When the heat of reaction is considered as function of C_s, the differential equation representing unsteady-state heat transfer which takes place in stationary packed beds after chemical reaction takes place, is solved by numerical calculation.
The fundamental equation is given by Eq. 15 and the numerical solution by Eq. 16, the latter being available under the boundary condition as expressed by Eq. 17.
An example of calculation is given by Figs. 4, 5, 6 and 7. An application of the solution to the decomposition of CaCO3 is described. The decomposition of CaCO₃ is performed in Apparatus 8. As shown by Figs. 14 and 15, the results of the numerical calculation coincide fairly well with the experimental data.

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In my previous paper. total reflux removal distillation as a kind of batch distillation was discussed. This paper introduces the concept of a standard separation where the average distillate composition at 80 per cent of nominal cut point corresponds to 95 mole per cent in a more volatile component. The calculation is made on the theoretical plates which are required for carrying out such a separation by the total reflux removal distillation.
Fig. 1 shows the calculated results. According to these results, the number of theoretical plates required for the standard separation is shown by the following simple equation having relation with the relative volatility, charge composition and holdup:
(7)
Eq. (7) is also applicable, together with the following Eq. (8), to the calculation of the standard separation by means of the usual batch reflux distillation having finite reflux ratio. R(α-1)=25 (8)
Assumption involved in the derivation of the above equations is as follows:
i) Mixture is binary component.
ii) Usual simplifying assumption of distillation is justified.
iii) Relative volatility is constant.
iv) Holdup on each plate is equal.

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In explaining the function of an extruder screw, that part of the instrument was divided, as usual, into 3 different sections:
a. The feed or solid-conveying section
b. The compr.ession or melting section
c. The metering section
The feed section which was placed right under the hopper picked up and conveyed the powdery or granular solid plastics to the adjoining section. It was commonly believed that the material confined in the helical channel of the screw moved "en bloc" under the frictional influence of the screw and of the walls of the barrel. Therefore, this material might as well be theoretically considered as a solid plug which filled the screw channel. On a similar basic assumption, from which W.H. Darnel and E.A.J. Mol had derived their equations, but which, in our case, was marked off by a concept of a screw channel as a modification of a confined vessel, (difference in pressure concept of the material), we, too, obtained some equations. However, our first experimental study of conveyillg of solid (plastics and standard sand) fed in a split-type extruder at room temperature showed deviations from the results obtained by means of the above theoretical equations, as some layers of materials confined in the screw channel did not move as a solid plug, and had inside sliding zones. Consequently, our empirical formulae have been rewritten as Equations (1), (18) and (14).

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Studies were conducted on the binary batch distillation at constant reflux ratio, on the assumption (for the sake of simplicity) that the holdup was negligible and molal down flow and relative volatility were constant. The results obtained may be summarized as follows:
1) Based on the same value of pole height for the sharpness of separation, the correlation between the number of theoretical plates and reflux ratio was obtained as shown in Fig. 3, where the values of (R-R')/(R+1) ranged from 0.15 to 0.50, said correlation being represented by the following equation.
2) Based on the average composition of distillate and yield of a more volatile component, for the sharpness of separation, the following equation for the minimum number of theoretical plates and minimum reflux ratio, respectively, were obtained.
where,
3) Based on the average composition of distillate and yield of a more volatile component for the sharpness of separation, the correlation between the number of theoretical plates and reflux ratio was obtained as shown in Fig. 5, where the values of (R-R')/(R+1) ranged from 0.15 to 0.50, said correlation being represented by the following equation.

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Using several kinds of materials and various types of pipe lines, pressure losses in pneumatic conveyors were measured. Figs. 1, 2 and 3 and Tables 1 and 2 show the results obtained with the aid of Eq. 1. The values of n and C were about 1 and 0.3-1.0, respectively, when the ratio m (mixture ratio) of solid to air in the mass flow was below 10.
Hold-up of solid-air flow in the pipe lines of a pneumatic conveyor was measured with the results as given in Fig. 5, and the velocity ratio of solid flow to air flow was obtained by means of a theoretical equation (Eq. 2).

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Solid-liquid equilibria of the system acetic acid-water are determined experimentally. The results are summarized in Fig. 4 and Table 1 and are compared with the data from the literature.

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