann constant, and $T$ is the temperature in kelvin. Therefore, doubling $T$ doubles the average translational kinetic energy.

For example, at $300\,\text{K}$,

At $600\,\text{K}$, the average becomes $1.24\times10^{-20}\,\text{J}$, exactly twice as large.

The Kelvin scale is essential because it begins at absolute zero, $0\,\text{K}$. Celsius cannot represent this proportionality directly: $20\,^{\circ}\text{C}$ is not twice as energetic as $10\,^{\circ}\text{C}$. Temperatures must first be converted using $T/\text{K}=\theta/^{\circ}\text{C}+273.15$.

A common misconception is that temperature measures total internal energy. It does not: temperature relates to average particle energy, while internal energy also depends on the number of particles and intermolecular potential energy. The equation above applies specifically to translational motion in an ideal monatomic gas.

Exam Technique

For an IB Explain question, link Kelvin temperature to random particle motion and state the proportional relationship $\overline{E_k}\propto T$. Always use kelvin in gas-law and particle-energy calculations.