Why is energy released during the process of adsorption? How is this energy change observed and how is it calculated?
Under normal conditions, atoms will bond to one another and produce a molecule, only if the bond formation process is exothermic (e.g. it releases energy) - this translates into the products (the molecule) being thermodynamically more stable that the starting material (the atoms). The same is true for the adsorption process. A gas will adsorb on a surface only if this configuration is more stable than a gas and a free surface.
Typically when a gas is adsorbed on a surface, something akin to bond formation between the surface and the gas takes place and we wind up with a chemisorbed species. There are many ways to study this process. One simple way is to measure the amount of gas admitted to the system containing the surface to be studied and measuring the change in pressure over time. When done in a calorimeter, the heat given of during the process can also be measured. Combining these two measurements(change in moles of free gas and energy released) allows one to understand the basic energetics of the process. The "isoteric method" is one experimental procedure for accomplishing this in a laboratory. It relies on measuring moles of gas vs. the pressure in the system (an isotherm) at various temperatures. From these measurements the enthalpy of adsorption can be determined.
The study of the adsorption of a gas on a surface is complicated. There is not a surface with a monolayer of gas adsorbed on it with free gas above this. Rather there is a surface and bulk gas and in between the two is a multilayer structure of adsorbed gas where the gas concentration varies throughout. Here is a link to a recent Cal Tech thesis on the characterization of hydrogen gas adsorption onto various surfaces; take a look at section 1.5 and the beginning of chapter 3 for a nice overview of the adsorption process and the interfaces involved. The rest of chapter 3 is a discussion of the thermodynamics and various experimental techniques used to study the process. It sounds like you might also be interested in performing calculations on the adsorption process. If so, section 5.8 delves into computational methods used on one of the surfaces studied.