I am not sure about what you are asking for, but if you consider the ideal gas law p=rho*R*T, it is valid ad any time scale. Therefore, you have also density involved.

@ Zwan

Thank you for your kind reply. If I understood correctly, then in case of equilibrium, change in temperature in expansion or compression will occur for the same change in pressure. However, if we are dealing or trying to capture non-equilibrium, then it may happen that  we can observe change in temperature due to compression for lower (or higher) value of pressure change.

To put in some quantification, say dP  is change in pressure and corresponding change in temperature is dT. So in case of equilibrium , whether it is +dP (compression) or -dP (expansion) , there be change in temperature dT for both these values. However, in case of non-equilibrium it may happen that to cause dT change in temperature in compression the corresponding change in pressure be dP1 and in expansion dP2 ( where dP1 may be greater or less than dP2).

Thanks

I am talking in terms of theoretical framework (numerical to be precise). The system is near critical SF6.

May you please elaborate little on what you mean by "a clue from the speed of sound in your medium, and its attenuation". Do you mean to see if my acoustic time scale is smaller than sampling time of instrument ( or for numerical studies, smaller than simulation time).

I understand that if relaxation time (time to attain equilibrium between mechanical and thermal states.) may be larger than time scale under consideration, it may be feasible to capture non-equilibrium. But how do I calculate or get information abut relaxation time. 

Thanks

Hello

Thanks for kind help. But just to be sure I understood correctly, by relaxation time you mean the time to attain equilibrium state, right? 

Hello to all,

                  Though the ideal gas equation may not be true in many cases, from that one can infer something. That when Volume kept constant, pressure is directly proportional to pressure. So in order to create low pressure/temperature we need to decrease either one of them.

If I understand the problem, the key is that time and lenght scales of variation are so small to go at the limit of the contunuum hypothesis? Therefore, no ideal gas law (as well as PDE for the transported variable) can be stated ...

Thanks for the answer... I am aware of cases where high temperature (for example hypersonic flows) drive to dissociation, ionization and general non-equilibrium.

I am not expert in measurement so I wonder what about the required frequency response of an experimental device to be able in measure that ...

@Zwan

In respect to your answer " It is equilibration time vs measurement time that is relevant here", if I talk in terms of typical Navier Stokes equation, then do you mean that there does not exist equilibrium between thermodynamic and mechanical pressure ? ( in other words stokes hypothesis is not valid)