Final answer:
A process can have the same initial and final temperatures and still not be isothermal, such as a non-quasi-static or cyclic process involving adiabatic and isobaric stages that return the system to its original temperature.
Step-by-step explanation:
Yes, it is possible for a process to have the same initial and final temperatures yet not be isothermal. An isothermal process is one where temperature remains constant throughout the process, which is typically achieved by slow quasi-static changes, ensuring thermal equilibrium with the environment or a heat bath. However, there are processes where the temperature may change during the process but returns to the initial value at the end.
Examples include various non-quasi-static processes where rapid changes prevent the system from staying in thermal equilibrium, or a cyclic process where the system undergoes multiple stages, including both heating and cooling, which eventually brings it back to the original temperature.
An adiabatic process followed by isobaric and then another adiabatic back to the initial temperature is an example of this. It is not isothermal because during the adiabatic stages there is no heat exchange with the environment, so the temperature changes.