# Heat of Fusion (Enthalpy change): Explanation with Examples

Heat of fusion is defined as the heat or enthalpy change when a solid substance is converted into a liquid state at its melting point. Greater the heat of fusion of a substance higher the magnitude of intermolecular forces. For example, Ice melts at its melting point, 0 oC ( 273K ). It is accompanied by the absorption of 1.43 kcal of heat. Whenever matter undergoes a physical change, it is accompanied by an energy change. It is the quantitative measurement of the difference in the strength of intermolecular forces. The change in energy is mostly in the form of heat. If it is take place at constant pressure, then the heat change during this process is called enthalpy change. It is denoted by delta H.

The enthalpy change is usually expressed per mole of the substance. There are different types of enthalpy change that are associated with physical changes.

• Molar heat of fusion.
• Latent heat of fusion.
• Specific heat of fusion.
• Molar heat of vaporization.
• Molar heat of sublimation.
• Molar heat of transition.

## Molar heat of fusion

Molar heat of fusion is the amount of heat absorbed by the one mole of a solid to convert into the liquid state. During the process, the pressure kept at 1 atm. The symbol for molar heat of fusion is delta HF. The standard pressure at which this process takes place is always one atm.

## Latent heat of fusion

The heat energy required to change a unit mass of the substance from solid to liquid state at its melting point without change in its temperature is known as latent heat of fusion. It is represented by the symbol delta HL.

When a substance is changed from solid to liquid state by adding heat, the process is called melting or fusion. The temperature at which the solid starts its melting is known as the fusion point or melting point. Different substances have different melting points. However, the freezing point of substances is the same as its fusion point.

• The latent heat of fusion of ice is 3.36 x 105 Jkg-1.

## Specific heat of fusion

It is the specific amount of heat that is required by a substance to change its state. Mostly solid is converted into a liquid state when a fixed or specific amount of heat energy is given. This process takes place at standard pressure that is one atmospheric pressure. It is represented by delta HS.

## Molar heat of vaporization

The molar heat of vaporization is defined as the enthalpy change when one mole of liquid is converted into a gaseous or vapor state at its boiling point. For example, when one mole of water is converted into steam or vapor at 100 oC (373 K), the heat absorbed is 9.71 kcal which is the heat of vaporization of water. The heat of vaporisation of benzene is 7.36 kcal mol-1. The value of heat of vaporization can also be used to compare the magnitude of intermolecular forces of attraction in liquids.

## Molar heat of sublimation

The heat change when one mole of a solid substance is directly converted into the gaseous state at a temperature below its fusion point. For example, the heat of sublimation of iodine is 14.92 kcal mol-1. The heat of sublimation is the process, in which solid changes directly into the gaseous state without changing into a liquid state. It occurs at a temperature below the fusion point of the solid.

## Molar heat of transition

The heat of transition is the change in enthalpy that occurs when one mole of an element changes from one allotropic form to another. For example, the transition of diamond into amorphous carbon may be represented as Where -0.016 kcal and -1.028 kcal are the heat of transition of monoclinic sulfur to rhombic sulfur and white phosphorus to red phosphorus respectively.

## Applications

• This process is used in melting ice into water.
• It is used in manufacturing industries.
• In the coin and glassmaking industry.
• It is also used for forging metal objects.

## Key Takeaway(s)

Take a beaker and place it on the stand. Put small pieces of ice in the beaker and suspend a thermometer in it to measure the temperature. Place a burner under the beaker. The ice starts to melt. The temperature of the mixture of ice and water will not increase above 0oC until the ice melt. Note the time at which the ice starts to melt completely into the water.

Continue heating the water. Its temperature will begin to increase. Now note the time at which the water in the beaker starts to reach its boiling point at 100oC from 0oC.

Calculation of heat of fusion of ice

 The formula is given by,ΔQ = mc.ΔTLet,The mass of ice = mTime take by ice to melt completely at 0oC = Tice = T2 – T1 = 3.6 minTime is taken by water to heat from 0oC to 100oC = Twater = T2 – T1 = 4.6 minSpecific heat of water = c = 4200 Jkg-1k-1Increase in the temperature of water = ΔT = 100 KPut the values in the formula,ΔQ = mc.ΔT= m x 4200 Jkg-1k-1 x 100 k= m x 420,000 Jkg-1OrΔQ = m x 4.2×105 Jkg-1Heat ΔQ is supplied to water in time Twater to raise its temperature from 0oC to 100oC.Hence, the rate of absorbing heat by water in the beaker and heat ΔQice absorbed by ice in time Tice.ΔQice = ΔQ x Tice / Twater Put the value of ΔQ, Tice, Twaterin above equation. we getΔQice = m x 4.2×105 Jkg-1 x 3.6 min / 4.6 minWe also know that ΔQice = m x Hf, so put this value in the above equation, we getm x Hf = m x 4.2×105 Jkg-1 x 3.6 min / 4.6 minHf = 4.2×105 Jkg-1 x 3.6 min / 4.6 minHf = 3.29 x 105 Jkg-1Hf = 3.29 x 105 Jkg-1 is the heat of fusion of ice.

## Concepts Berg

What is the heat of fusion for dry ice?

The heat energy is given to change a unit mass of the substance from solid to liquid state at its melting point without changing the temperature. The latent heat of fusion for dry ice is about 85 BTU/Ib (69.9oF).

What is between the latent heat of vaporization and the latent heat of fusion?

The main difference between them is a state of matter. The latent heat of vaporization shows the conversion from liquid to vapor state while the latent heat of fusion shows the change from solid to liquid state at its melting point without change in the temperature.

How do you find the heat of fusion?

We can calculate it by the formula q = m.ΔHf.

What is the heat of fusion in Joules?

The heat of fusion of water in joules is 334.

What is the difference between specific heat of vaporization and heat of vaporization?

In specific heat of vaporization, we have to give a specific amount of heat energy while in heat of vaporization there is a limit to give heat energy till its melting point.