The particle model says that all matter is made of tiny particles that are always moving. In a gas, these particles are far apart and bounce around like a crowded dance floor. The faster they move, the higher the temperature of the gas. Think of the particles as energetic dancers: when the music (heat) gets louder, they dance faster and the room feels warmer.
Relate the temperature of a gas to the average kinetic energy of its particles and remember the simple conversion between Celsius and Kelvin:
\$T(\text{K}) = \theta(\degree\text{C}) + 273\$
In a gas, the average kinetic energy of the particles is directly proportional to the temperature:
\$\langle KE \rangle \propto T\$
If you double the temperature, the particles move roughly twice as fast on average. This is why a hot cup of coffee feels warmer than a cold one – the coffee’s molecules are dancing faster!
| °C (Celsius) | K (Kelvin) |
|---|---|
| 0 | 273 |
| 25 | 298 |
| 100 | 373 |
Suppose a gas is at \$25\degree\text{C}\$.
1. Convert: \$T = 25 + 273 = 298\,\text{K}\$.
2. Calculate: \$\langle KE \rangle = \frac{3}{2} (1.38 \times 10^{-23}) (298) \approx 6.2 \times 10^{-21}\,\text{J}\$.
Temperature is a *measure* of how fast the particles are moving on average. The higher the temperature, the higher the average kinetic energy. And the simple conversion \$T(\text{K}) = \theta(\degree\text{C}) + 273\$ lets you switch between the two units in a snap. 🚀