Reversible process specific heat capacity

Next, a constant, irreversible thermal process with a latent heat is added to the modulation cycles, as is found on cold crystallization of PET (see Figs. 4.74 and 4.136-139). A latent heat does not change the temperatures of Fig. A. 13.1, so that the heat-flow rates need to be modified, as is shown in the upper graph of Fig. A. 13.2. The constant latent heat is indicated by the vertically shaded blocks and is chosen to compensate the effect of the underlying heating rate, so that the level of Ps is moved to zero. The reversing specific heat capacity is given by ... 

Depolymerization of superhard phase B is accompanied by the exothermal evolution of heat. During the heating of a sample of phase B up to the maximal temperature the reverse transformation into the molecular phase occured already in the first DSC cycle, and was accompanied by an exothermal peak with the maximum at 477 K (Figure 16.12) on the curve of the dependence of the specific heat capacity on temperature. The occurrence of an exothermal peak at 480 K characterizes the rupture of (3 -I- 3) bonds, the thermal effect of this process is 60 J/g. 

The specific heats have simple formulas. At constant volume, the heat absorbed equals the increase of internal energy, since no work is done. Since the heat absorbed also equals the temperature times the change of entropy, for a reversible process, and since the heat capacity at constant volume Cv is the heat absorbed per unit change of temperature at constant volume, we have the alternative formulas... 

In the fine chemicals and pharmaceutical industries, reactors are often used for diverse processes. In such a case, it is difficult to define a scenario for the design of the pressure relief system. Nevertheless, this is required by law in many countries. Thus, a specific approach must be found to solve the problem. One possibility, that is applicable for tempered systems, consists of reversing the approach. Instead of dimensioning the safety valve or bursting disk, one can choose a practicable size and calculate its relief capacity for two-phase flow with commonly-used solvents. This relief capacity will impose a maximum heat release rate for the reaction at the temperature corresponding to the relief pressure. 

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