Why is adsorption always exothermic?

when a gas is adsorbed on the surface of a solid its entropy
decreases, i.e.$\mathrm{\Delta S} \mathrm{is} - \mathrm{ve}.\mathrm{Now}, \mathrm{\Delta G}=\mathrm{\Delta H}-\mathrm{T\Delta S}$ and for the process to be spontaneous, free energy change,$\mathrm{\Delta G}$ must be negative.
As $\mathrm{T\Delta S}$ is negative $\mathrm{\Delta G}$ can be negative only if $\mathrm{\Delta H}$ is negative. Hence, adsorption is always exothermic.