Why ice is hard, water pours and steam spreads: the particle model, density, latent heat and the gas laws, explained step by step with diagrams and worked examples.
A block of ice, a glass of water and a cloud of steam look nothing alike, yet all three are made of exactly the same kind of molecule, H₂O. The difference is not what they are made of but how their particles are arranged and how much energy those particles have. This simple idea, called the particle model of matter, explains why ice is hard, water pours, steam fills a room, and why a kettle needs so much energy just to turn boiling water into steam.
Matter is anything that has mass and takes up space (has volume). Your desk, the water you drink and the air you breathe are all matter. Light and sound are not matter, because they are forms of energy carried by waves. Matter is made of tiny particles, which may be atoms, molecules (groups of atoms joined together) or ions (charged atoms). These particles are far too small to see with an ordinary microscope, but their behaviour explains most of what we observe.
The three common states of matter are solid, liquid and gas. Which one a substance is in depends on its temperature and the pressure around it.
The particle model (also called the kinetic theory) rests on a few ideas:
In a solid, the attractive forces are strong enough to hold the particles in fixed positions, and they can only vibrate. In a liquid, the particles are still touching, but they have enough energy to slide past each other. In a gas, the particles have so much energy that the forces between them hardly matter; they fly about independently and are very far apart compared with their size.
| Property | Solid | Liquid | Gas |
|---|---|---|---|
| Shape | Fixed | Takes the shape of its container | Takes the shape of its container |
| Volume | Fixed | Fixed | Fills the whole container |
| Particle spacing | Very close | Close | Very far apart |
| Particle movement | Vibrate in place | Slide past each other | Move quickly and freely |
| Compressible? | No | Almost not | Easily |
| Typical density | High | High (a little lower than the solid) | Very low |
Some solids, such as salt and metals, have particles arranged in a regular repeating pattern called a crystal. Others, such as glass, have particles that are fixed but not in a regular pattern; these are called amorphous solids. Glass is not a very slow liquid, as is sometimes claimed; it is an amorphous solid.
A fluid is any substance that can flow, so liquids and gases are both fluids. How easily a liquid flows is called its viscosity: honey has a high viscosity and water a low one.
Density is the mass of a substance in each unit of volume. It tells you how tightly the matter is packed.
ρ = m ÷ V (density = mass ÷ volume)
In SI units, mass is in kilograms (kg), volume in cubic metres (m³), and density in kg/m³. In the laboratory, g/cm³ is also common: 1 g/cm³ = 1000 kg/m³.
| Material | Approximate density (kg/m³) |
|---|---|
| Air (about 20 °C, sea level) | 1.2 |
| Ice | 920 |
| Water | 1000 |
| Aluminium | 2700 |
| Iron | 7900 |
| Copper | 8900–9000 |
Values are rounded and vary a little with temperature and purity. The very low density of gases is a direct result of their particles being so far apart.
A metal block has a mass of 540 g and a volume of 200 cm³. Find its density and identify the likely metal.
Step 1. ρ = m ÷ V = 540 g ÷ 200 cm³.
Step 2. Calculate: ρ = 2.7 g/cm³, which is 2700 kg/m³.
Step 3. Compare with the table: this matches aluminium.
A tank holds 0.50 m³ of water. What is the mass of the water? (ρ = 1000 kg/m³)
m = ρ × V = 1000 kg/m³ × 0.50 m³ = 500 kg.
To find the density of an irregular solid in the lab, you measure its mass with a balance and find its volume by displacement: lower it into a measuring cylinder of water and note how much the water level rises.
A change of state is a physical change: the substance stays the same, but its particles rearrange. No new substance is formed, and the change can be reversed.
If you heat ice steadily and record the temperature, the graph is a heating curve. It has sloping parts and two flat parts.
During the flat sections, heat energy is still being supplied, but the temperature does not change. The energy is being used to pull the particles apart against the attractive forces between them (when melting and boiling) rather than to make them move faster. This hidden energy is called latent heat ("latent" means hidden). It is released again when the substance freezes or condenses; this is why steam can cause a worse burn than boiling water at the same temperature, because the steam also releases its latent heat as it condenses on skin.
The energy needed to change the state of a mass m is:
Q = m × L (during a change of state; L is the specific latent heat in J/kg)
Q = m × c × ΔT (while the temperature changes; c is the specific heat capacity in J/kg°C)
Approximate values for water: specific latent heat of fusion (ice) L ≈ 3.34 × 10⁵ J/kg; specific latent heat of vaporisation L ≈ 2.26 × 10⁶ J/kg; specific heat capacity c ≈ 4200 J/kg°C.
How much energy melts 0.50 kg of ice at 0 °C?
Q = mL = 0.50 kg × 3.34 × 10⁵ J/kg = 1.67 × 10⁵ J = 167 kJ.
How much energy changes 0.50 kg of ice at 0 °C into water at 20 °C?
Step 1. Melt the ice: Q₁ = mL = 0.50 × 3.34 × 10⁵ = 1.67 × 10⁵ J.
Step 2. Warm the water: Q₂ = mcΔT = 0.50 kg × 4200 J/kg°C × 20 °C = 4.2 × 10⁴ J.
Step 3. Total: Q = 1.67 × 10⁵ + 0.42 × 10⁵ = 2.09 × 10⁵ J (about 209 kJ).
How much energy turns 0.20 kg of boiling water at 100 °C into steam at 100 °C?
Q = mL = 0.20 kg × 2.26 × 10⁶ J/kg = 4.52 × 10⁵ J = 452 kJ.
Notice how much more energy is needed to boil a kilogram of water than to melt a kilogram of ice. Pulling particles completely apart takes far more energy than letting them slide.
Both processes turn a liquid into a gas, but they are not the same:
| Evaporation | Boiling | |
|---|---|---|
| Where | Only at the surface | Throughout the liquid (bubbles form) |
| Temperature | At any temperature above freezing | Only at the boiling point |
| Speed | Slow | Fast |
| Energy | Taken from the liquid, which cools | Supplied continuously from the heat source |
In any liquid the particles move at different speeds. The fastest particles near the surface can escape into the air. Because the faster particles are the ones leaving, the average energy of the remaining liquid falls, so evaporation causes cooling. This is how sweating cools your body and why wet clothes feel cold. Evaporation is faster if the liquid is warmer, has a larger surface area, there is a draught or wind, and the surrounding air is dry (low humidity).
The boiling point depends on the pressure above the liquid. Water boils at 100 °C at standard atmospheric pressure (about 101 kPa). At the top of a very high mountain the air pressure is much lower, so water boils at a lower temperature (roughly 70 °C near the top of Mount Everest), which is why food takes longer to cook there. A pressure cooker does the opposite: it raises the pressure so the water boils above 100 °C and food cooks faster.
Gas pressure is caused by particles hitting the walls of their container. Each tiny collision gives the wall a small push, and billions of them every second add up to a steady force on each unit of area. Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m².
Boyle's law. For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume: p₁V₁ = p₂V₂. Squeezing the gas into a smaller volume makes the particles hit the walls more often, so the pressure rises.
A gas occupies 600 cm³ at a pressure of 100 kPa. It is compressed to 200 cm³ at constant temperature. Find the new pressure.
Step 1. p₁V₁ = p₂V₂, so p₂ = p₁V₁ ÷ V₂.
Step 2. p₂ = (100 kPa × 600 cm³) ÷ 200 cm³ = 300 kPa.
Charles's law. For a fixed mass of gas at constant pressure, volume is directly proportional to the absolute (kelvin) temperature: V₁ ÷ T₁ = V₂ ÷ T₂. The kelvin scale starts at absolute zero, the lowest possible temperature, which is −273.15 °C. To convert, T (K) = θ (°C) + 273 (273.15 for more precision). You must always use kelvin in gas-law calculations.
A balloon contains 2.0 litres of air at 27 °C. It is warmed to 127 °C at constant pressure. Find its new volume.
Step 1. Convert to kelvin: T₁ = 27 + 273 = 300 K; T₂ = 127 + 273 = 400 K.
Step 2. V₂ = V₁ × T₂ ÷ T₁ = 2.0 L × 400 ÷ 300.
Step 3. V₂ ≈ 2.7 L.
A third relation says that at constant volume, the pressure of a gas rises in proportion to its kelvin temperature. This is why a sealed can can burst if it is heated, and why a car tyre's pressure rises after a long drive.
In 1827 the Scottish botanist Robert Brown looked through a microscope at tiny pollen grains in water and saw them jiggling in an irregular way. In 1905 Albert Einstein showed mathematically that this Brownian motion is caused by countless collisions with fast-moving water molecules, which strike the grain unevenly from different sides. Later experiments, notably by Jean Perrin, supported this explanation, and it became strong evidence that particles exist. You can see a similar effect with smoke particles in air under a microscope.
Diffusion is the spreading of particles from a region of high concentration to a region of lower concentration, caused by their random motion. A smell of cooking spreads across a house this way. Diffusion is fastest in gases, slower in liquids and extremely slow in solids. At the same temperature, lighter gas molecules move faster on average and diffuse faster than heavier ones. Higher temperature also speeds diffusion.
For most substances the solid is denser than the liquid. Water is unusual. As water cools it contracts until about 4 °C, where it is densest. Below that it expands slightly as it approaches freezing, and when it becomes ice the molecules lock into an open, regular arrangement that holds them slightly further apart than in liquid water. Ice is therefore about 8–9% less dense than liquid water, so it floats. This matters in nature: in cold weather a lake freezes from the top, and the ice layer insulates the water beneath, which often stays liquid so that fish and other life can survive. It also explains why a bottle of water left in a freezer can crack: the freezing water expands.
These states are not usually needed at O-Level, but they show that the three everyday states are only part of the picture.
Try each question before opening the answer.
Gas particles are very far apart with mostly empty space between them, so they can be pushed closer. Solid particles are already touching, so there is almost no room to squeeze them.
ρ = 250 g ÷ 100 cm³ = 2.5 g/cm³ = 2500 kg/m³.
The energy supplied is used to separate the particles (latent heat), not to increase their average kinetic energy, so the temperature does not rise.
The fastest-moving water molecules escape from the skin surface as the sweat evaporates. This removes energy, so the remaining liquid and the skin become cooler.
p₂ = 200 × 3.0 ÷ 6.0 = 100 kPa.
T = 25 + 273 = 298 K (298.15 K using 273.15).
Q = mL = 2.0 × 3.34 × 10⁵ = 6.68 × 10⁵ J.
Ice is less dense than liquid water because its molecules are held in an open, regular arrangement that takes up more space.
Useful safe activities: use a syringe with the nozzle sealed to feel how a gas compresses but a liquid does not; heat ice with a thermometer and record temperature every minute to draw a real heating curve (the plateau is a striking result); measure density of regular blocks by weighing and measuring, and of stones by displacement; compare evaporation of the same amount of water on a plate in a warm place, a cool place and in a breeze. Hot water, steam and dry ice need adult supervision. All numerical values are rounded, so please check that they match the data booklet used by your examination board.
This article is original EDUSAMBAM writing. Definitions and typical values were checked against the sources below. Diagrams are original and were not copied from any source.
Note on the numbers: latent heat and density values are rounded standard values for water and common materials. Please check them against your own syllabus or exam board specification before relying on them.
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