Latent Heat of Fusion

Latent Heat of Fusion is one of the latent heats in chemistry like the latent heat of vaporization and latent heat of sublimation. When a substance is changing its phase from liquid to solid or solid to the gas of gas to a liquid, this latent heat comes in handy to find the energy of the reaction. Latent Heat of Fusion is related to the solid-to-liquid phase change. In this article, we will explore all the topics related to the latent heat of fusion and its formula. We’ll also learn about the latent heat of fusion for various different elements as well as compounds. 

Let’s start our learning about the concept with the name “Latent Heat of Fusion”.

What is Latent Heat of Fusion?

Latent Heat of Fusion can be interpreted as the energy that is required for the phase transition between solid and liquid phases. Suppose we have 1 Kg of Butter (cold and solid) and we want liquid butter. So, we need some energy which can be used in the process of liquidation of butter. That required energy here is the Latent heat of Fusion.

Latent Heat of Fusion Definition

Latent heat of fusion is defined as the amount of heat received by a solid body to transform it into a liquid without raising the temperature of the substance.

For example, we have 5kg of ice at 0°C 

SI Unit of Latent Heat of Fusion

The SI unit of latent heat of fusion is joules per kilogram (J/kg). Other units of latent heat of fusion are calorie/kilogram, joule/gram, calorie/gram, erg/gram, kilojoule/kilogram, etc. For example, the latent heat of fusion for water in the form of ice is 334 J/kg. This means that it takes 334 J of heat to melt 1 kg of ice at 0 degrees Celsius.

Note: Dimensional formula for the latent heat of fusion is given by [M⁰L²T⁻²].

Examples of Latent Heat of Fusion

There are various examples of latent heat of fusion. Some of these values are discussed in the following headings.

Latent Heat of Fusion of Ice

Latent heat of fusion of ice is the heat required to change the state of ice, i.e. it is the amount of heat required to change the ice into the water without changing its temperature. The latent heat of Ice is 334 J/g.

Latent Heat of Fusion of Other Substances

The latent heat of Fusion for various elements and compounds can be calculated using the formula which we will learn in further headings. The latent heat of fusion for some common elements is given in the following table:

Elements	Latent Heat of Fusion (J/g)	Latent Heat of Fusion (Cal/g)
Aluminum (Al)	397	94.89
Chlorine (Cl2)	181	43.26
Copper (Cu)	209	49.95
Gold (Au)	63.7	15.22
Hydrogen (H2)	59.5	14.22
Iron (Fe)	247	59.03
Lead (Pb)	23	5.5
Mercury (Hg)	11.4	2.72
Nitrogen (N2)	25.3	6.05
Oxygen (O2)	13.7	3.27
Silver (Ag)	105	25.1
Sodium (Na)	113	27.01
Tungsten (W)	285	68.12
Zinc (Zn)	112	26.77

For some common compounds, the latent heat of fusion is given in the following table:

Compounds	Latent Heat of Fusion (J/g)	Latent Heat of Fusion (Cal/g)
Water (H2O)	334	79.83
Methane (CH4)	58.4	13.96
Ethane (C2H6)	95.1	22.73
Propane (C3H8)	80.1	19.14
Butane (C4H10)	80.2	19.17
Carbon Dioxide (CO2)	195	46.61
Ammonia (NH3)	334	79.83
Ethanol (C2H5OH)	109	26.05
Methanol (CH3OH)	352	84.13
Benzene (C6H6)	102	24.38
Chloroform (CHCl3)	78.4	18.74
Acetone (CH3COCH3)	92	21.99

Latent Heat of Fusion Formula

We can calculate the Latent Heat of Fusion using the following formula:

 Q = mL + mcΔT

Where,

• Q is the latent heat of fusion,
• m is the mass of body,
• L is the specific latent heat of fusion,
• c is the specific heat of body,
• ΔT is the temperature change during heat absorption.

If there is no change in temperature(ΔT = 0) and energy provided to the matter is only used for the transition of phase, then

 Q = mL

Where,

• Q is the latent heat of fusion,
• m is the mass of body,
• L is the specific latent heat of fusion,

Specific Heat of Fusion

The specific heat of fusion is the amount of energy required to change the phase of a unit mass of a substance from solid to liquid, without changing its temperature. As there is phase change happening in this transfer of energy the substance should be at the melting point in temperature already. As specific heat of fusion varies for different substances. Some commonly known values are:

• Specific Heat of Fusion of Water: 334 J/g or 79.7 cal/g
• Specific Heat of Fusion of Lead: 24.5 J/g or 5.85 cal/g
• Specific Heat of Fusion of Iron: 272 J/g or 65 cal/g
• Specific Heat of Fusion of Copper: 205 J/g or 49 cal/g
• Specific Heat of Fusion of Gold: 63 J/g or 15 cal/g

These values represent the amount of heat energy required to change 1 gram of the substance from solid to liquid at its melting point.

Molar Heat of Fusion

Similar to specific heat of fusion, molar heat of fusion is defined as the amount of energy required to change the phase of a unit mass of a substance from solid to liquid, without changing its temperature. As phase change only happens when a substance is heated to the melting point, thus the substance under consideration for molar heat of fusion is already at the melting point.

Read More,

• Latent Heat
• Heat of Vaporization
• Heat Capacity

Sample Problems on Latent Heat of Fusion

Problem 1: Calculate the latent heat of fusion for a body of mass of 40 g at 20°C if it absorbs heat at 80°C. It is given that the specific latent heat of steam is 540 cal/g and the specific heat of the body is 0.5 cal/g °C.

Solution:

We have,

m = 40, ΔT = 80 – 20 = 60, L = 540 and c = 0.5

Using the formula we get,

Q = mL + mcΔt

⇒ Q = (40 × 540) + (40 × 0.5 × 60)

⇒ Q = 21600 + 1200

⇒ Q = 22800 Cal

Problem 2: Calculate the latent heat of fusion for a body of mass 20 g at 40°C if it absorbs heat at 100°C. It is given that the specific latent heat of steam is 540 cal/g and the specific heat of the body is 0.1 cal/g °C.

Solution:

We have,

m = 20, ΔT = 100 – 40 = 60, L = 540, and c = 0.1

Using the formula we get,

Q = mL + mcΔt

⇒ Q = (20 × 540) + (20 × 0.1 × 60)

⇒ Q = 10800 + 120

⇒ Q = 10920 Cal

Problem 3: Calculate the latent heat of fusion for 7 g of water getting converted into ice. It is given that the specific latent heat of ice is 80 cal/g.

Solution:

We have,

m = 7, and L = 80

Using the formula we get,

Q = mL

⇒ Q = 7 (80)

⇒ Q = 560 Cal

Problem 4: Calculate the latent heat of fusion for 60 g of steam getting converted into water. It is given that the specific latent heat of water is 533 cal/g.

Solution:

We have,

m = 60

L = 533

Using the formula we get,

Q = mL

⇒ Q = 60 (533)

⇒ Q = 31980 cal

Problem 5: Calculate the mass of water that gets converted into ice given that the specific latent heat of ice is 80 cal/g and the latent heat of fusion is 200 cal.

Solution:

We have,

Q = 200

L = 80

Using the formula we get,

Q = mL

⇒ m = Q/L

⇒ m = 200/80

⇒ m = 2.5 g

Problem 6: Calculate the mass of steam getting converted into water given that the specific latent heat of water is 533 cal/g and the latent heat of fusion is 700 cal.

Solution:

We have,

Q = 700

L = 533

Using the formula we get,

Q = mL

⇒ m = Q/L

⇒ m = 700/533

⇒ m = 1.31 g

Problem 7: Calculate the latent heat of fusion for a body of mass 30 g if its specific latent heat of steam is 540 cal/g and the heat absorbed by it is 200 calories.

Solution:

We have,

m = 30

L = 540

Q’ = 200

Using the formula we get,

Q = mL + Q’

⇒ Q = (30 × 540) + 200

⇒ Q = 16200 + 200

⇒ Q = 16400 Cal

FAQs on Latent Heat of Fusion

Q1: Define Latent Heat of Fusion.

Answer:

The latent heat of fusion is the heat absorbed or released during the phase transition from a solid to a liquid, or vice versa, without a change in temperature.

Q2: How is Latent Heat of Fusion measured?

Answer:

The latent heat of fusion is typically measured using calorimetry techniques. A known mass of the substance is heated until it completely melts or cooled until it solidifies, while the temperature is monitored. The amount of heat energy absorbed or released is calculated by measuring the temperature change and using the equation 

Q = m × L

Where 

• Q is the heat energy, 
• m is the mass, and 
• L is the latent heat of fusion.

Q3: Is the Latent Heat of Fusion Same for all Substances?

Answer:

No, the latent heat of fusion is not the same for all substances. Each substance has a different value for the latent heat of fusion based on the intermolecular forces and the structure of the substance.

Q4: What are Some Examples of Substances with High Latent Heat of Fusion?

Answer:

Substances with high latent heat of fusion include water (334 kilojoules per kilogram), paraffin wax (200 kJ/kg) and lead (24 kJ/kg).

Q5: Can Latent Heat of Fusion be Negative?

Answer:

No, the latent heat of fusion cannot be negative. It is always a positive value because it represents the amount of energy required to change a substance from a solid to a liquid state. 

Q6: How does Pressure Affect Latent Heat of Fusion?

Answer:

For most of substances, pressure does not affect the latent heat of fusion. But substances that exhibit unusual phase behaviour under high pressures can have different values of latent heat of fusion for different pressure.