Evaluation of a dimensionless group number to determine second-einstein temperatures in a heat capacity model for all coal ranks

A dimensionless group number is proposed to characterize the differences in chemical structures and physical properties between coal-like materials varying from lignites to anthracites, including graphite as a limiting case. This dimensionless number provides a simple and efficient correlation to determine second-Einstein temperatures (θ2) in a specific heat capacity (C) model for all coal ranks, using information derived directly from the chemical composition (proximate and ultimate analyses) and the calorifie value (H) of each substance. The nondimensional correlation has the form Rθ2/H = ƒ(FC), where R is the gas constant for the heterogeneous material and FC is the amount of fixed carbon in the parent coal. Properties of 50 coal-like materials were used to obtain this functional dependence. It was found that a linear function provides a good fit of the experimental data. This dimensionless correlation allows calculations of the behavior of the specific heat capacities of the materials studied here with an average value of 3.55% for the mean deviation in relation to experimental curves in the important temperature range of 300–600 K. The applicability of Einstein theory of heat capacity is analyzed for the special case of coal-like materials, and a generalization of Merrickʹs model for all coals of industrial interest is presented.