# Why is the volume of an isolated system conserved? [closed]

Consider a system(S) + reservoir(R) that surrounds the system(S). The system(S) is not in thermodynamic equilibrium but the combined system (system + reservoir or say SR) is isolated i.e. the walls of the reservoir(R) are made impermeable for all forms of matter, energy, force exchange with the outside world. The system (S) is allowed to interact with the reservoir(R) by exchanging particles, energy etc.. If we use first and 2nd law of thermodynamics to show that the Gibbs free energy of the system(S) always decreases (and becomes minimum when it reaches equilibrium), there is an assumption that the internal energy and volume of the combined system (SR) do not change with time. I have the following questions:

1. I do not understand why the volume of the combined system (SR) remains constant with time ? Is this coming from conservation of mass ? I do understand that the boundaries of the combined system (SR) can not change as such a change requires external work on the boundaries of the combined system (SR) which is prohibited by the definition of isolated system.
2. Assume that there is an internal process that leads to discontinuities (for ex. voids, holes, cracks etc.) within the system(S)/reservoir(R) and therefore changes the volume (= original volume of combined system - volume of discontinuity) of the combined system. In such a case, the volume of SR is not constant. However, this situation leads to creation of additional internal boundaries. Is this even a possible scenario or is it contradicting some of the assumptions ? Creation of internal boundaries appears to contradict some of the assumptions.

It would be great if some one can throw light on these questions perhaps with the help of equations with clear assumptions.

• Your description "system + reservoir" is too vague please elaborate. Apr 10 at 21:06
• The system is open and it is allowed to exchange particles, energy with the reservoir and its volume is allowed to change. Can you please ask a more specific question if my answer is not sufficient ? Thanks Apr 10 at 21:11
• What do you mean by the "combined" system? Exactly what does the system consist of? You stated to trula that the system is "open". A system cannot be open and isolated at the same time. Your post lacks sufficient detail to understand your question no less than answer it. Apr 10 at 21:17
• Suppose that the combined system is bounded by a rigid insulated room. Apr 10 at 21:20
• If your system’s volume isn’t constant, don’t make that assumption. But then your system needs to be surrounded by a vacuum, or work done on or by the surroundings violates the premise of isolation. Does this get at what you’re asking about? Apr 10 at 23:08