Heat Of Fusion Formula: Introduction, Equation, Symbol

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Namrata Das

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The heat of fusion is the amount of energy needed per unit to change a substance from a solid into a liquid. Fusion literally means melting so the heat of fusion is the quantity of energy, usually heat, required while converting a substance from solid to liquid form at its melting point. The heat of fusion is also known as the enthalpy of fusion and the specific latent heat of a substance that comes in the form of heat in order to bring a change in its original physical state, converting it into the liquid state. In the liquid state, the pressure of the environment is maintained at constant. This article explains the concept of the heat of fusion along with the formula and solved examples. 

Also Read: Difference Between Equinox and Solstice


Concept of the Heat of Fusion 

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The concept of Heat of fusion is there to calculate the quantity of energy, typically heat, required in order to melt a given amount of a solid (physical form) at its melting point temperature. Meanwhile, the pressure is constant. Right from our childhood, we observe that the ice melts into water and changes its form from solid to liquid. However, the science behind this process comes across in Physics while studying the Heat of fusion. 

Concept of the Heat of Fusion
Concept of the Heat of Fusion

The units of the heat of fusion are usually Joules per gram (J/g) or calories per gram (cal/g). Along with that, enthalpy or heat of fusion also indicates the amount of energy lost when a given mass of liquid converts its form into a solid. To give an example, the heat of fusion can calculate the heat required to melt ice into liquid water. On the other hand, it can also measure the heat (latent heat which is there hidden in every substance) used to solidify the water into ice. Inevitably, the value of heat of fusion will change according to the substance or material used.

You would have learned that whenever a change of physical form or state takes place then, a certain amount of heat energy is transferred between the substance and its surroundings. It is known as the latent heat, the heat per unit that is transferred during the change of state.

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Symbol of the Heat of Fusion

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Usually, concepts in physics are provided with a symbol to make them easy to remember and standardize the symbols at the same time. The heat of fusion also has a symbol. The heat of fusion is denoted by the symbol ΔHf in physics. 


Formula of the Heat of Fusion

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The heat of fusion formula as:

ΔHf = q/m

This formula is also written as

q = m·ΔHf

In whichever form you write it according to the value you need to find out. In both these formulas, â??Hf is the heat of fusion, q means heat and m indicates the mass. 

Also Read: Helmholtz Equation


Things to Remember 

  • The symbol of the heat of fusion is ΔHf
  • The formula of the heat of fusion is ΔHf = q/m or q = m·ΔHf (both are the same, anyhow). 
  • Note: the temperature does not really change when matter changes its state, so the temperature is not in the equation or required for the calculation.
  • The melting of helium is the only exception. Otherwise, the heat of fusion is always a positive value.
  • The most common example of the heat of fusion is the melting or turning of ice into water.

Also Read: Value of g on Moon


Sample Questions 

Ques: What is the heat in Joules required to melt 25 grams of ice? What is the heat in calories? (4 marks)
Useful information: Heat of fusion of water = 334 J/g = 80 cal/g 

Ans: In this question, the heat of fusion is already provided. The mass of solid (m) ice, in that case, is also given which is 25 grams. Temperature is not given as it is not required. Now, we directly need to find the heat in joules. 

To start with, we will write the formula and put the given values in it. 

The formula for the heat of fusion: q = m·ΔHf

The formula is straightforward. Just make sure that you are putting the right values in it. 

q=?, m= 25g, ΔHf= 334J/g

Now, to get heat in Joules

q= (25g)×(334J/g)

q= 8,350 J.

We can also express the heat in Calories, like this…

Provided: Heat of fusion of water = 334 J/g = 80 cal/g

Putting the value in the formula of the heat of fusion...

q = m·ΔHf

q= (25g)×(80Cal/g)

q= 2000 Cal.

Therefore, the amount of heat needed to melt 25 grams of ice is 8,350 in Joules or 2,000 in calories.

Ques: Find the amount of heat needed to melt 48gms of ice, if the heat of fusion of ice is 334 J/gm. (4 marks)

Ans: In this question, the heat of fusion is already provided. The mass of solid (m) ice, is also given which is 48 grams. Temperature is not required in the heat of fusion. Now, we directly need to find the amount of heat.

To find it, we will simply put the given values in the formula.

The formula for the heat of fusion: q = m·ΔHf

q=?, m= 48g, ΔHf= 334J/g

To find the amount of Heat in Joules

q= (48g)×(334J/g)

q= 16,032J.

To find the amount of heat in calories

Provided: Heat of fusion of water = 334 J/g = 80 cal/g

Putting the value in the formula of the heat of fusion

q = m·ΔHf

q= (48g)×(80Cal/g)

q= 3840 Cal.

Therefore, the amount of heat needed to melt 48 grams of ice is 16,032 in Joules. 

Ques: Find the amount of heat needed to melt 36gms of ice, if the heat of fusion of ice is 334 J/gm. (4 marks)

Ans: In this question also, the heat of fusion is already provided. The mass of solid (m) ice, is also given which is 36 grams. Temperature is not required in the heat of fusion. Now, we will directly jump to find the amount of heat.

To find it, we will simply put the given values in the formula.

The formula for the heat of fusion: q = m·ΔHf

q=?, m= 36g, ΔHf= 334J/g

To find the amount of Heat in Joules…

q= (36334g)×(334J/g)

q= 12,024J.

We can also express the heat in Calories,

Provided: Heat of fusion of water = 334 J/g = 80 cal/g

We will put the value of heat of fusion of water in calories/g in the formula of the heat of fusion, as given...

q = m·ΔHf

q= (36g)×(80Cal/g)

q= 2880 Cal.

Therefore, the amount of heat needed to melt 36grams of ice is 12,024 in Joules and 2880 in calories.

Ques: What do you mean by specific heat at constant volume and constant pressure? (2 marks)

Ans: Specific heat at constant and constant volume and constant pressure are referred to as the intensive properties denoted by cV and cP respectively; and these properties are defined for pure, simple, and compressible substances. 

Ques: What is meant by latent heat of fusion? (2 marks)

Ans: The energy is required to separate entirely the molecules, moving from liquid to gas is much greater than if we are just to reduce their separation from solid to liquid.

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