Final answer:
To determine the total work produced in heating water within a piston-cylinder, one needs to use the First Law of Thermodynamics and steam tables to find specific volumes before applying the pressure-volume work relation. Lack of specific volume data in the problem prevents the determination of work.
Step-by-step explanation:
The given problem involves calculating the total work produced when a 1.5-kg water sample in a piston-cylinder device is heated from an initial state of 90°C with a quality of 5 percent to a final state of 280°C and a pressure of 900kPa. To solve this, we need to apply concepts from thermodynamics, specifically the First Law of Thermodynamics for open systems and the steam tables to determine the specific volumes at the initial and final states and then use the pressure-volume work relation for processes involving a piston-cylinder device.
The work done by a system under constant pressure is given by W = P(V2 - V1), where P is the pressure, V1 is the initial volume, and V2 is the final volume. As no initial and final volumes are given nor the method to calculate them, we cannot solve the problem from the data provided directly. Instead, the problem would typically require the use of steam tables and possibly the ideal gas law, depending on whether the water remains as a steam (gas) throughout the entire process.