Kinetic Theory of Temperature and Pressure
| English | Chinese | Pinyin |
|---|---|---|
| kinetic theory | 分子运动论 | fēn zǐ yùn dòng lùn |
| kelvin | 开尔文 | kāi ěr wén |
Heat a gas — and you just make its particles fly faster
- Warm up a gas and nothing visible changes, yet its tiny particles start racing around faster.
- Temperature is, at heart, a measure of how fast the particles jiggle and fly.
- The gas also pushes on its container — pressure — because particles keep hitting the walls.
- The kinetic theory 分子运动论 explains both from one picture: countless particles in constant motion.
A gas is mostly empty space
- A gas is a swarm of tiny particles, far apart, in constant random motion.
- They fly in straight lines until they collide with each other or the walls.
- Between collisions they barely feel any force — the space is mostly empty.
- This simple model predicts real gas behaviour remarkably well.
Faster at higher temperature
Raise the temperature and watch the particle-speed distribution shift to higher speeds.
A hotter gas has particles that move ____ on average.
Higher temperature means more average kinetic energy, so faster particles.
Temperature is average kinetic energy
- Temperature is proportional to the average kinetic energy of the particles.
- Hotter gas ⇒ faster particles ⇒ more kinetic energy per particle.
- On the kelvin 开尔文 scale, doubling the temperature doubles the average kinetic energy.
- At absolute zero ($0\ \text{K}$) particle motion is at its absolute minimum.
In kinetic theory, the temperature of a gas is a measure of the particles':
Temperature is proportional to the average kinetic energy of the particles.
Doubling the kelvin temperature of a gas doubles the average kinetic energy of its particles.
On the kelvin scale, average kinetic energy is proportional to temperature.
Pressure comes from collisions
- Each particle bouncing off a wall gives it a tiny push.
- Pressure is the total force of all those collisions, spread over the wall's area.
- More particles, faster particles, or a smaller box all mean more collisions and higher pressure.
- So temperature and pressure both trace back to particle motion.
What causes the pressure a gas exerts on its container?
Each collision with a wall gives a tiny push; together they make the pressure.
Select all ways to increase the pressure of a gas in a fixed container.
More or faster particles, or less space, all mean more frequent, harder collisions. Cooling lowers pressure.
Temperature must be measured in kelvin for the kinetic-theory relations. "Doubling the temperature doubles the average kinetic energy" is only true on the kelvin scale — never in $^\circ\text{C}$. Convert to kelvin first: $T_K = T_C + 273$.
Convert $27\ ^\circ\text{C}$ to kelvin (use $T_K = T_C + 273$).
$T_K = 27 + 273 = 300\ \text{K}$.
A sealed rigid box of gas is heated so its kelvin temperature doubles.
- The average kinetic energy of the particles also doubles.
- The particles hit the walls harder and more often, so the pressure roughly doubles too.
Kinetic theory models a gas as many tiny particles in constant random motion. Temperature (in kelvin) is proportional to their average kinetic energy, and pressure comes from their collisions with the walls. Hotter and more crowded both mean higher pressure.