State Changes and Latent Heat for the ESAT

Understanding Melting Point and Boiling Point

Most pure substances have a specific temperature at which they change state. While most substances progress through solid, liquid, and gas phases, some, like carbon dioxide, undergo sublimation, which is the direct change from solid to gas.

The melting point is the temperature at which a substance transitions between solid and liquid states. Melting occurs when a solid is at its melting point and continues to absorb energy, while freezing occurs when a liquid is at the same temperature and loses energy.

The boiling point is the temperature at which a substance transitions between liquid and gas throughout the entire bulk of the material. Boiling occurs above this temperature, while condensation occurs when a gas falls below it.

The table below outlines the state of a substance based on its temperature relative to these points:

1. Below the melting point: Solid.
2. At the melting point: Solid and liquid.
3. Between the melting point and boiling point: Liquid.
4. At the boiling point: Liquid and gas.
5. Above the boiling point: Gas.

Pure substances have fixed melting and boiling points, but impure substances melt and boil over a range of temperatures. Therefore, an impure substance does not have a single, specific melting or boiling point.

Worked Example: Determining State at a Given Temperature

Determine the state of the following substances at 24 degrees Celsius:

1. Bromine (melting point -7 degrees Celsius, boiling point 59 degrees Celsius): Liquid. This is because 24 degrees Celsius is higher than the melting point but lower than the boiling point.
2. Fluorine (melting point -220 degrees Celsius, boiling point -188 degrees Celsius): Gas. This is because 24 degrees Celsius is significantly above the boiling point.
3. Iodine (melting point 114 degrees Celsius, boiling point 184 degrees Celsius): Solid. This is because 24 degrees Celsius is below the melting point.

Latent Heat of Fusion and Vaporisation

Normally, transferring thermal energy to a body increases its temperature. However, during a state change, the temperature remains constant. While a pure substance melts or boils, the thermal energy it absorbs is used to increase the separations between particles rather than increasing their kinetic energy. This energy is called latent heat.

Conversely, when a substance freezes or condenses, it releases thermal energy to its surroundings. This happens as the attractions between particles increase and their separations decrease. The temperature will only begin to fall again once the entire sample has finished changing state.

1. Latent heat of fusion applies to the transition between solid and liquid (melting or freezing).
2. Latent heat of vaporisation applies to the transition between liquid and gas (boiling or condensing).

The graph above shows that temperature increases when the substance is in a single state but plateaus during the state change. If thermal energy is transferred at a constant rate, a temperature versus time graph will look identical to a temperature versus energy graph, only scaled differently.

Worked Example: Identifying Latent Heat Types

Identify the type of latent heat involved and whether it is absorbed or released in the following processes:

1. Ice melting: Latent heat of fusion is absorbed. The substance is changing from solid to liquid, so it must absorb thermal energy to overcome particle attractions at a constant temperature.
2. Gaseous propane changing to liquid: Latent heat of vaporisation is released. This is condensation, where the gas transfers energy to the surroundings as it becomes a liquid.

Specific Latent Heat Calculations

The term specific in physics means per unit mass. The specific latent heat, $L$, is the thermal energy required to change the state of 1 kg of a substance without changing its temperature. The formula is:

$E = mL$

Where:

• $E$ is the thermal energy transferred in Joules (J).
• $m$ is the mass of the sample in kilograms (kg).
• $L$ is the specific latent heat in $J kg^{-1}$.

When calculating energy for a process involving both temperature changes and state changes, you must calculate the energy for each stage separately and add them together. For example, to turn ice at -10 degrees Celsius into water at 0 degrees Celsius, you would calculate the energy to heat the ice to its melting point using specific heat capacity, and then the energy to melt it using specific latent heat.

Worked Example: Energy Calculation

Calculate the energy required to turn 3.0 kg of ice at 0 degrees Celsius into liquid water at 0 degrees Celsius. The specific latent heat of fusion for water is 330 kJ/kg.

1. Identify variables: $m = 3.0 kg$, $L = 330,000 J kg^{-1}$.
2. Use the formula: $E = mL$.
3. Calculate: $E = 3.0 \times 330,000 = 990,000 J$ or 990 kJ.

Worked Example: Finding Specific Latent Heat

Calculate the specific latent heat of vaporisation if 6900 kJ of thermal energy is released when 3.0 kg of water vapour at 100 degrees Celsius condenses to liquid water at 100 degrees Celsius.

1. Rearrange the formula: $L = \frac{E}{m}$.
2. Substitute values: $L = \frac{6,900,000}{3.0}$.
3. Calculate: $L = 2,300,000 J kg^{-1}$ or 2300 kJ/kg.