Testing thermodynamic consistency of vapor-liquid equilibrium data is commonly based on the Gibbs-Duhem equation under the condition of constant pressure and temperature. But the equation is under a hypothetical condition when it is used for a binary system at two-phase equilibrium, since it is shown by the phase rule that one cannot vary the concentration at constant temperature and pressure while keeping the phase equilibrium. Therefore some allowance must be made for the equilibrium data or for the equation.
In the first place, the thermodynamical equations, in which the values of heat of mixing were used for carrying out the exact test of the vapor-liquid equilibrium data at low pressures, were discussed as to their applications to experimental data, and then the methods of calculating the properties which were necessary for the exact test were shown.
By use of these thermodynamical relations and of the experimental data on heat of mixing, which had been reported in a previous paper, exact tests of vapor-liquid equilibrium data on the methanol-water and isopropanol-water systems were conducted and the activity coefficients, defined by Equation (3), of these two systems were calculated at various temperatures
The isobaric data at atmospheric pressure by Uchida-Kato on methanol-water, and by Wilson-Simons on isopropanol-water were utilized as the basic data for calculating the activity coefficients at various temperatures, as shown in Tables 1 and 2, and in Figures 5 and 13, because these data are thermodynamically self-consistent.
Isobaric and isothermal data available on methanol-water system at reduced pressures were tested of their validity by comparing the values of activity coefficient calculated from the data with the values given in Table 1. Othmer's isobaric data at 500, 350 and 200mm Hg, shown in Figures 6 and 7, appear to be reliable although these data show some inconsistencies in the area test. Similar comparisons on the isothermal data below the normal boiling point are shown in Figures8, 9, 10 and 11.
For the isopropanol-water system, the same comparisons as in the case of methanol-water system were performed on the isobaric data of Wilson-Simons at 95, 190, 380 and 3087mmHg, and good agreements were obtained between the values of activity coefficient calculated from these data and values in Table 2, proving that Wilson's data are fully reliable.
Using Tables 1, 2, and Figure 1, along with the vapor pressure data from the literature, one can calculate isothermal or isobaric x-y values for these systems at low pressures.

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Analytical studies were attempted to make clear the flow patterns of the liquid in the cylindrical mixing vessel without baffles, as the experimental results had already been obtained as shown in the previous reports.
We could not well explain the details of the liquid flow patterns in the vessel by means of the so-called “Rankine's combined vortex” model (Refer to Fig. 1 and Eq.(1)). Therefore, we studied three important factors contributing to the momentum transfer in the agitated liquid; i.e., the liquid viscosity, the displacement of the liquid by the agitating impeller and the secondary circulation flow which is induced by the discharge flow from the tips of the impeller blades.
In the range where Reynolds number was very small, the momentum transfer due to the viscosity effect was found to be predominant, so that the analytical results, obtained upon the assumption that the effects of the two factors other than the liquid viscosity are negligible, had a tendency to show good agreement with the experimental data on the tangential velocity distribution of the liquid in the vessel, as shown in Figs. 4 and 5.
On the other hand, in the turbulent flow range where Reynolds number was very large, the secondary circulation flow had considerably important effects on the liquid flow pattern. Considering its contribution to the momentum transfer (Refer to Fig. 6), Eqs.(10) and (13) were analytically derived to express the tangential velocity distribution of the agitated liquid. The comparisons between the experimental data and the calculated results by these equations are shown in Fig. 8. They show good agreement.
Furthermore, there were obtained data on the distributions of the turbulent kinematic viscosity and the static pressure in the vessel, as shown in Figs. 9 and 10, respectively.
These results are considered to show the utility of the analysis.

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Energy balance and energy consumption in an agitating system, consisting of cylindrical mixing vessel and an impeller, are analyzed in this report, as the flow patterns of agitated liquid were made clear in the previous studies.
In the first place, based upon the results of the calculation of the energy balance on the cylindrical boundary surface, where the impeller is placed as shown in Fig. 1, it is made clear that the agitating energy loss is greatest in the liquid near the impeller (refer to Table 1).
Then, the mechanisms of the energy consumption in the agitated liquid are examined.
According to the analytical consideration, the energy consumption in the liquid inside the impeller is caused mainly by the head loss due to abrupt change in the liquid velocity and that outside the impeller, by the energy dissipation due to the turbulent viscosity, under non-baffled condition. However, under fully-baffled condition, the head loss due to the abrupt change in the liquid velocity prevails everywhere in the agitated liquid (refer to Table 2).
Furthermore, the general considerations are made on the energy consumption in a simplified model, which shows the flow patterns in the vessel as the combination of so-called compound vortex flow and vertical circulation flow, as given in Fig. 5.
In short, it is emphasized in this report that both the liquid-circulating capacity and the turbulencegenerating ability of an impeller are important factors in the performance of an agitator.

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From the operation data on fludized gasification furnaces, in which pulverized brown coal was gasified by using steam and air as fludizing agents, the effects of operating conditions on the gasification and the activation were derived as follows.
1) The reactivity of materials used, the average holding time and the average concentration (C_d) of particles within the furnace, the reaction temperature, the pressure drop, steam-coal ratio and the feed rate, etc. are important factors.
2) There are the optimum feed rates according to the scales of furnaces. The optimum conditions for the gasification and for the activation are approximately the same. The activation is remarkably accelerated when C_d<ca. 3%.
Based on the analytical data on cyclone dusts produced in continuous operations, their characteristics were discussed as follows.
3) When dusts are sifted into three groups (x, y, and z), usually certain relations are observed to exist among the ash contents, the activities and the sifting yields of these groups.
4) In proportion to the reduction of particle size, the ash content increases and the activity decreases gradually. In each particle, the activity is found to be highest on the surface and lowest at the core, so that it is possible to prepare higher active carbon by collecting more activated parts ground away from the surface of these particles.
5) On the basis of such experimental data, industrial plant was built, and the mechanisms of the activation were studied.

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