The amount of thermal energy needed to melt a solid and the amount of thermal energy needed to freeze the same liquid are equal in magnitude, but they have opposite signs.
This statement is correct. The amount of thermal energy needed to melt a solid and the amount of thermal energy needed to freeze the same liquid, under identical conditions, are equal in magnitude but have opposite signs.
When a solid is heated and reaches its melting point, the thermal energy supplied is used to break the intermolecular forces holding the solid together, allowing the particles to move more freely and form a liquid. This process is called melting, and the energy required is known as the heat of fusion.
On the other hand, when a liquid is cooled and reaches its freezing point, thermal energy is released as the particles slow down and form a more ordered solid structure. This process is called freezing, and the energy released is equivalent to the heat of fusion.
Since these processes are reversible, the quantities of energy involved are equal in magnitude but have opposite signs. This means that the energy required to melt a solid is the same as the energy released during the freezing of the liquid, but they are opposite in nature.