Entropy State Variable: Thermal Equilibrium Questions

[TomWhite87]

I have a few questions about entropy and path
Scenario
I have a closed system of Ideal Gas- Volume is Fixed , Mol Vol is fixed.
At room temperature the system is in thermal equilibrium with its surroundings
I then cool this system removing Q .
To this system I then re-add Q until it is again in thermal equilibrium at room temperature.
At all points of this process within this system, all subsets of the gas have an equal distribution of energy and mass

In this process have I increased the entropy of the System since the end state is equal to the beginning
and
Is the system in equilibrium as energy and mass cannot be dispersed further ?
Is how I added the energy to the system (the path) ever relevant ?

 

[DrClaude]

In this process have I increased the entropy of the System since the end state is equal to the beginning

I guess you mean you have not increased the entropy of the system.

Is the system in equilibrium as energy and mass cannot be dispersed further ?

What equilibrium are you talking about? If you are talking about internal equilibrium, you have stated that it is maintained by construction.

Is how I added the energy to the system (the path) ever relevant ?

With respect to the system, I would say no. Since the volume is fixed, there is no work involved, hence only an exchange of energy. If you consider the system plus the environment, then yes, the way you remove the energy and put it back in will be relevant.

 

[Chestermiller]

Is how I added the energy to the system (the path) ever relevant ?

To expand on what Dr. Claude said, as far as the system is concerned, the entropy is an equilibrium physical property of the material comprising the system, so between an initial thermodynamic equilibrium state and a final thermodynamic equilibrium state, the change in its entropy is independent of the path at took it between the two thermodynamic equilibrium states.

Chet