Ideal Gases

What "temperature" really measures

• Temperature is a measure of the average kinetic energy of the particles in a substance
• Hotter substance means particles moving on average faster, which means higher average kinetic energy
• The link is proportional when temperature is measured in kelvin:

T (in K) ∝ average kinetic energy of particles

• This is why Kelvin is the right scale for gas laws: doubling the Kelvin temperature genuinely doubles the average kinetic energy of the molecules. Doubling the Celsius temperature does not: going from 1 °C to 2 °C is only 0.36 % more average kinetic energy

Why all states show this behaviour

• The temperature–KE link applies to every state of matter:
  • in a gas, almost all the internal energy sits in the kinetic store (molecules barely interact), so KE and temperature are tightly linked
  • in a solid, most of the kinetic energy is vibrational rather than translational, but the rule still holds, so hotter solids vibrate harder
  • in a liquid, similarly, particles slide past each other faster as the temperature climbs

Evaporation cools the liquid that's left behind

• When a liquid evaporates, only the most energetic surface molecules can break free of the intermolecular bonds and escape as vapour
• The molecules left behind have a lower average kinetic energy than before
• Lower average KE means lower temperature, so the remaining liquid cools
• This is the physics behind sweating, why a wet swimsuit feels cold in a breeze, and why fridges and air conditioners use an evaporating refrigerant to extract heat