  Polyatomic gases find numerous applications across various scientific and
technological fields, necessitating a quantitative understanding of their
behavior in non-equilibrium conditions. In this study, we investigate the
behavior of rarefied polyatomic gases, particularly focusing on heat transfer
and sound propagation phenomena. By utilizing a two-temperature model, we
establish constitutive equations for internal and translational heat fluxes
based on the second law of thermodynamics. A novel reduced two-temperature
model is proposed, which accurately describes the system's behavior while
reducing computational complexity. Additionally, we develop phenomenological
boundary conditions adhering to the second law, enabling the simulation of
gas-surface interactions. The phenomenological coefficients in the constitutive
equations and boundary conditions are determined by comparison with relevant
literature. Our computational analysis includes conductive heat transfer
between parallel plates, examination of sound wave behavior, and exploration of
spontaneous Rayleigh-Brillouin scattering. The results provide valuable
insights into the dynamics of polyatomic gases, contributing to various
technological applications involving heat transfer and sound propagation.
