Concept:
Physics - Thermodynamics Processes.
Step 1: Analyze the terminology.
The word "Isothermal" is derived from two Greek words: 'iso' meaning equal/same and 'therme' meaning heat/temperature.
Step 2: Define the process.
An isothermal process is a thermodynamic process in which the temperature of the system remains constant ($\Delta T = 0$) throughout the change.
Step 3: Relate to Ideal Gas Laws.
For an ideal gas undergoing an isothermal process, Boyle's Law applies:
$$ PV = \text{constant} $$
Since internal energy ($U$) of an ideal gas depends only on temperature, $\Delta U = 0$ in an isothermal process.
Step 4: Conclusion.
The quantity that remains constant by definition is Temperature.