Step 1: Understanding the Question:
An isothermal process is one of the four basic thermodynamic processes. The question asks to identify the identifying physical characteristic that remains fixed throughout this specific change.
Step 2: Detailed Explanation:
The word "isothermal" comes from the Greek words "isos" meaning same and "therme" meaning heat/temperature. Thus, by definition, an isothermal process is a thermodynamic change of state that takes place at a constant temperature.
During such a process, any heat (\(Q\)) added to the system is used solely to do work (\(W\)) on the surroundings, or work done on the system is released as heat, to ensure that the internal temperature remains absolutely steady (\(dT = 0\)).
For an ideal gas, internal energy (\(U\)) depends only on temperature (\(U \propto T\)). Since \(T\) is constant in an isothermal process, the change in internal energy (\(\Delta U\)) is zero. This contradicts Option A.
In an isothermal process, the pressure and volume change according to Boyle's Law: \(PV = \text{constant}\). Therefore, volume does NOT remain constant, which contradicts Option C.
Heat energy is exchanged with the environment to maintain the temperature, so the total heat energy within the system does not necessarily stay constant, contradicting Option B.
To achieve an isothermal process, the system must be in thermal contact with a large heat reservoir and the process must be carried out extremely slowly (quasi-statically).
Step 3: Final Answer:
The fundamental property of an isothermal process is that the temperature of the system remains constant throughout.