What would happen to the specific heat of water if salt is added?

Increasing the concentration of the salt decreases the specific heat capacity of the water.

Explanation:

When we heat a sample of water, the energy goes into raising the energy levels of its various vibrational, rotational, and translational motions.

When we dissolve

NaCl

in water, the ions are held in a rigid cage of water molecules.

The cage is rigid enough so that the motions of its molecules are "frozen out".