Proving Global Optima Condition in Temperature Model for Inhibiting Zero-Order Reactions
Januardi*, Aditya Sukma Nugraha**

*Department of Agroindustrial Technology, Universitas Padjadjaran
**Research Center for Smart Mechatronics, National Research and Innovation Agency (BRIN)

Abstract

This article builds a temperature optimization model from Arrhenius Equation, as the relationship of temperature with the reaction rates, and heat capacity. The Arrhenius and heat capacity model establish a heat accumulation model to estimate the total heat for a specific time given any temperature change. From the first-order derivative, this article finds the optimal temperature setting to decelerate zero-order reactions. From the second-order derivative, the optimal temperature must be set lower than the environment temperature to make the model has concavity form. A successive linear programming as the exact method in nonlinear programming is utilized to prove the global optima condition of the analytical solution. This study lays a foundation of analytical modelling and solutions to inhibit specific reaction. Later on, the basic model can be applied by food and pharmaceutical scientist and engineer to keep the product nutrition in specific time.

Keywords: Arrhenius Equation- Derivative Solution- Zero-order reactions

Topic: Minisymposia Differential Equations