Approximation Formula for Calculating the Heat Capacity of Liquid Lead from the Melting Point to the Boiling Point

Abstract—An analysis of the relationships for calculating the thermal properties of liquid lead (hereinafter referred to as lead) was carried out, and the method for determining its heat capacity over a wide range of temperatures, including at high values, was chosen. This is especially important for numerical studies to justify the safety of designed reactor installations with liquid metal coolants, such as BREST-OD-300 and BR-1200. Measuring the properties of lead at temperatures close to the boiling point is often difficult due to the lack of reliable methods and materials that can withstand temperatures above 2273 K. At present, theoretical approaches to calculating the properties of simple liquids based on phonon theory are being actively developed. Such approaches can be used to derive semiempirical relations for the heat capacity of liquid lead that would allow physically correct extrapolation of the data to the high-temperature region. In this regard, the aim of this work is to obtain a relationship for calculating the heat capacity of liquid lead from its melting point to its boiling point based on modern theoretical approaches. To achieve the set goal, the following tasks were solved. Firstly, an analysis of the works of various authors was carried out and empirical formulas were selected that make it possible to reliably calculate the heat capacity at a constant volume cv (isochoric heat capacity) for a lead coolant from the melting point to 1500 K. Secondly, based on them, using phonon theory, an approximating formula was constructed, thanks to which it is possible to physically correctly extrapolate the properties of lead to the boiling point (2022 K).