Empirical formula for specific heat of solids based on atomic constants and a universal subzero limiting temperature

¹ I-SERVE, Survey no-42, Hitech city, Hyderabad-84, Telangana, India
² Quality Assurance Dept, Casting, DIP Division, Electrosteel Castings Ltd, Srikalahasthi, AP, India
³ Dept. of Nuclear Physics, Andhra University, Visakhapatnam-03, AP, India
⁴ Dept. of Physics, Aditya Institute of Technology and Management, Tekkali- 532201, AP, India

^* Corresponding author: seshavatharam.uvs@gmail.com

Published online: 7 January 2026

Abstract

We present a novel empirical approach to understand the specific heat capacities of solids by introducing a characteristic subzero reference temperature derived from fundamental atomic constants. Using the total energy of the electron associated with the Bohr radius and the proton- electron mass ratio, we define a universal lower temperature limit as 3.87862×10⁻¹⁴ K. Based on this temperature and a room temperature of 300 K, we propose a simple empirical relation for specific heat capacity expressed in terms of atomic mass number A: C = 25416.852/A J/kg.K. The formula accurately predicts experimental specific heat capacities across various elemental solids, providing a fundamental link between atomic-scale constants and macroscopic thermodynamic behaviour. Considering ‘grams to kilograms’ and ‘moles to kilomoles’ and with reference to Dulong-Petit law, it can be expressed as, C = [3 x 1000 x R]/A. It needs further study.