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Heat of Fusion Formula

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The heat of fusion is defined as the amount of energy lost when a certain mass of liquid solidifies. In other words, it is the amount of energy required to melt a given amount of a material at its melting point temperature. It is the change in the value of the enthalpy caused by the provision of energy, i.e. heat, for a certain amount of the material. The heat of fusion of any sample can be interpreted as the amount of heat required to transform its crystalline portion into a disordered condition.

Heat of Fusion Formula

The heat of fusion formula is equal to the ratio of heat supplied to the given sample to its mass. It is denoted by the symbol ΔHf. Its standard unit of measurement is joules per kg (J/kg) and the dimensional formula is given by [M0L2T-2]. It has a constant value for each type of material. For example, the heat of fusion of water is 334 J/g. It indicates that 334 J of energy is required to melt 1g of ice into the water at 0°C.

ΔHf = Q/m

where,

ΔHf is the heat of fusion,

Q is the amount of heat supplied,

m is the mass of sample.

Sample Problems

Problem 1. Calculate the heat supplied to melt 12 g of ice into the water if its heat of fusion is 334 J/g.

Solution:

We have,

ΔHf = 334

m = 12

Using the formula we get,

Q = m ΔHf

= 334 (12)

= 4008 J

Problem 2. Calculate the heat supplied to melt 50 g of ice into the water if its heat of fusion is 334 J/g.

Solution:

We have,

ΔHf = 334

m = 50

Using the formula we get,

Q = m ΔHf

= 334 (50)

= 16700 J

Problem 3. Calculate the heat supplied to melt 29 g of ice into the water if its heat of fusion is 334 J/g.

Solution:

We have,

ΔHf = 334

m = 29

Using the formula we get,

Q = m ΔHf

= 334 (29)

= 9686 J

Problem 4. Calculate the heat of fusion if 1336 J heat is supplied to melt 4 g of ice.

Solution:

We have,

Q = 1336

m = 4

Using the formula we get,

ΔHf = Q/m

= 1336/4

= 334 J/g

Problem 5. Calculate the heat of fusion if 3006 J heat is supplied to melt 9 g of ice.

Solution:

We have,

Q = 3006

m = 9

Using the formula we get,

ΔHf = Q/m

= 3006/9

= 334 J/g

Problem 6. Calculate the mass of ice melted when 1372 J energy is supplied and the heat of fusion is 334 J/g.

Solution:

We have,

Q = 1372

ΔHf = 334

Using the formula we get,

m = Q/ΔHf

= 1372/334

= 4.11 g

Problem 7. Calculate the mass of ice melted when 2500 J energy is supplied and the heat of fusion is 334 J/g.

Solution:

We have,

Q = 2500

ΔHf = 334

Using the formula we get,

m = Q/ΔHf

= 2500/334

= 7.48 g


Last Updated : 03 Feb, 2024
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