Specific heat of adsorbents

Specific heat of adsorbent (carbon), possibly a function of temperature. 

Specific heat of adsorbed phase at constant volume. 

It is advantageous to use a low-retentivity carbon to enable the adsorbate to be stripped out easily. When empirical data are not available, the following heat requirements have to be taken into consideration (1) heat to the adsorbent and vessel, (2) heat of adsorption and specific heat of adsorbate leaving the adsorbent, (3) latent and specific heat of water vapor accompanying the adsorbate, (4) heat in condensed, indirect steam, (5) radiation and convection heat losses. 

M mass of solute to be separated N number of effective theoretical plates P pressure Q flow rate R resolution S peak capacity Sm specific heat of mobile phase Ss specific heat of adsorbent Sg specific heat of detector cell walls V volume in conventional units Vo system dead volume Vr retention volume V r corrected retention volume Vm volume of mobile phase in the column Vs volume of stationary phase in the column Ve extra column volume... 

The integrated terms are simply the specific heat of the unit mass of adsorbent and its associated adsorbate. The specific heat at constant volume has been used for the adsorbate since, theoretically, there is no expansion of the adsorbate volume and the heat required to raise the temperature is the change in internal energy. In practice there will be some expansion and a pessimistically high estimate could use the specific heat at constant pressure The specific heat of the adsorbed phase is in any case difficult to estimate and it is common to approximate it to that of saturated liquid adsorbate at the same temperature. 

These ideas have been tested by calculations on the ferromagnetic Ising model and the 10-state Potts model , where exact results on T, +, are available , and excellent agreement with the theoretical predictions Eqs. (45)-(50) was found. As an example. Fig. 10 shows the specific heat for finite 10-state Potts lattices and the scaling representation of these data resulting from Eq. (47). Also experimental data on rounded specific heats of O2 adsorbed on grafoil can be accounted by Eq. (47) quantitatively . 

In this connection, it is interesting to consider questions of the heat of adsorption on a non-uniform surface, of the fraction of the specific heat of the adsorbed gas related to redistribution of the gas on the surface for a change in temperature, and so on—both for the general case and for a distribution of the form (17). The elaboration of these problems, however, at present would necessarily be nothing more than a mathematical exercise. We note only that for the distribution equation (17), the smaller the value of q, the sharper is the maximum of the specific heat near T = 7, while the differential heat of absorption at T = 0 obeys the equation... 

Adsorption is normally exothermic thus a decrease in temperature will increase the extent of adsorption whereas an increase in temperature will increase the adsorption capacity for chemisorption (normally endothermic). The heat of adsorption, AHads, is defined as the total amount of heat evolved per a specific amount of adsorbate adsorbed on an adsorbent. Because adsorption from an aqueous solution occurs, AHads is small, and thus small changes in temperature do not alter the adsorption process much. The effect of temperature on adsorption can be expressed by ... 

One thing that we can see from this expression is that ft is reduced as St (or L) is increased. The more latent heat that is released in the transformation from liquid to solid, the slower the interface moves. This is because the process becomes limited by the rate at which heat can be removed from the interface. As more heat is released, the process is slowed down. In contrast, as the specific heat of the solid increases, the rate of freezing increases because more of the heat can be adsorbed with a decreased need to transport the heat away from the interface. 

In the gas phase, each molecule has three degrees of translational plus two of rotational freedom so that cp iR, plus a small contribution from vibration which will increase to R at higher temperatures. At low temperatures the atoms in the adsorbed layer will be localized and vibrationally unexcited. In this temperature range the isosteric heat therefore increases as iR. As the temperature is raised, however, and surface vibrations begin to contribute, the specific heat of the adatoms will approach that of the gas and finally exceed it, causing a diminution of the heat. This trend reverses once the adsorbed layer approaches the two dimensional gas. Presumably the vibration perpendicular to the surface contributes somewhat before the vibrations in the gas phase become important. The specific heat of the adsorbed layer will therefore continue to exceed that of the gas by a quantity of the order of iR, until all vibrational degrees of freedom are excited and the gas again dominates. 

Here and Cp ate the specific heats of the solid adsorbent and of the fluid, respectively, and AX denotes the change of the loading X of the adsorbent. Af is the reduction of the loading in the fluid phase. Such combined fronts are existing when... 

SPECIFIC HEATS OF ALCOHOLS ADSORBED ON GRAPHITIZED CARBON BLACK. 

SPECIFIC HEAT OF N-PROPANOL ADSORBED ON GRAPHITIZED THERMAL CARBON BLACK. 

Here, Cp is the specific heat of the regeneration gas. The CO 2-desorption is subjected to the same mechanism. The excess heat, which is transported by the regeneration gas into the adsorber and which is not needed for the desorption, will only be transported to the outlet of the molsieve, after all components have been desorbed at their respective plateau temperatures. This leads to the aforesaid temperature maximum. A maximal temperature value of about 100 °C guarantees a complete desorption. 

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