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Question
0.5 kg of water initially at 400 kPa and 0.3 m3/kg is contained within a piston-cylinder device fitted with retractable stops (initially retracted) so that the water supports the weight of the piston and the force of the atmosphere (state 1). The water is heated until it reaches the saturated vapor state (state 2). The stops are then engaged with the piston against the stops, and the water is further heated until the pressure reaches 600 kPa (state3).
a) Determine the phase and temperature of each state
b) What is the volume capacity of the cylinder with stops engaged?
c) Sketch the process on a P-v and T-v diagram, labeling the states and drawing a line from state 1 to 2 to 3 to represent the process. For the T-v diagram, label the axes with the T and v values of each state. For the P-v diagram, label the axes with the P and v values of each state. Include the saturation dome (saturation lines) in your sketch.
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To solve this problem, we need to use the principles of thermodynamics and the properties of water.

a) To determine the phase and temperature of each state, we need to refer to the water phase diagram. The given initial state of the water is 0.5 kg at 400 kPa and 0.3 m3/kg. From the phase diagram, we can see that at this pressure and specific volume, the water is in the liquid phase. Therefore, state 1 is a saturated liquid. To find the temperature, we can use the saturation temperature corresponding to the given pressure.

b) The volume capacity of the cylinder can be determined by finding the specific volume at state 3, where the pressure is 600 kPa. From the phase diagram, we can observe that this pressure corresponds to the saturated vapor phase. We can use the saturated specific volume to find the volume capacity of the cylinder.

c) To sketch the process on a P-v and T-v diagram, we need to label the states and draw a line from state 1 to 2 to 3 to represent the process. On the T-v diagram, we label the axes with the T and v values of each state. On the P-v diagram, we label the axes with the P and v values of each state. Additionally, we include the saturation dome (saturation lines) to indicate the phase boundaries of water.

To find the specific values for each state and the sketch, we need the specific temperature and specific volume values from the water tables or properties of water tables. These tables provide the properties of water at different pressures and temperatures, including the enthalpy, entropy, specific volume, etc. With these values, we can solve the problem and create the required diagram.

Since this problem contains specific data such as pressure, volume, and the process of heating water, it is recommended to refer to the appropriate thermodynamic tables or equations to obtain accurate solutions. These tables are often found in textbooks or online resources specifically meant for thermodynamics or fluid mechanics courses.