# Particle model of matter

In this chapter you will learn:

1. What is Particle model of matter?

2. What is density, and how to calculate it?

3. What is internal energy?

4. Temperature changes in a system

5. What is specific heat capacity?

6. What is change of state?

7. What is specific latent heat?

8. Particle motion in gases

9. Pressure, temperature and volume

## What is particle model?

All matter is made up of tiny particles called atoms and molecules.

Density of an object depends on the material and how its particles are arranged.

Density describes the number of particles and how tightly packed they are in a solid, liquid or gas.

## Density in Solids, liquids and gases

In a dense material the particles are packed tightly together. Whereas, in a less dense material particles are more spread out.

• The density of solids is highest.

• Liquids are less dense than solids, but, more dense than gases.

• The density of gases is lowest.

Density can be calculated using the following equation:

density = mass ÷ volume

The units used in the equation above are as follows:

• density is measured in kilograms per metre cubed, kg/m3

• mass is measured in kilograms, kg

• volume is measured in metres cubed, m3

Worked example:

Question 1

What is the density of a material if 4 cubic metres (m3) of it has a mass of 1,200 kg?

density = mass ÷ volume

density = 1,200 ÷ 4

density = 300 kg/m3

## Internal energy

Internal energy is the sum of kinetic energy and potential energy of all the particles that make up a system.

Internal energy of a system increases when the system is heated. Particles gain energy in their kinetic energy store and vibrates faster when a system is heated.

The internal energy decreases when the system loses heat.

## Temperature changes in a system

When a substance (system) is heated its temperature will rise. The rise in temperature depends on:

• The mass of the substance heated

• The type of material being heated

• The amount of energy input to the system

The amount of thermal energy stored or released can be can be calculated using the following equation:

change in thermal energy = mass × specific heat capacity × temperature change

The units used in the equation above are as follows:

• change in thermal energy is measured in joules, J

• mass is measured in kilograms, kg

• specific heat capacity is measured in joules per kilogram per degree Celsius, J/kg°C

• temperature change is measured in degree Celsius, °C

## Specific heat capacity

The specific heat capacity of a substance is the amount of energy required to raise the temperature of 1 kilogram of the substance by 1 degree Celsius.

Worked examples:

Question 1

How much energy is needed to raise the temperature of 2 kg of copper by 10°C?

The specific heat capacity for copper is 385 J/kg°C

change in thermal energy = mass × specific heat capacity × temperature change

change in thermal energy = 2 × 385 × 10

change in thermal energy = 7,700 J

Question 2

How much energy is needed to heat up 2 litres of water from 30°C to 100°C?

1 litre of water has a mass of 1 kg

Specific heat capacity of water = 4,186 J/kg/°C

mass of 2 litre = 2 kg

Change in temperature = 100 - 30 = 70 °C

change in thermal energy = mass × specific heat capacity × temperature change

change in thermal energy = 2 × 4186 × 70

change in thermal energy = 586,040 J

## Change of state and specific latent heat

Substances can change state when they are heated or cooled.

Water, which is a liquid, turns into steam, which is a gas, when it is heated.

Water turns into ice, which is a solid, when it is cooled.

The energy needed to change the state of a material without changing its temperature is known as the latent heat.

When a substance is heated, its internal energy increases. When a substance is cooled, its internal energy decreases.

When a change of state takes place, the energy supplied changes the internal energy of the substance but not the temperature.

The specific latent heat is the energy needed to change the state of a 1 kg of a substance without changing its temperature.

Specific latent heat is measured in joules per kilogram (J/kg). Specific latent heat is different for different materials.

• In cooling a material to effect a state change, like condensing or freezing, the specific latent is the energy released from the system.

• In heating a material to effect a state change, like melting or boiling, the specific latent heat must be added.

The amount of energy required to change the state of a given mass of a substance can be calculated using the following equation:

energy for a change of state = mass × specific latent heat

The units used in the equation above are as follows:

• energy is measured in joules, J

• mass is measured in kilograms, kg

• specific latent heat is measured in joules per kilogram, J/kg

Worked examples:

Question 1

How much energy is required to melt 3 kg of ice?

Latent heat of fusion for water = 334,000 J/kg

energy for a change of state = mass × specific latent heat

energy = 3 x 334,000 = 1,002,000 J

Latent Heat of Fusion: The latent heat related with melting a solid, or freezing a liquid, is called the latent heat of fusion.

Latent Heat of Vaporisation: The latent heat for the change of state between a liquid and a gas is called the specific latent heat of vaporisation.

## Evaporation and boiling

Both evaporation and boiling involve a change of state where a liquid turns in to a gas. Boiling is an active process. It is a fast process compared to evaporation.

In order to boil a liquid, you need to actively apply enough heat to the liquid to raise its temperature to its boiling point.

When the temperature reaches its boiling point the liquid rapidly begins to change its state to gas. Heat can be applied using a heat source such as an electric heater.

• Boiling is an active process.

• It is a fast process.

• It happens at temperatures equal to or higher than boiling point.

On the other hand, evaporation is a passive process. It is a slow process. The liquid slowly absorbs energy from its surroundings and some of its particles gain enough energy to change state from liquid to gas. Evaporation happens at much lower temperature compared to boiling, it does not require the temperature to be as high as the boiling point.

• Evaporation is a passive process.

• It is a slow process.

• It usually happens at temperatures much lower than boiling point.

Note: A change of state is a physical change, not a chemical change. The chemical nature of the substance does not change.

In a change of state the mass of the substance does not change. This is called conservation of mass.

## Particle motion in gases

The gas particles move very quickly in random direction.

When these gas particles collide with surface, they exert a pressure. Increasing temperature increases the pressure of gas.

## Pressure, temperature and volume

The particles in a gas are loosely packed; hence, they have more space to move around. The particles in a gas are moving in random directions at high speeds. Because of this random motion, they collide with each other and the wall of the container. This collision exerts pressure on the container.

Pressure is directly proportional to temperature. As the temperature increases, the pressure increases.

Increasing the temperature of a gas, increases the amount of energy in the kinetic energy store of the gas particles. This results in more frequent collision, which increases pressure.

Volume and pressure are inversely proportional. When volume increases, pressure decreases, and when volume decreases, pressure increases.

If the temperature is kept constant and the volume is increased, the particles get more spread out and hit the wall less frequently, per unit area, so the pressure decreases.

• Pressure is measured in pascals (Pa).

• Volume is measured in metres cubed (m3).