No, an "adiabatic process in a closed system" is not the same as an "isolated system." Let's clarify the definitions of these terms:
Adiabatic Process: An adiabatic process refers to a thermodynamic process in which no heat is exchanged between the system and its surroundings. In other words, during an adiabatic process, there is no transfer of thermal energy in or out of the system. However, work can still be done on or by the system, and internal energy can change. Adiabatic processes can occur in systems that are not isolated.
Closed System: A closed system is a thermodynamic system that can exchange energy (in the form of work) with its surroundings, but not matter. In a closed system, there can be both heat transfer and work done across its boundaries, but the total mass of the system remains constant. The exchange of energy can occur through heat transfer and work, but there is no exchange of matter.
Isolated System: An isolated system is a thermodynamic system that does not exchange energy or matter with its surroundings. It is completely sealed off from its environment. In an isolated system, neither heat nor work can be exchanged across its boundaries.
In summary, while an adiabatic process can occur in a closed system, it does not imply that the system is isolated. A closed system allows for energy exchange (both heat and work) with its surroundings, whereas an isolated system is completely sealed off from any exchange of energy or matter.