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Melting is, in fact, a state transition. It is a physical process by which a substance changes its state from solid to liquid.
In the microscopic theory, substances conatin molecules which are held together by an intermolecular attractive force. When a substance is heated, its molecules acquire energy, hence their vibrational motion increases and at the same time they have got sufficient energy to overcome the intermolecular attractive force. As a result, separation between these molecules increases. This explains why for most substances, they increase in volume on heating.
When the energy possessed by the molecules are strong enough to break the intermolecular attractive force to a certain extent and become free to move. The free motion of these molecules is observed macroscopically that the substance has become a liquid.
Certain substances undergo "sublimation". They change to the gas state directly from the solid state on heating, without transiting through the liquide state. A common example is carbon dioxide, the solid state of which (dry ice) changes to gaseous carbon dioxide at room temperature. Another example is iodine, which also undergoes sublimation on heating.