Asample of potassium nitrate (49.0 g) is dissolved in 101 g of water at 100 °c, with precautions taken to avoid evaporation of any water. the solution is cooled to 30.0 °c and no precipitate is observed. this solution is

This solution is "supersaturated".

A supersaturated solution is a solution that contains a higher than than the concentration of solute, slight unsettling influence or seeding causes crystallization of abundance solute. 
Supersaturation is a condition of a solution that contains a greater amount of the dissolved material than could be dissolved by the solvent under ordinary conditions.

Heat of fusion= heat/mass  heat of fusion = 12.03kj/36 g= 0.3342 kj/g or 334.2 j/g