# Latent Heat Formula

Latent heat is the energy required to change a solid into a liquid or gas phase without changing its temperature. It is also known by various names depending on the phase transition, such as the heat of condensation or the heat of vaporization. Latent heat refers to the amount of heat energy absorbed or released during a phase change. In this article, we will explore the concept of latent heat and the formula for calculating it, along with examples.

## What is Latent Heat?

The energy or heat that is released or absorbed during a phase change of a material is referred to as latent heat. This can occur when a substance transitions from a gas to a liquid, from a liquid to a solid, or vice versa. During the process of phase transition, the temperature of the substance remains constant. Latent heat represents the energy needed to overcome the attractive forces that hold atoms and molecules together, allowing a substance to change phases. When a solid transitions to a liquid, it absorbs energy to separate the atoms and molecules. Conversely, when a substance changes from a gas to a liquid, it releases energy as the molecules come closer together. The absorbed or released heat during these transitions is known as latent heat.

### Definition of Latent Heat

Latent heat is the amount of energy that is released or absorbed at constant temperature and pressure during a substance’s phase change. This phase change can be from gas to liquid, liquid to solid, or the reverse. Latent heat is associated with the thermodynamic property known as enthalpy.

### Examples of Latent Heat

There are two primary examples of latent heat:

Heat of Vaporization: This is the amount of heat required to convert a liquid into a gas.

Heat of Freezing: This is the amount of heat that must be released for a liquid to solidify.

In both cases, latent heat is the energy exchanged to change the phase of a substance without altering its temperature.

## Latent Heat Formula

The formula for latent heat is expressed as:

Q = m×L

Where:

• Q is the amount of heat absorbed or released,
• m is the mass of the substance, and
• L is the specific latent heat.

The equation represents the heat Q that must be added or removed for an object of mass m to undergo a phase change. The specific latent heat is denoted by the symbol L.

### Unit of Latent Heat

Latent heat refers to the amount of heat needed per kilogram to change the phase of a substance. Its unit is joules per kilogram (J/kg) or kilojoules per kilogram (kJ/kg).

The dimensional formula for latent heat is [M0L2T−2]

## Types of Latent Heat

Latent heat transfer can occur mainly in three forms:

• Latent Heat of Fusion
• Latent Heat of Vaporization
• Latent Heat of Sublimation

Here is a detailed description of each type:

### Latent Heat of Fusion

The latent heat of fusion is the heat absorbed or released at a constant temperature when a substance changes from solid to liquid or vice versa. In simpler terms, it is the heat required to melt a solid into a liquid or freeze a liquid into a solid without changing the temperature.

In the liquid state, the internal energy is higher than in the solid state. Therefore, energy must be supplied to melt a solid and released to solidify a liquid. When a liquid cools, its temperature decreases until it reaches just below the freezing point. The temperature remains constant at this point as the liquid solidifies. The latent heat of fusion for ice is 3.34 x 105 joules per kilogram.

### Latent Heat of Vaporization

The latent heat of vaporization refers to the heat absorbed or released at a constant temperature when a substance transitions from a liquid to a gaseous state. It quantifies the amount of heat required to change a liquid into vapor without any change in temperature. Specifically, it is the amount of heat needed to convert 1 gram of liquid into vapor at a constant temperature.

Water has the highest latent heat of vaporization. Water vapor at 100°C (373 K) contains more energy than liquid water at the same temperature. This additional energy is due to the latent heat of vaporization present in the water vapor.

### Latent Heat of Sublimation

Certain substances, such as naphthalene and camphor, can transition directly from a solid to a gaseous state without passing through the liquid phase. The latent heat of sublimation refers to the amount of heat absorbed or released by a substance during this direct transition from solid to gas or from gas to solid, without any change in temperature.

### Sensible Heat

Sensible heat is the heat transferred to or from a body or thermodynamic system that results in a change in its temperature. This type of heat transfer affects the temperature and other macroscopic properties of the system, excluding pressure and volume.

### Sensible Heat and Meteorology

Meteorologists use sensible heat to analyze various climate parameters and predict natural events. When latent heat is released into the atmosphere, it influences the climate. The sensible heat absorbed and released into the atmosphere interacts with hot or cold air, altering climatic conditions and potentially leading to extreme weather events.

## Examples of Latent and Sensible Heat

We encounter various examples of latent heat in our daily lives. Some common examples include:

• The temperature of steam remains constant until all the water has evaporated, even though heat is continuously supplied.
• Vertical movements of air or wind are driven by the latent heat released or absorbed by land or water.
• Water freezes at a constant temperature, even as heat is continually removed.

## Specific Latent Heat

Specific latent heat is a measure of the energy needed per unit mass of a substance, such as ice, to undergo a change in its physical state, for instance, from solid to liquid (water), all while maintaining a constant temperature. This specific latent heat can be determined using the formula:

𝐿=Δ𝑄/𝑚

Here,

• L represents the specific latent heat,
• ΔQ denotes the heat energy added to or released from the substance, and
• m stands for the mass of the substance undergoing the change in its physical state.

## Solved Examples on Latent Heat

Example 1: Suppose a substance weighing 20 kg undergoes a phase change, requiring 600 kcal of heat. What is the latent heat of this substance?

Solution:

Given:

Q = 600kcal

M=20 kg

Using the formula for latent heat:

L = Q/M

Put the given values:

L=600/20

​L=30kcal/kg

Therefore, the latent heat required for the phase change is 30 kcal/kg.

Example 2: 300 kcal heat is required to change the state of a 10 kg substance. Calculate its latent heat.

Solution:

Given:

Q=300kcal

M=10 kg

Using the formula for latent heat:

𝐿=𝑄/𝑀

Put the given values:

𝐿=300/10

​𝐿=30kcal/kg

Therefore, the latent heat required for the phase change is 30 kcal/kg.

Example 3:  Determine the energy required for the phase change of 0.65 kg of ice at 0°C into the water at 0°.

Solution:

Latent heat of fusion of ice: 3.34 x 105 J/kg

The latent heat formula is

L = Q/m

Q = L × m

L = 3.34 x 105 J/kg

m = 0.65 kg

Thus,

Q = 3.34 × 105 × 0.65

= 217100 J

Thus, the heat energy required to melt 0.65 kg water is 217100 J

### 1. What is latent heat, and how do we find it?

Latent heat represents the energy absorbed or released during a phase change at a constant temperature. To calculate it, we use the formula 𝐿=𝑄/𝑚 , where L is the latent heat, Q is the heat energy, and m is the mass undergoing the phase change.

### 2. How does latent heat influence phase transitions?

Latent heat plays a critical role in phase changes by determining the energy required to alter the state of a substance without changing its temperature. It’s vital for processes like melting, freezing, vaporization, and condensation.

### 3. What are the common units for measuring latent heat?

Latent heat is commonly measured in joules per kilogram (J/kg) or kilojoules per kilogram (kJ/kg) in the SI system. Sometimes, it can also be expressed in calories per gram (cal/g) or kilocalories per kilogram (kcal/kg) depending on the context.

### 4. How does specific latent heat relate to latent heat?

Specific latent heat refers to the amount of energy needed per unit mass of a substance to undergo a phase change. It’s essentially the same concept as latent heat but expressed on a per-unit-mass basis. The formula for specific latent heat is 𝐿 = 𝑄/𝑚.

### 5. Can latent heat ever be negative?

Latent heat is a form of energy, so it’s always positive when heat is absorbed and negative when heat is released. However, in certain contexts, the sign convention might be inverted based on the direction of heat flow.