Partial differential equations characteristics with reaction

In this simple problem not all these equations are needed. Dividing the first by the second gives dcf/dd = —R cf) which is simply the defining Eq. (7.1.1) with the optimal policy T = Tn in use. This is important for it shows that the characteristics of the partial differential equation (3) are actual trajectories or reaction paths. The principle of optimality thus shows that the optimal temperature policy for any reaction is just the temperature specified in the integration of (6) along the characteristic. Separating variables we have... 

A differential characteristic which demands a lower degree of standardization is the reaction rate. The rate of a chemical reaction with respect to compound B at a given point is defined as the rate of formation of B in moles per unit time per unit volume. It cannot be measured directly and is determined from the rates of change of some observable quantities such as the amount of substance, concentration, partial pressure, which are subject to measurements. Reaction rates are obtained from observable quantities by use of the conservation equations resulting from the mass balance for the given reactor type. 

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