The quantification of entropy for multicomponent systems: Application to microwave-assisted comminution

Abstract The second law of thermodynamics, through exergy analysis, is commonly applied to quantify process inefficiencies in metallurgical reactors, however, it has not yet been used to understand physical processes and changes in particle-based systems. Correlating the state of mixing of particle texture and homogeneous liquid mixtures is of importance. This paper applies the exergy analysis and excess entropy method to two sets of experiments highlighting the differential breakage as microwave pre-treatment is applied to a gold-copper ore. Grinding kinetic properties were measured following the top-size fraction method and calculated using the population balance model. The approach combines the mixing entropy on the system level (streams) and the entropy for multicomponent particle systems, using automated mineralogy data to quantify the effects of intergrowth and improvements in grinding performance. This is a first step towards understanding mineral processing not only in terms of energy conservation (first law of thermodynamics) but also in terms of the quality of energy available at multicomponent systems (second law of thermodynamics). When applied to comminution processes, this methodology enables us to understand the change in particle composition (its degree of liberation) as well as changes in particle size, being an important measure of process efficiency and selectivity.