# Latent Heat Introduction and Latent Heat of Fusion | Physics Grade XI

### Latent Heat of Fusion # Latent Heat Introduction and Latent Heat of Fusion

Latent Heat
Latent heat of a substance is the amount of heat required to change the state of a unit mass of the substance from solid to liquid or from liquid to vapor without a change in temperature.

Latent heat of Fusion
Latent heat of fusion is defined as the amount of heat required to change a unit mass of a substance from the solid-state to a liquid state at a constant temperature. Thus, the latent heat of fusion of ice is defined as the amount of heat required to change one gram of ice from 0 degree Celsius to water at 0 degree Celsius.

For ice, the latent heat of fusion is 80 Cal g-1 in CGS-system.

Determination of Latent Heat of Fusion of Ice by the Method of Mixture
Let us consider a dry and clean calorimeter with a stirrer of mass m1. It is filled one-third of its volume with warm water whose mass is m2. let the initial temperature of calorimeter and its contents be θ1degree Celsius. Some small pieces of ice are taken and water in them is soaked with blotting paper. Then, the ice pieces are dropped into the water in the calorimeter and the mixture is stirred gently until the temperature of calorimeter and mixture decreases to a smaller value of temperature. Let the final temperature of the mixture be θ. Finally, the calorimeter and mixture are weighted to note the mass of ice. Let m3 be the mass of ice. Now, the amount of heat lost by calorimeter and water from θ1 degree Celsius to θ degree Celsius,
= m1s11 – θ) + m2s21 – θ)
= (θ1 – θ) (m1s1 + m2s2) …... (i)
Where sand s2 are the specific heat capacities of calorimeter and water respectively.

Here, the amount of heat gained by ice in two steps:
i. When the ice at 0-degree Celsius changes to water at 0 degree Celsius, the amount of heat gained is = m3 L (Where L is latent heat of fusion of ice)
ii. When the temperature of water from ice increases from 0 degree Celsius to θ degree Celsius. The heat gained during this process is = m3s2(θ-0) = m3s2θ

Thus, total amount of heat gained by ice = m3 L + m3s2θ ….... (ii)

From the principle of calorimetry, we have
Heat gained = heat lost
or, m3L+ m3s2θ = (θ1 – θ) (m1s1 + m2s2)
or, L = [(θ1 – θ) (m1s1 + m2s2)/ m3] – s2θ
This relation gives the latent heat of fusion of ice.

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