# Latent Heat of State Change

This topic is part of the HSC Physics course under the section Thermodynamics.

### HSC Physics Syllabus

• conduct an investigation to analyse qualitatively and quantitatively the latent heat involved in a change of state

### Latent Heat Involved in Change of State Explained

In this video, we discuss the concept of latent heat of state change including latent heat of fusion (melting) and vapourisation.

### What is Latent Heat of State Change?

Latent heat is the amount of energy, in the form of heat, that is absorbed or released by a substance during a phase change, without any change in temperature.

The word "latent" means hidden, suggesting that even though the substance is absorbing or releasing heat, this doesn't manifest as a temperature change. This is because the heat being absorbed is not being used to increase the kinetic energy of the particles. Rather, it is being used to overcome the intermolecular attractions between the particles and increase the distance between them.

There are two main types of latent heat:

1. Latent Heat of Fusion: The energy required to change a substance from solid to liquid (or vice versa) without changing its temperature. For instance, when ice melts, it absorbs heat from the surroundings but remains at 0°C until fully melted.

2. Latent Heat of Vaporisation: The energy required to change a substance from liquid to gas (or vice versa) without a temperature change. An example is boiling water: the water remains at 100°C until it has completely turned into steam.

The energy Q required to change the phase of a substance can be calculated using the equation:

Where:

• Q is the energy (in joules, J)
• m is the mass of the substance (in kilograms, kg)
• L is the specific latent heat (in joules per kilogram, J/kg)

The specific latent heat, L, is a property unique to each substance and phase change.

While energy is absorbed during solid to liquid (melting) and liquid to gas (vapourisation) state changes, energy is released during liquid to solid (freezing) and gas to liquid (condensation) state changes.

### Example 1: Melting Ice

Suppose you have 100 g (0.1 kg) of ice at 0°C and you want to melt it. The latent heat of fusion for water is . How much energy is required to melt the ice?

Solution:

$$Q = m \times L$$

$$Q = 0.1 \times 334000 = 33400 \, \text{J}$$

### Example 2: Boiling Water

Imagine you have 200 g (0.2 kg) of water at 100°C. The latent heat of vaporisation for water is . How much energy is needed to completely evaporate this amount of water?

﻿Solution:

$$Q = m \times L$$

How much heat energy must be transferred to a 500.0 g sample of water at 25.0 ºC for it to completely boil at 100 ºC?

Use the following information for this question.

• Specific heat capacity of water = 4180 J / kg / K
• Latent heat of vapourisation of water = 2260 kJ / kg

Solution:

Heat is used to achieved two things in this scenario:

• Raise the temperature of water in liquid state from 25 ºC to 100 ºC
• Change the state of water from liquid to gas state

Firstly, calculate the amount of energy required to increase the temperature:

$$Q = mc\Delta T$$

$$Q = (0.500)(4180)(100 - 25)$$

$$Q = 156750 \text{ J}$$

Secondly, calculate the amount of energy required to change the state of water using the latent heat of vaporisation:

$$Q = mL$$

$$Q = (0.500)(2260)$$

$$Q = 1130 \text{ kJ}$$

Note that the second Q value is in kilojoules.

$$Q_{\text{total}} = 156750 + 1130 \times 1000 = 1.29 \times 10^6 \text{ J}$$