Adsorbent dimensionless temperature

Figure 8 shows the effect of p on the dimensionless temperature profile at x =0. Since p is not an explicit variable in equation (8), a single curve describes the dimensionless temperature profile in terms of X. The actual temperature rise is lower as p decreases and the adsorbent takes longer time to cool down. 

After the adsorbed CO rapidly relaxes to its ground electronic state g due to electronic dissipation, the s-region reaches equilibrium at a temperature T, but the p-region is yet found in a distribution of vibrational states r, with r = vg = 0,1,2,. The kernel matrix for delayed dissipation of vibrational energy has been given in terms of the dimensionless CO displacement q = h1/2/(mCooJv)1/2 x for a frustrated translation of frequency wy and mass rrico in the p-region. 

Adsorption isotherms describe one macroscopic consequence of these interactions, i.e., the relation between the amount of molecules adsorbed on a unit (mass, surface) of the solid and the sorbate equilibrium pressure (or relative pressure) at a given temperature. Below the critical temperature, the pressure is commonly normalized to the saturation pressure po which then leads to a dimensionless expression of the relative pressure p/pc,. The quantity of gas adsorbed is usually expressed as the mass of the sorbate or the volume of gas reduced to STP (standard temperature and pressure) adsorbed per mass of solid sorbent. 

As a first approach, the linear driving force (LDF) model is adopted with negligible temperature effect. Mass conservation of adsorbate is given in dimensionless form as... 

Excitability and oscillations are created by introducing - besides the temperature T (which by itself gives rise to bistability) - at least one additional variable , which describes a local chemical property such as a reactant concentration or the catalytic activity (which may in turn be related to the coverage of a poisoning adsorbate or the surface structure). The basic equations take the general (dimensionless) form... 

Adsorption is described through isotherms, i.e., through the functions connecting the amount of adsorbate taken up by the adsorbent (or the change of any other physical parameter related to the adsorption of matter) with the adsorptive equilibrium pressure p, the temperature T and all other parameters being constant. Below the critical temperature the pressure is properly normalized to the saturation vapor pressure p°, and the adsorbed amounts are so referred to the dimensionless relative pressure, p. 

Thus K(T) is dimensionless. The adsorption process of a gas on a solid can occur only in a restricted pressure range limited by the saturated vapour pressure of the component i at the same temperature as the adsorption temperature. If the vapour pressure is above ps then adsorption is replaced by liquefaction (Fig. 7.3). The saturation of the adsorbent is established when p is equal to ps. We often use the notion of relative pressure defined by the ratio p/ps. Its value lies between 0 and 1. When the relative pressure is equal to one, the filling coefficient is also equal to one. 

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