15 Due 3/27

1. Construct the phase of
   1. water if the entropy is 7.70 kJ/kg K, $P$ = 25 kPa, using the $Ts$ diagram. Then find the values of the enthalpy, $T$, and $x$ if defined.
   2. water, if $u$ = 3400 kJ/kg and $P$ = 10 MPa, using the $Pv$ diagram. Then find the values of $T$, $s$, and $x$ if defined
   In each diagram, list no more than is needed to construct the phase, but do list the values of the curves/points.

2. A Carnot-cycle heat pump uses R-134a as refrigerant. Heat is absorbed from the outside at -10$\POW9,{\circ}$C. It is delivered to the heated space at 40$\POW9,{\circ}$C. Assume that the R-134a enters the hot-side heat exchanger as saturated vapor and exits it as saturated liquid.
   1. Show the cycle in the $Ts$ diagram. List the entry to the hot side heat exchanger as 1, the exit of it as 2, and so on.
   2. Find the quality of the R-134a at the beginning and end of the isothermal heat addition process at -10$\POW9,{\circ}$C.
   3. Determine the coefficient of performance for the cycle.

3. Two kilogram R-134a in a piston/cylinder at 40$\POW9,{\circ}$C, 1000 kPa is expanded in a reversible isothermal process to 100 kPa.
   1. Construct the initial phase of the R-134a in both the $Ts$ and $Pv$ diagrams. Draw temperature first. In each diagram, list no more than is needed to construct the phase, but do list the values of the curves/points used.
   2. Add the final state to the diagrams and then draw the process in them as a fat curve. (A ``curve'' might have straight parts.)
   3. Find the work and heat transfer.

4. Water in a piston/cylinder at 400$\POW9,{\circ}$C, 2000 kPa is expanded in a reversible adiabatic process. The specific work is measured to be 417 kJ/kg out.
   1. Construct the initial phase of the water in both the $Ts$ and $Pv$ diagrams. In each diagram, list no more than is needed to construct the phase, but do list the values of the curves/points used. Watch it: the temperature of the critical point is 374.1$\POW9,{\circ}$C, less than 400$\POW9,{\circ}$C.
   2. Find two intensive variables for the final state. Then use table A-4, not A-5, to find the saturated value(s) needed to figure out the phase.
   3. Show the final state, and also the process line as a fat curve, in the two diagrams.
   4. Find the final pressure and temperature.