Final answer:
The process undergone by water when it cools from a saturated vapor to a saturated liquid at constant temperature is an isothermal process, characterized by constant temperature and heat transfer.
Step-by-step explanation:
The process the water in the piston cylinder assembly is undergoing is known as an isothermal process. During this process, the water is cooled from a saturated vapor to a saturated liquid at constant temperature, which is a characteristic behavior of isothermal processes. This implies that the temperature remains the same throughout the process, while the phase change suggests there is heat transfer occurring.
An illustration of an isothermal process can be visualized with a piston cylinder where the piston is in equilibrium with an external pressure, facilitated by weights. When weights are added or removed and the motion of the piston is slow enough, the system can stay at a constant temperature, denoting a quasi-static process. It's important to note that this process is different from an isobaric process, where pressure remains constant but temperature can change, and an adiabatic process, where no heat is transferred in or out of the system, usually resulting in a change in temperature.