Final answer:
The entropy change of the water when heated gradually from 0°C to 80°C in steps is positive, as the water absorbs heat and its disorder increases.
Step-by-step explanation:
When two hundred grams of water at 0°C is brought into contact and brought to thermal equilibrium successively with reservoirs at 20°C, 40°C, 60°C, and 80°C, the entropy change of the water will be positive. This is because entropy, a measure of disorder or randomness in a system, tends to increase when a system absorbs heat. As the water is gradually heated by each reservoir, it absorbs energy and its temperature rises, resulting in an increase in entropy.