This paper deals with the modelling of adiabatic adsorption. The main aim of the computations was the study of the effect of coverage dependence of the heat of adsorption on the breakthrough curves. This is particularly important in the case of outlet gas concentration monitoring by the measurement of temperature. For comparison, similar computations for models with coverage independent of heat of adsorption have been carried out. The dependence of heat of adsorption on the coverage has been described by a linear equation (4). The equilibrium dependence is described by equation (6). The isotherms of adsorption based on Eq. (6) are shown in Fig. 1. There is a good agreement with experimental data. Mass transfer resistances both in the particles (macropore diffusion) and in external film have been taken into account. The parabolic profile of the adsorbate in the particle has been postulated, leading to Eq. (9) for the adsorbate concentration gradient on the particle surface. The effect of equilibrium nonlinearity on the kinetics of adsorption has been taken into account by applying Vermeulen＇s equation (10). The external-film mass transfer coefficient has been computed from Eq. (13). The temperature gradient inside the particle is assumed to be negligible. The external-film heat transfer coefficient has been computed from Eq. (14). Axial dispersion and radial concentration as well as temperature gradients in the column are assumed to be negligible. With these assumptions the equations describing the dynamic behaviour of the system are as follows: gas phase mass balance (Eq. (18)), solid phase mass balance (Eq. 27)) and equilibrium equation (Eq. (6)). The boundary conditions are described by Eqs. (28) and (29). The coupled PDEs were solved by a finite difference technique. In Figures 2-7 the results are shown as follows: Line 1 - the model assuming the dependence of the heat of adsorption on the coverage. Line 2 - the model assuming that the heat of adsorption (DELTAh0) does not depend on the coverage. Line 3 -the model assuming that the heat of adsorption (DELTAh(q0/2)) does not depend on the coverage. Line 4 - the model assuming that the heat of adsorption (DELTAh(q0)) does not depend on the coverage. Furthermore, in Figs. 4 and 7 the temperature breakthrough curves computed from Eq. (45) are shown. In this case line 2a, 3a and 4a correspond to DELTAh0, DELTAh(q0/2) and DELTAh(q0), respectively. The parameters of the model used in the computations are shown in Table 2. The computations were carried out for the case of adsorption of water vapour on molecular sieves 4A. The results of these computations show that although the heat effects in the process are remarkable, the temperature of both phases can be considered to be equal. The assumption on the dependence of the heat of adsorption on the coverage has a considerable effect on the temperature breakthrough curves and much smaller effect on the concentration breakthrough curves. In most adsorption systems the thermal wave moves ahead of the adsorbate front. This is observed when gamma > 1. For the parameters applied in these computations 25.3 > gamma > 47.0. In such cases it is possible to monitore the concentration front by the measurement of gas temperature at the outlet of the bed. The results of these computations showed that when the bed length is greater than the mass transfer zone, well-defined plateau intervals are observed in the temperature breakthrough curves (Fig. 4). In the case of short beds, plateau intervals are visible only for the models in which there is assumed that the heat of adsorption is independent on the coverage. For the model presented in this paper the temperature breakthrough curves exhibit different shapes (line 1, Fig. 7). Because of the gradual changes in the curve shapes it becomes difficult to observe the breakthrough by the measurements of the gas temperature. During the front formation (that is, at the beginning of the process) more heat is generated than during the later stages of the process, which results from the higher value of the heat of adsorption for low coverage. This is the reason for formation of peaks at the beginning of line 1 (Figs. 4, 7). A further observation is that after the initial stage of the front formation line 1 in Figs. 4, 7 lies lower than line 3. This results from the fact that the heat generated at later stages of the process is smaller than the average value of heat of adsorption.