The correct statement for both the processes of physisorption and chemisorption is

Adsorption means adherence of molecules from the bulk (gas / solution) on the surface of a solid. For any spontaneous adsorption process the Gibbs free-energy change $$\Delta G$$ must be negative:

$$\Delta G = \Delta H - T\Delta S \lt 0$$

The adsorbate particles lose translational freedom when they stick to a surface, so the entropy change $$\Delta S$$ is negative. For $$\Delta G$$ to remain negative, the enthalpy change $$\Delta H$$ must therefore be negative, i.e. heat must be released. Hence any spontaneous adsorption is an exothermic process.

• Physisorption (physical adsorption) involves weak van der Waals forces. Its heat of adsorption is small, typically $$20\text{-}40\;{\rm kJ\,mol^{-1}}$$, but still negative.

• Chemisorption (chemical adsorption) involves formation of chemical bonds with the surface. The heat of adsorption is much larger, often $$80\text{-}200\;{\rm kJ\,mol^{-1}}$$, yet again negative.

Thus, in both physisorption and chemisorption the enthalpy change is negative; they are exothermic.

Therefore the correct statement is:
Option C which is: both are exothermic