Why is adsorption always exothermic?

when a gas is adsorbed on the surface of a solid its entropydecreases, i.e.ΔS is − ve.Now, ΔG=ΔH−TΔS and for the process to be spontaneous, free energy change,ΔG must be negative.As TΔS is negative ΔG can be negative only if ΔH is negative. Hence, adsorption is always exothermic.