The kinetic particle model
Introduced| English | Meaning |
|---|---|
| particles/ˈpɑːtɪklz/ | Small units of matter, such as atoms, molecules, ions or subatomic entities. |
| kinetic particle model/kɪˈnetɪk ˈpɑːtɪkl ˈmɒdl/ | The model that explains matter as tiny moving particles, linking temperature to particle energy. |
| solid/ˈsɒlɪd/ | A state of matter with fixed shape and volume; particles vibrate about fixed positions. |
| liquid/ˈlɪkwɪd/ | A state of matter with a definite volume but no fixed shape, which flows to fit its container. |
| gas/ɡæs/ | A state of matter with neither a fixed shape nor a fixed volume, which expands to fill its container. |
| temperature/ˈtemprɪtʃə/ | A measure of how hot or cold something is. |
| absolute zero/ˈæbsəluːt ˈzɪərəʊ/ | The lowest temperature on the thermodynamic temperature scale, equal to zero kelvin. |
| kelvin/ˈkelvɪn/ | The SI unit of thermodynamic temperature, with zero at absolute zero. |
| Brownian motion/ˈbraʊnɪən ˈməʊʃn/ | The random motion of tiny visible particles caused by collisions with invisible fast-moving molecules; evidence for the particle model. |
Everything is made of particles 粒子
- Look closely enough and all matter is tiny particles that never stop moving.
- This one idea — the kinetic particle model 分子动理论 — explains solids 固体, liquids 液体, gases 气体, heat and pressure.
- Let's see what the particles are doing.
The three states of matter
- Solid — particles packed in a regular pattern, only vibrating. Fixed shape and volume.
- Liquid — particles still close but jumbled; they slide past each other. Fixed volume, takes the container's shape.
- Gas — particles far apart, fast and random. Fills the whole container.
Squeeze a gas (Boyle's law)
Slide the piston in to shrink the volume. The same particles get crammed into less space, so they hit the walls more often and the pressure climbs — while pressure × volume stays constant.
In which state are the particles far apart, fast, and moving in random directions?
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Gas particles are far apart and move quickly in random directions, filling the container. Solids only vibrate; liquids slide past each other.
Temperature 温度 and particle energy
- Heat a substance and its particles move faster — they gain kinetic energy.
- Temperature is a measure of the average kinetic energy of the particles.
- The lowest possible temperature is absolute zero 绝对零度, $-273\ {}^{\circ}\text{C}$ — particles have the least energy.
The particle model of solids, liquids and gases
Temperature is a measure of:
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Hotter means the particles move faster, so temperature measures their average kinetic energy.
The kelvin 开尔文 scale
- Scientists often measure temperature in kelvin (K), starting from absolute zero.
- To convert:
- So $0\ {}^{\circ}\text{C} = 273\ \text{K}$ and $27\ {}^{\circ}\text{C} = 300\ \text{K}$.
Convert $27\ {}^{\circ}\text{C}$ to kelvin.
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$T = \theta + 273 = 27 + 273 = 300\ \text{K}$.
Gas pressure
- Gas particles constantly hit the walls of their container. Each hit is a tiny push.
- The pressure is the total force of these hits on each unit of area.
- Heat the gas (fixed volume) → faster, harder, more frequent hits → higher pressure.
- Squeeze it smaller (fixed temperature) → more hits per second on each area → higher pressure.
- For a fixed mass of gas at constant temperature, $pV = \text{constant}$ (halve the volume → double the pressure).
A gas has a volume of $200\ \text{cm}^3$ at $100\ \text{kPa}$. It is squeezed to $100\ \text{cm}^3$ at constant temperature. What is the new pressure, in kPa?
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$pV$ is constant: $100 \times 200 = p \times 100$, so $p = 200\ \text{kPa}$. Halving the volume doubles the pressure.
Heating a gas in a sealed, fixed-volume can increases its pressure.
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Hotter particles move faster and hit the walls harder and more often, so the pressure rises.
Brownian motion 布朗运动
- Under a microscope, smoke specks in air jiggle along jerky, random paths.
- This is Brownian motion: the big specks are knocked about by fast, invisible air particles.
- It is strong evidence that matter really is made of moving particles.
Random hits from fast, invisible air particles push a smoke grain along a jerky, random path
Smoke specks seen under a microscope jiggle randomly. This is because:
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Brownian motion: tiny fast air particles knock the larger smoke specks about, evidence for moving particles.
Worked examples
1. A gas at $100\ \text{kPa}$ fills $2.0\ \text{m}^3$. It is squeezed to $0.50\ \text{m}^3$ at constant temperature. $pV$ stays constant: $100 \times 2.0 = p \times 0.50$, so $p = 400\ \text{kPa}$. A quarter of the volume gives four times the pressure.
2. Convert $27\ {}^{\circ}\text{C}$ and $-73\ {}^{\circ}\text{C}$ to kelvin: add 273, giving $300\ \text{K}$ and $200\ \text{K}$.
Change to kelvin only when the formula needs it. A temperature change is the same in °C and K, but $0\ {}^{\circ}\text{C}$ is not zero energy: absolute zero is $-273\ {}^{\circ}\text{C}$. In $pV = \text{constant}$, keep the units of $p$ and $V$ the same on both sides.
Convert 15 degrees Celsius to kelvin. A gas at 80 kPa occupies 60 cubic centimetres and is compressed to 40 cubic centimetres at constant temperature. What is the new pressure?
15 plus 273 is 288. 80 times 60 divided by 40 is 120 kilopascals.
What is the new pressure?
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80 times 1.5 is 120 kilopascals.
You've got it
- solid (fixed, vibrating) · liquid (close, sliding) · gas (far apart, fast)
- temperature = average kinetic energy of particles; absolute zero $= -273\ {}^{\circ}\text{C}$
- $T\,(\text{K}) = \theta\,({}^{\circ}\text{C}) + 273$
- gas pressure = particle hits per unit area; at constant temperature $pV = \text{constant}$
Write from a pressure of 120 kilopascals
- 15 degrees Celsius is converted to kelvin. A gas at 80 kPa occupies 60 cubic centimetres and is squeezed to 40 cubic centimetres at the same temperature.
- Find the kelvin temperature and the new pressure.