Change of State and Latent Heat

Change Of State

Matter can exist in different states or phases: solid, liquid, and gas (and plasma at very high temperatures). A change of state, or phase transition, is a physical process where a substance changes from one state to another due to the transfer of heat at a constant temperature and pressure.

Common changes of state include:

Melting (Fusion): Solid to liquid (e.g., ice melting into water). Occurs at the melting point.
Freezing (Solidification): Liquid to solid (e.g., water freezing into ice). Occurs at the freezing point (same temperature as melting point at a given pressure).
Boiling (Vaporisation): Liquid to gas (e.g., water boiling into steam). Occurs at the boiling point.
Condensation (Liquefaction): Gas to liquid (e.g., steam condensing into water droplets). Occurs at the condensation point (same temperature as boiling point at a given pressure).
Sublimation: Solid directly to gas (e.g., dry ice ($CO_2$) turning into gas).
Deposition (Desublimation): Gas directly to solid (e.g., frost forming from water vapour).

During a change of state, the heat energy supplied or removed is used to break or form intermolecular bonds, rather than increasing the kinetic energy of the molecules (which would increase the temperature). Consequently, the temperature of the substance remains constant during the phase transition, provided the pressure is constant.

For example, when ice melts at 0°C, adding heat does not immediately raise the temperature of the ice or the resulting water above 0°C. All the added heat is used to overcome the forces holding the water molecules in the rigid structure of ice, converting it into liquid water. Only after all the ice has melted will the temperature of the water start to rise as more heat is added.

Latent Heat ($ L = \frac{Q}{m} $)

The heat energy absorbed or released during a change of state at a constant temperature is called latent heat (latent means "hidden", as this heat does not cause a temperature change). The amount of heat required or released depends on the amount of substance undergoing the change of state and the specific type of phase transition.

Latent Heat ($L$) is defined as the amount of heat energy absorbed or released per unit mass during a change of state at a constant temperature and pressure.

$ L = \frac{\text{Heat Energy (Q)}}{\text{Mass (m)}} $

So, the heat energy $Q$ required for a change of state of mass $m$ is given by:

$ Q = mL $

The units of latent heat are Joules per kilogram (J/kg).

Types of Latent Heat

Latent Heat of Fusion ($L_f$): The amount of heat energy absorbed by a unit mass of a solid when it changes into a liquid at its melting point and standard pressure. This heat is absorbed to break the bonds in the solid structure. For freezing, the same amount of heat is released (Latent Heat of Solidification). $ L_f = \frac{Q_{fusion}}{m} $
Latent Heat of Vaporisation ($L_v$): The amount of heat energy absorbed by a unit mass of a liquid when it changes into a gas (vapour) at its boiling point and standard pressure. This heat is absorbed to overcome the intermolecular forces in the liquid state and do work against the external pressure during expansion. For condensation, the same amount of heat is released (Latent Heat of Condensation). $ L_v = \frac{Q_{vaporisation}}{m} $

Latent heat of vaporisation is usually significantly larger than the latent heat of fusion for a given substance because converting a liquid to a gas requires much more energy to completely separate the molecules and overcome intermolecular attractions than converting a solid to a liquid (where molecules are still relatively close).

For water at standard atmospheric pressure:

Melting point: 0°C (273.15 K)
Boiling point: 100°C (373.15 K)
Latent Heat of Fusion of ice: $L_f \approx 3.34 \times 10^5$ J/kg
Latent Heat of Vaporisation of water: $L_v \approx 2.26 \times 10^6$ J/kg

Heating Curve

A heating curve shows how the temperature of a substance changes as heat is added at a constant rate, starting from a solid state. It typically shows regions where the temperature increases (within a single phase) and plateaus where the temperature remains constant (during a change of state).

(Image Placeholder: A graph with Heat Added (or Time, if heat is added at a constant rate) on the x-axis and Temperature on the y-axis. Show a curve starting from low temp (Solid phase, slope related to specific heat of solid). Then a flat horizontal line at the melting point (Solid + Liquid phase, heat added is latent heat of fusion). Then a rising line (Liquid phase, slope related to specific heat of liquid). Then another flat horizontal line at the boiling point (Liquid + Gas phase, heat added is latent heat of vaporisation). Then a rising line at high temp (Gas phase, slope related to specific heat of gas).)

The slope of the rising portions of the curve is related to the specific heat capacity of the substance in that phase ($ \text{slope} = \frac{\Delta T}{Q} = \frac{1}{mc} $ if plotting T vs Q, or $ \text{slope} \propto \frac{1}{mc} $ if plotting T vs time with constant heat rate). The length of the horizontal plateaus is proportional to the latent heat for that phase transition ($ Q = mL $, so $L = Q/m$).

Applications of Latent Heat

Cooling by Evaporation: When a liquid evaporates, it absorbs latent heat of vaporisation from the surroundings, causing cooling. This is why sweating cools the body and why water kept in earthen pots (matkas) stays cool (water evaporates from the porous surface).
Freezing Mixtures: Mixtures of ice and salt are used as freezing mixtures. When salt dissolves in water, it lowers the freezing point of water. For the ice to melt at this lower temperature, it needs heat, which it absorbs from the surroundings (including the substance to be frozen), causing cooling.
Steam Burns: Steam at 100°C causes more severe burns than boiling water at 100°C because steam contains the extra latent heat of vaporisation (2.26 MJ/kg) which is released when it condenses on the skin.
Refrigeration: Refrigerators and air conditioners work by using phase transitions of a refrigerant substance (e.g., vaporisation absorbing heat from inside, condensation releasing heat outside).

Example 1. How much heat energy is required to convert 2 kg of ice at 0°C into water at 20°C? (Latent heat of fusion of ice = $3.34 \times 10^5$ J/kg, specific heat capacity of water = 4200 J/kg·°C).

Answer:

Mass of ice, $m = 2$ kg.

Initial temperature of ice = 0°C.

Final state required: water at 20°C.

This process involves two steps:

Melting the ice at 0°C into water at 0°C.
Heating the water from 0°C to 20°C.

Step 1: Heat required to melt the ice ($Q_1$).

This is a change of state (solid to liquid) at the melting point (0°C). The heat required is given by $Q_1 = mL_f$, where $L_f$ is the latent heat of fusion of ice.

$ Q_1 = (2 \text{ kg}) \times (3.34 \times 10^5 \text{ J/kg}) = 6.68 \times 10^5 $ J.

Step 2: Heat required to heat the water from 0°C to 20°C ($Q_2$).

This is a temperature change within the liquid phase. The heat required is given by $Q_2 = mc\Delta T$, where $c$ is the specific heat capacity of water, and $\Delta T$ is the temperature change.

$ Q_2 = (2 \text{ kg}) \times (4200 \text{ J/kg} \cdot ^\circ\text{C}) \times (20^\circ\text{C} - 0^\circ\text{C}) $

$ Q_2 = 2 \times 4200 \times 20 $ J

$ Q_2 = 8400 \times 20 = 168000 $ J.

$ Q_2 = 1.68 \times 10^5 $ J.

Total heat energy required ($Q_{total}$) is the sum of the heat required for each step:

$ Q_{total} = Q_1 + Q_2 $

$ Q_{total} = (6.68 \times 10^5 \text{ J}) + (1.68 \times 10^5 \text{ J}) $

$ Q_{total} = (6.68 + 1.68) \times 10^5 \text{ J} = 8.36 \times 10^5 $ J.

The total heat energy required is $8.36 \times 10^5$ Joules, or 836 kJ.