5 Due 1/28

1. A constant pressure cylinder contains 2 kg water at 4 bar that is cooling down. The water is just starting to condense at the start of the process. At the end of the process the volume is half that at the start.
   1. Find the initial phase.
   2. Construct the final phase in the $Pv$ diagram. Label all lines to do so with their values. Do not put more in the diagram than is needed to construct the phase.
   3. Find the final temperature and volume to 5 digits accurate.
   4. Find the work done by the substance in the process.
   5. Show the work done graphically in the $Pv$ diagram. How about the sign?

2. A steel container with a volume of 300 L contains 3kg of water at 20 $\POW9,{\circ}$C. The water is heated. What is the temperature at which all liquid water is gone, to five digits accurate? What is the work done by the water in the process? Show the process in the $Pv$ diagram and so identify the work done graphically.

3. A piston-cylinder configuration contains 2 kg of air at standard atmospheric pressure and 25$\POW9,{\circ}$C. The piston is held by a linear spring. The air is now heated until the volume becomes 4 m$\POW9,{3}$ and the pressure 200 kPa. What is the final temperature in $\POW9,{\circ}$C? What is the work done in the process? Show the work done also graphically in the $PV$ diagram.

4. A piston cylinder combination contains 0.2 m$\POW9,{3}$ of nitrogen at 5 bar and 25$\POW9,{\circ}$C. The nitrogen is now allowed to expand to the ambient pressure of 100 kPa. It can be assumed that the expansion is sufficiently slow that the temperature remains at 25dg. Find the work done by the nitrogen in the process. Show the process in a very neat $PV$ diagram and graphically indicate the work.