Chapter 8: Particle model of matter

The chapter problem: the mountain weather station

A weather station stands high on a mountain. In winter the station has no liquid water. It stores its water as ice in an insulated box.

These are the facts to use all the way through the chapter.

• The block of ice has a volume of $2.5 \times 10^{-3}\,\text{m}^3$.
• The density of ice is $920\,\text{kg/m}^3$.
• The station melts the ice, then warms the meltwater from $0\,^\circ\text{C}$ to $45\,^\circ\text{C}$.
• The specific heat capacity of water is $4200\,\text{J/kg}\,^\circ\text{C}$.
• The specific latent heat of fusion of ice is $3.3 \times 10^5\,\text{J/kg}$.
• The station also launches a weather balloon. The balloon holds $2.0\,\text{m}^3$ of gas at $100\,\text{kPa}$ when it is filled in the valley. High above, the pressure is $25\,\text{kPa}$ and the temperature of the gas is the same.

By the end of the chapter you will find the mass of the ice, the energy needed to melt it, and the energy needed to warm the meltwater. You will find the volume of the weather balloon high above the valley. You will also explain each answer using the particles inside the material.

First contact: no working yet. Predict. The ice is melted, and then the meltwater is warmed by $45\,^\circ\text{C}$. Which needs more energy: melting the ice, or warming the melted water? Write your prediction down.

By the end of this chapter

You will be able to:

• use the particle model to describe a solid, a liquid and a gas;
• calculate density, and measure the density of a solid or a liquid;
• describe melting, freezing, boiling, evaporating, condensing and sublimating;
• explain why mass is conserved when a substance changes state;
• describe internal energy, and explain how heating changes it;
• calculate the energy transferred using $\Delta E = mc\Delta\theta$ and $E = mL$;
• tell specific heat capacity and specific latent heat apart;
• interpret a heating or cooling graph, including the flat parts;
• explain gas pressure using the motion of the particles;
• use $pV = \text{constant}$ for a fixed mass of gas at constant temperature.

At Higher tier you will also explain how doing work on a gas can raise its temperature.

Where it is used

Engineers who design pressure vessels, refrigerators and spacecraft all use the particle model. So do weather forecasters, who track how the air cools and expands as it rises. The same ideas explain why a bicycle pump gets warm, why a pressure cooker cooks food faster, and why ice floats on water.

Your turn to connect it

Where in your own week does a substance change state, and where does something warm up without changing state? Write two examples. One should be a change of state, such as melting or boiling. The other should be a change in temperature with no change of state.

Roadmap

1. 8.1 Changes of state and the particle model
2. 8.2 Internal energy, energy transfers and particle motions
3. 8.3 Particle model and pressure
4. Review