Calculating macroscopic gas molar heat capacity of SO molecule based on rovibrational energy level

Abstract

<sec>Sulfur oxide (SO) is a kind of well-known diatomic molecule which becomes one of the major pollutants in the atmosphere. Control of the heat capacity of SO molecule is of great significance for elucidating its macroscopic evolution process. In the research of macroscopic systems composed of many particles as well as several matters, it is an important approach to obtain macroscopic thermodynamic quantities of the system by constructing a partition function from the microscopic information of molecule. For diatomic molecules in a certain electronic state, the partition function can directly be obtained by calculating the rovibrational energy of the system to acquire the macroscopic molar heat capacities.</sec><sec>In this work, the contribution of rotational behavior to molar heat capacity is further considered. The potential energy function for the ground electronic state of SO is constructed by the variational algebraic method (VAM) and RKR (Rydberg-Klein-Rees) method, in which the former one can determine the complete vibrational energy levels of an electronic state of a molecule. The rovibrational energy level of the system is obtained by analytical solution, and then the molar heat capacity of SO macroscopic gas in the temperature range of 300–6000 K is calculated by quantum statistical ensemble theory The above calculation depends only on the experimental vibrational energy, experimental rotational spectral constant and the dissociation energy of SO molecule. Fortunately, through comparison between theoretical calculation results and experimental data, we find that the molar heat capacity of gaseous SO molecule can be well predicted by employing the full set of rovibrational energy to describe the internal vibration and rotation of SO molecule. The idea of calculating the molar heat capacity by using the full set of rovibrational energy makes up for the shortcomings of previous work where molar heat capacity is calculated by using the approximate model characterizing the molecular rotational behavior, and also provides a new research paradigm for solving macro thermodynamic quantities based on micro statistical processes .</sec>