Question

Temperature measures the total kinetic energy of all particles in a system

Answer 1

Not quite — temperature is not the total kinetic energy. Temperature is (roughly) a measure of the average energy per degree of freedom of the particles, not the sum over all particles.

Key points:
- Intensive vs extensive: Temperature is an intensive property (doesn't depend on system size). Total kinetic energy is extensive (scales with particle number).
- Ideal monatomic gas: the average translational kinetic energy per particle is (3/2)kT, so
- average KE per particle = (3/2) kT
- total KE = N × (3/2) kT
Thus two gases at the same T have the same average KE per particle even if one contains many more particles and so has a larger total KE.
- Equipartition: In classical systems each quadratic degree of freedom contributes (1/2)kT on average. For molecules with rotational or vibrational modes, temperature relates to the average energy distributed among those modes.
- Limitations and caveats:
- In interacting systems some energy is stored as potential energy, so total internal energy ≠ total kinetic energy.
- Quantum effects at low temperature can break classical equipartition (heat capacities drop).
- “Negative temperature” is a special, non‑intuitive case possible only in systems with bounded energy spectra — it does not mean “colder” than zero.

Short summary: temperature ≈ average energy per particle (per degree of freedom); total kinetic energy depends on number of particles and is not what temperature measures.