During the process of physical adsorption, at very low relative pressure, the first sites to be covered are the more energetic ones. Those sites with higher energy on a chemically pure surface reside within narrow pores where the pore walls provide overlapping potentials. Other high-energy sites lie between the horizontal and vertical edges of surface steps where the adsorbate can interact with surface atoms in two planes. In general, wherever the adsorbate is afforded the opportunity to interact with overlapping potentials, or an increased number of surface atoms, there will be a higher energy site. On surfaces consisting of heteroatoms, such as organic solids or impure materials, there will be variations in adsorption potential depending upon the nature of the atoms of functional groups exposed at the surface.

That the more energetic sites are covered first as the pressure is increased does not imply that no adsorption occurs on sites of lower potential. Rather, it implies that the average residence time of a physically adsorbed molecule is longer on the higher-energy sites. Accordingly, as the adsorbate pressure is allowed to increase, the surface becomes progressively coated and the probability increases that a gas molecule will strike and be adsorbed on a previously bound molecule. Clearly then, prior to complete surface coverage the formation of second and higher adsorbed layers will commence. In reality, there exists no pressure at which the surface is covered with exactly a completed physically adsorbed monolayer. The effectiveness of the Brunauer, Emmett and Teller (BET) theory is that it enables an experimental determination of the number of molecules required to form a monolayer despite the fact that exactly one monomolecular layer is never actually formed.

Brunauer, Emmett, and Teller, in 1938, extended Langmuir's kinetic theory to multilayer adsorption. The BET theory assumes that the uppermost molecules in adsorbed stacks are in dynamic equilibrium with the vapor. This means that where the surface is covered with only one layer of adsorbate, an equilibrium exists between that layer and the vapor; where two layers are adsorbed, the upper layer is in equilibrium with the vapor, and so forth. Since the equilibrium is dynamic, the actual location of the surface sites covered by one, two or more layers may vary but the number of molecules in each layer will remain constant.

Using the Langmuir theory and equation (1) as a starting point to describe the equilibrium between the vapor and the adsorbate in the first layer,

 （1）

By analogy, for the fraction of surface covered by only two layers one may write

（2）

In general, for the nth layer one obtains

（3）

The BET theory assumes that the terms v, E, and A remain constant for the second and higher layers. This assumption is justifiable only on the grounds that the second and higher layers are all equivalent to the liquid state. This undoubtedly approaches reality as the layers proceed away from the surface but is somewhat questionable for the layers nearer the surface because of polarizing forces. Nevertheless, using this assumption one can write a series of equations, using L as the heat of liquefaction

（4）

（5）

（6）

and, in general, for the second and higher layers

（7）

From these equations, it follows that

（8）

（9）

（10）

（11）

then

（12）

（13）

（14）

（15）

The total number of molecules adsorbed at equilibrium is

（16）

Substituting for ...from equations (12-15) gives

（17）

（18）

Since both  are assumed to be constants, one can write

（19）

This defines C by using equations (8) and (9-11) as

（20）

Substituting  ain equation (17-18) yields

（21）

The preceding summation is just . Therefore,

（22）

Necessarily

（23）

Then

（24）

Substituting equation (24) into (22) gives

（25）

Replacing  in equation (25) with from equation (15)

yields

（26）

and introducing  from equation (19) in place of  gives

（27）

The summation in equation (27) is

（28）

Then

（29）

From equation (30) we have

（30）

Then equation (29) becomes

（31）

and

（32）

Introducing  from equation (32) into (22) yields

（33）

When  equals unity  becomes infinite. This can physically occur when adsorbate condenses on the surface or when P/P0=1。

Rewriting equation (11) for P = Po, gives

（34）

but

（35）

then

（36）

Introducing this value for  into (33) gives

（37）

Recalling that N/Nm = W/Wm and rearranging equation (37) gives the BET equation in final form,

(38)

If adsorption occurs in pores limiting the number of layers then the summation in equation (37) is limited to n and the BET equation takes the form

（39）

Equation (39) reduces to (38) with  and to the Langmuir equation with n = 1.