Question

If a closed system has adiabatic boundaries, then at least one boundary must be

• A. Permeable
• B. Imaginary
• C. Movable
• D. Fixed

Answer 1

Answer: (C)

Movable

Answer 2

A closed system is defined as one that can exchange energy (heat and work) but not matter with its surroundings. Adiabatic boundaries are boundaries that do not allow heat transfer (Q=0). Therefore, a closed system with adiabatic boundaries is a system that cannot exchange matter and cannot exchange heat with its surroundings. According to the first law of thermodynamics, for such a system, the change in internal energy ($\Delta U$) is equal to the work done (W), since Q=0 ($\Delta U = W$).

For work (W) to be done on or by the system (e.g., expansion or compression work), there must be a change in the system's volume. A change in volume necessitates that at least one boundary of the system is movable. If all boundaries were fixed, no volume change could occur, and thus no PV work could be done. While a closed adiabatic system with fixed boundaries (like an adiabatic rigid container) is a valid thermodynamic system where W=0, the general definition of a closed system with adiabatic boundaries allows for the possibility of work exchange. For this possibility to exist, at least one boundary must be movable.