Heating water at constant volume and pressure

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The discussion revolves around a rigid tank containing saturated water at 200°C and a quality of 0.4, which is heated until all liquid vaporizes. Jared has calculated the total molar volume and mass using the quality and steam tables but is uncertain about the next steps. He questions whether the heat transfer (Q) equals the change in internal energy (U) and how to account for the energy leaving with the vapor. The key challenge is determining the heat required to achieve complete vaporization while maintaining constant pressure. Understanding these thermodynamic principles is essential for solving the problem accurately.
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A rigid tank has a volume of 0.01m3. It initially contains saturated water at a temperature of 200°C and a quality of 0.4. The top of the tank contains a pressure-regulating valve that maintains the vapor at constant pressure. This system undergoes a process whereby it is heated until all the liquid vaporizes. How much head (in kJ) is required? You may assume that there is no pressure drop in the exit line.
 
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Please could you provide your attempt at the solution.

Jared
 
So far I have used the quality given, and the steam tables to calculate the total molar volume and total mass of the water:

Vm=(1-x)Vml+xVmv
m=V/Vm

I am assuming that the temperature of the system won't change because vapor will continue to leave as more vapor is created. I'm not sure where to go from here. Does Q=change in U? How do I keep track of the energy that is leaving with the vapor?
 
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