Reduced form of the Semenov equation

For the derivation of the reduced form of the Semenov equation, refer to Subsection 5.3.2, The plot of In d t versus 1 /f, made in accordance with Eq. (44) is a sort of the so-called Arrhenius plot. 

It is possible to calculate the for an arbitrary volume of a liquid charged in an arbitrary container and placed in the atmosphere imder isothermal conditions by applying the reduced form of the Semenov equation. ... 

It is also of course possible to calculate the A for an arbitrary volume of a liquid confined in an arbitrary closed container and placed in the atmosphere under isothermal conditions by applying the reduced form of the Semenov equation. It is, however, required in such a case to obtain both the heat generation data and the heat transfer data of the liquid under confined conditions. In this connection, the adiabatic self-heating tests were performed, in the present chapter, at atmospheric pressure for nine organic liquid peroxides, other than DTBP, respectively, because these nine peroxides are not very volatile or do not decompose to evolve corrosive and/or toxic gases while tested, respectively. 

In any event, the Tc for an arbitrary volume of a liquid charged in an arbitrary container and placed in the atmosphere under isothermal conditions is calculated by substituting the five heat transfer data above referred to and the heat generation data, a and b, as well as the base of natural logarithm, e, and the definite value of AT of 1.25 K, into Eq. (72), i.e., the reduced form of the Semenov equation. 

For the above reasons, as will be explained in detail in Section 2.4, it is presupposed herein that it is valid to substitute the two coefficients, a and b, of Eq. (44) into the F-K equation as well as the Semenov equation, in order to reduce them to the simpler forms, respectively. 

It, however, becomes very easy to calculate the if both the Semenov and the F-K equation are reduced to the simpler forms by substituting the two coefficients, a and b, of an empirical formula, nAt = atT + b, i.e., Eq. (44), which is derived in Section 2.4, into each equation, respectively. 

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