Heat of Fusion Formula

Heat of fusion of a substance is the change in its enthalpy by providing energy, typically heat, to a specific quantity of the substance to change its state from a solid to a liquid keeping pressure constant.

The heat of fusion of a sample is the measure of the amount of heat that needs to be introduced to convert its crystalline fraction into the disordered state. It is uniquely dependent upon the degree of crystallinity of the substance and the theoretical heat of fusion of a sample which is 100% crystalline.

For example, heat gained by ice is equal to the heat lost by the water.
The Heat of fusion is denoted by ΔHf

The heat of fusion formula is given as
q = m·ΔHf

q is heat energy
m is mass
ΔHf is heat of fusion

Example 1
Calculate the heat in Joules required to melt 26 grams of ice. Given that heat of fusion of water = 334 J/g = 80 cal/g
Given parameters are
Mass, m = 26g
We know that
q = m·ΔHf
q = (25 g) x (334 J/g)
= 8684 J

q = m·ΔHf
q = (26 g)x(80 cal/g)
q = 2080 cal

Example 2
How much quantity of ice at 0oC can be melted by 100 joules of heat.

Heat to fuse (melt) a substance = heat of fusion of the substance × mass of the substance

this quantity can be expressed by the formula where
q denotes the heat measurement in calorimeter.

q = m(mass) x c(heat of fusion)

Solve for m
we get

m = q / C

= 100 / 3.34×102

= 29.9 × 10-2g of ice melted


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