  In this work, we will introduce a general framework to derive the
thermodynamics of a fluid mechanical system, which guarantees the consistence
between the energetic variational approaches with the laws of thermodynamics.
In particular, we will focus on the coupling between the thermal and mechanical
forces. We follow the framework for a classical gas with ideal gas equilibrium
and present the existences of weak solutions to this thermodynamic system
coupled with the Brinkman-type equation to govern the velocity field.
