ANALYSIS OF EXAMPLES OF APPLYING DIFFERENTIAL EQUATIONS IN CHEMICAL AND FOOD TECHNOLOGIES

Abstract

The article deals with applying mathematics in chemistry and chemistry-technology. Specifically, differential equations are extensively used in various fields of science and technology. That is why the theory of differential equations, as a separate topic in the course of higher mathematics, is of major importance in educational system of future mechanics, physicists, electrical engineers, chemists, mechanical engineers etc. A possibility of using differential equations in solving various chemical problems is demonstrated. Some chemical technology problems are exemplified whose general solution is reduced to separating variables equations, first-order linear differential equations, second-order linear homogeneous differential equations. It is noteworthy that in solving chemical technology problems we deal with all of these types of differential equations. First-order homogeneous differential equations are applied in solving the following problems: chemical compounds chlorination; chemical agent consumption with maximum end product yield in complex reactions. Second-order non-homogeneous differential equations with constant coefficients are used in solving problems of a system of reverse reactions running at constant volume; continuous hydrolysis of solid fat in a spray column. Second-order differential equations which allow reduction of order are utilized for problems such as liquid movement in capillaries. Second-order linear non-homogeneous differential equations with constant coefficients are applied to solve various problems, e.g. to find a law of motion of a particle that falls as a precipitate in a liquid having no initial velocity.