# Specific Latent Heat

## Specific Latent Heat Revision

**Specific Heat Capacity and Specific Latent Heat**

If a system is **heated** and increases in **temperature**, the amount it increases by depends on the **mass**, **material **and **energy **input of the system. This section will look at the definitions and equations you need to know for **specific heat capacity **and** specific latent heat**.

**Specific Heat Capacity**

The** temperature increase **of a heated system depends on the **mass**, the **specific heat capacity** of the material and the **thermal energy input** into the system. This is given by the following equation:

\textcolor{aa57ff}{\Delta E = m c \Delta \theta}

- \textcolor{aa57ff}{\Delta E} is the
**change in thermal energ****y**in joules \left(\text{J}\right). - \textcolor{aa57ff}{m} is the
**mass**in kilograms \left(\text{kg}\right). - \textcolor{aa57ff}{c} is the
**specific heat capacity**in Joules per kilogram per degree Celsius \left( \text{J/kg°C} \right).

The **specific heat capacity** \textcolor{aa57ff}{c} , is the amount of **energy** needed to increase the temperature of \text{1 kg} of the substance by \text{1°C} .

Different substances have different values of \textcolor{aa57ff}{c} . For example, water has a **specific heat capacity** of \text{4200 J/kg°C} and aluminium has a** specific heat capacity** of \text{900 J/kg°C} . Therefore more **energy** is required to increase the temperature of water (as long as the masses are the same).

**Latent Heat**

When a **change of state** happens, energy is required. This energy required to change the state of a substance is called the** latent heat**.

When a change of state involving heating occurs, such as boiling or melting, this energy supplied to the system increases the **internal energy**. The substance changes state only and **does not change in temperature**. This is because the energy is being used to break apart the bonds between particles in the substance, and is not increasing the temperature.

When a change of state involving cooling occurs, such as condensation or freezing, the system decreases in internal energy. This is because **energy is being released** to make bonds between the particles. Again, the** latent heat** does **not** change the temperature, it only changes the state.

**Specific Latent Heat**

**Specific Latent Heat** is the** energy **required to change the state of \text{1 kg }of of a substance. The formula is:

\textcolor{00bfa8}{E = m L}

- \textcolor{00bfa8}{E} is the
**energy**needed or released in Joules \left(\text{J}\right). - \textcolor{00bfa8}{m} is the
**mass**of the substance in kilograms \left(\text{kg}\right). - \textcolor{00bfa8}{L} is the
**specific latent heat**of a substance in Joules per kilogram \left(\text{J/kg}\right).

Specific latent heat has different names for different changes of state.

**Specific latent heat of fusion** – the specific latent heat for a change from a solid to a liquid.

**Specific latent heat of vaporisation** – the specific latent heat for a change from a liquid to a vapour (gas).

**Heating and Cooling graphs**

The process of a substance **changing state** or **increasing in temperature** can be shown in a **heating** or **cooling graph**.

The graph on the right is a **heating graph**. As the substance is heated over time, the temperature increases. However, notice the flat sections of the graph. This is where the substance is **changing state**.

As mentioned, when changing state, **latent heat** is involved and hence the **temperature stays constant**. The internal energy increases because there is an energy input into the system, but no energy is used to raise the temperature.

The graph on the right is a **cooling graph**. As the substance is cooled over time, the temperature decreases. The flat sections again show where the substance is **changing stat****e** at a **constant temperature**. The internal energy decreases because energy is being released during cooling.

## Specific Latent Heat Example Questions

**Question 1: **State the definition of latent heat.

**[2 marks]**

Latent heat is the **energy required** (or released) during a **change of state** of a substance.

**Question 2**: A student heats up a beaker of \text{0.7 kg} of water using a bunsen burner. The water increases temperature from \text{25°C} to \text{100°C}. What is the change in thermal energy of the water?

Specific heat capacity of water =\text{4200 J/kg°C}

**[3 marks]**

Change in temperature = \bold{100°C - 25°C = 75°C}

\Delta E = m c \Delta \theta

\bold{\Delta E = 0.7 \times 4200 \times (75)}

\bold{\Delta E = 220500} \: \textbf{J}

**Question 3**: A pot of \text{7 kg} of water is heated to \text{100°C} and starts to boil. What is the energy required for the water to evaporate? Give your answer in kilojoules \left(\text{kJ}\right).

Specific latent heat of fusion for water is \text{3340 kJ/kg}

**[2 marks]**

E = m L

\bold{E = 7 \times 3340}

\bold{E = 23380 \: \textbf{kJ}}

**Question 4**: What type of process is this graph representing?

Label the graph with each state and change of state.

**[3 marks]**

It is a **cooling graph**.