Final answer:
The entropy change of water during a free expansion from 400 kPa and 60°C into a vacuum can be calculated using the mass of water, the specific entropy values from the steam tables at the initial and final states, and the second law of thermodynamics.
Step-by-step explanation:
When considering the entropy change of water during a free expansion process, one must take into account that the process is irreversible. In the scenario where water initially at 60°C and 400 kPa expands into a vacuum once a partition is removed, the entropy will inevitably increase due to the spontaneous nature of this expansion. Without the exact volume of the tank and the specific properties of water at the final stage, an accurate calculation cannot be provided. However, generally, the entropy increase can be found using steam tables and applying the second law of thermodynamics to calculate the change in entropy (ΔS) through ΔS = m(s_2 - s_1), where s_1 and s_2 are the initial and final specific entropy values of the water respectively, and m is the mass of the water. Since the final pressure is 40 kPa, one would look up the specific entropy of the final saturated vapor state at this pressure in the steam tables to find s_2. The initial specific entropy, s_1, corresponds to the compressed liquid state at 400 kPa and 60°C.