7 Due 10/5

1. Construct the phases of the below states in both the $Pv$ and $Tv$ diagrams, labeling all lines with their values. Make a separate diagram for each case, six diagrams in total. Find the missing properties of $T$, $P$, $v$, $u$, $h$ and $x$ if applicable.
   1. Water at 5000 kPa, $u$ = 800 kJ/kg
   2. Water at 5000 kPa, $v$ = 0.06 m$\POW9,{3}$/kg
   3. R-134a at 35$\POW9,{\circ}$C, $v$ = 0.01 m$\POW9,{3}$/kg

2. Water in a rigid container at 300$\POW9,{\circ}$C, 1200 kPa has a mass of 0.75 kg. The water is cooled to 300 kPa. Find the final temperature, the work and the heat transfer in the process. Construct all phases that are not given in a $Pv$ diagram. Label the lines with their values. Show a $Pv$ diagram of the process. So your solution must have a total of three diagrams.

3. A constant-pressure piston/cylinder has 2 lbm of water at 1100 F and 2.26 ft$^3$. It is now cooled to occupy 1/10 of the original volume. Find the heat transfer in the process. Construct all phases that are not given in a $Pv$ diagram. Label the lines with their values. Show a $Pv$ diagram of the process. Use British units throughout.

4. There is 2 kg of water at 500 kPa and 200$\POW9,{\circ}$C in a piston/cylinder combination. The water is expanded to 100 kPa in a process that is polytropic with $n=1.3$. Construct the initial phase in a $Pv$ diagram. Label the lines with their values. Find out enough info about state 2 without guessing its phase to construct the final phase in a second $Pv$ diagram. Then find the final temperature and the heat lost in the expansion.