Pommersheim and Chandra (1975) present analytical solutions for the general problem of the optimal policy of batch reactor operation (and tubular reactor operation when catalyst with no slip moves with the reaction fluid) for catalyst decay rates which depend on temperature, activity and concentration.The optimal temperature and corresponding concentration and activity formulas which they present are valid whenever the Legendre-Clebsch (L-C) condition is obeyed. They list three other criteria which they claim are equiualent to the criterion employed by Szepe and Levenspiel (1968) for the case of concentration independent decay. This is criterion (i) ofTable 1, which requires minimizing the final concentration (CAf), or maximizing the final conversion, for fixed run times (t,) and desired final activities (uf).The entire problem is shown in Table 1 with all four criteria stated. Solutions for the optimal policy can be shown to be identical for all four criteria. But for the optimal policy equations to be valid, the appropriate L-C conditions must be shown not to be violated. The L-C conditions may be different for these criteria, as they are derived employing the transversality conditions. The purpose of this note is to elucidate these restrictions on optimal temperature policies for the problem discussed by Pommersheim and Chandra and by example to further define the ranges of applicability of their solution. NTH ORDER SINGLE IRREVERSIBLE REACTIONThe reaction and activity rate functions considered are rA = KA am CAn respectively, can be shown to the independent of the nature of the criteria which specifies the Legendre-Clebsch condition. In order that Equation (2)-(4) specify optimal profiles, the L-C Functions* C.4 (t), 4 t h Y(t)Constraints 6 = C.4 + r.4 (C.!, a, Y) = 0 6 2 = a' + 6 (C,, a, y) = 0 End Conditions and Objectitje FunctionsCriterion (i) Criterion (ii) Criterion (iii) Criterion (iv)