5 Due 9/21

1. 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.

2. A steel container with a volume of 300 L contains 3 kg 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 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?

4. Consider a Stirling cycle with ideal-gas nitrogen as the working substance. The nitrogen is kept in a piston/cylinder combination during the entire cycle.
   • At the start of the cycle, the volume is 0.2 m$\POW9,{3}$ of nitrogen at 5 bar and 127$\POW9,{\circ}$C. The nitrogen is now allowed to isothermally expand to a pressure of 100 kPa. (Heat must be added during the expansion to keep the temperature at 127dg.) What is the final volume? What is the work done by the nitrogen in this process?
   • Next the nitrogen is allowed to cool to room temperature, 27$\POW9,{\circ}$C, while kept at the volume that you just computed. Find the work done by the nitrogen in this second process?
   • Next the nitrogen is compressed back to 0.2 m$\POW9,{3}$, but sufficiently slowly that it stays at the room temperature of 27$\POW9,{\circ}$C. What is the work done by the nitrogen in this process?
   • Next the nitrogen is heated back to 127$\POW9,{\circ}$C while being kept at volume 0.2 m$\POW9,{3}$, thus returning to the original state and completing the cycle. What is the work done during this final process?
   • What is the net work produced by the nitrogen during the complete cycle?
   • Show the process in a very neat $PV$ diagram and graphically indicate the work.