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Kinetic interpretation of temperature
Intermediate
Temperature is proportional to mean translational kinetic energy.
⟨K⟩ = (3/2)k_BTComparing P = ⅓nm⟨v²⟩ with PV = NkT gives ⟨½mv²⟩ = (3/2)kT: temperature is proportional to the mean translational kinetic energy.
At 300 K the average kinetic energy is 6.2×10⁻²¹ J (0.039 eV).
It applies to translational energy, independent of molecule mass.
In more detail
Temperature is proportional to the average translational kinetic energy of gas molecules, ⟨KE⟩ = (3/2)kT. Higher temperature means faster average motion.
Real-world uses
- Explaining why hot gases expand and pressurise containers.
- Relating temperature in engineering to molecular energy.
- Physicists use the average kinetic energy of gas molecules to explain why temperature has a sharp meaning at the particle level.
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Frequently asked questions
Is temperature the average speed?
No, it is proportional to the average kinetic energy, which depends on speed squared.
What is k?
The Boltzmann constant, linking temperature to energy.
Is temperature the same as the energy of one molecule?
No. Temperature relates to the average kinetic energy across many molecules, not the energy of any single one.
Related topics in Kinetic Theory & Statistical Physics
Brownian motion · Ideal gas assumptions · Pressure from molecular collisions · Boltzmann constant · RMS speed · Mean free path