17 Due 4/3

1. Two kg of hot saturated water vapor is in a cylinder closed by a weighted piston that pressurizes it to 200 kPa. Since the surroundings are at 20$\POW9,{\circ}$C, the hot water cools down until the volume becomes half the original one.
   1. Construct the final phase of the water in the $Pv$ diagram. In the diagram, list no more than is needed to construct the phase, but do list the values of the curves/points used.
   2. Find the work done by the water.
   3. Find the heat that has leaked out of the water.
   4. Find the net entropy generated in the system and surroundings in the cool-down process.

2. A piston-cylinder contains 20 L of water at 200 kPa and 200$\POW9,{\circ}$C. The piston is now pushed into the cylinder at a rate so that $PV$ stays constant, while the pressure increases to 800 kPa. The heat that leaks out of the cylinder ends up in the 20$\POW9,{\circ}$C surrounding room.
   1. Construct the initial and final phases of the water in separate $Pv$ diagrams. In the diagrams, list no more than is needed to construct the phase, but do list the values of the curves/points used. In a third $Pv$ diagram, show the process as a fat curve.
   2. Find the work done by and heat added to the water in the process.
   3. Does the total process satisfy the second law of thermo? Is it reversible?

3. Two kg of air at the ambient pressure of 100 kPa and at the ambient temperature of 15$\POW9,{\circ}$C is confined within a steel container. A heating element within the tank now adds 100 kJ of heat to the air, and the air then ends up at 75$\POW9,{\circ}$C. Find the net entropy generated by the process and comment on whether this process is possible. Use table A-2(a) values, do not use table A-17. If this question makes sense to you, please explain.

4. One kg of methane gas at 100 kPa and 20$\POW9,{\circ}$C is compressed isentropically to 800 kPa. Calculate the final temperature using the polytropic relations. Then calculate the work done in the process. Calculate the work done directly, do not use the first law to do it. Assume constant specific heats from table A-2(a) (even though that is a lousy approximation).