When we derive the Navier-Stokes Equation, we come across a a common assumption made by Stokes that makes the two quantities namely Mechanical pressure and Thermodynamic pressure equal to each other.
It is claimed that Thermodynamic pressure represents the energy over all the degrees of freedom of the molecules while the Mechanical pressure is related to only translational degrees of freedom. When a system is subjected to abrupt change in the properties, the molecules don't get enough time to adjust to that changes that is they don't have enough time to convert all its energy from all the degrees of freedom into translational ones.
J. Chem. Phys. 39, 654 (1963); https://doi.org/10.1063/1.1734304 39, 654
© 1963 American Institute of Physics.
Formal Kinetic Theory of Transport Phenomena in Polyatomic Gas Mixtures Cite as: J. Chem. Phys. 39, 654 (1963); https://doi.org/10.1063/1.1734304 Submitted: 05 April 1963 .
Published Online: 29 June 2004 L. Monchick, K. S. Yun, and E. A. Mason
It has long been known, from a phenomenological point of view, that the volume viscosity is proportional to a relaxation time, T, which is a measure of the rate of transfer of molecular energy between internal and translational degrees of freedom.
In this citation the author speaks about the relation of bulk viscosity with Relaxation time for the molecules. This clearly hints that mechanical pressure is a result of only translational degrees of freedom. As when the bulk viscosity cancels only then the thermodynamic pressure equals mechanical pressure like in the case of monoatomic ideal gas that exhibits only translational degrees of freedom.
My question here is how mechanical pressure is related to translational degrees of freedom? Any insights from Kinetic Theory of gases or statistical mechanics would be appreciated.