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Why does the temperature of a substance ...

Why does the temperature of a substance remain constant during its melting point or boiling point ?

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The temperature of a substance remains constant during melting and boiling points till the completion of melting and boiling. It is because substance makes use of latent heat of fusion to overcome force of attraction between particles of solid to change into liquid during melting and latent heat of vaporisation to overcome force of attraction between particles of liquid to change into vapours during boiling.
Therefore, temperature remains constant.
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