15 C8a. Due 11/2

1. Construct the phase of
   1. water if $s$ = 7.70 kJ/kg K, $P$ = 25 kPa, using the $Ts$ diagram. Then find the values of $h$, $T$, and $x$ if defined.
   2. UNGRADED: 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. UNGRADED: 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 ammonia in a piston/cylinder at 50$\POW9,{\circ}$C, 1000 kPa is expanded in a reversible isothermal process to 100 kPa.
   1. Construct the initial phase of the ammonia 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.
   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 415.72 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. You should find state 1 is SUV.
   2. Find a second intensive variable for the final state. WARNING: Hardcovers have in B.1.3 $u$ = 2945.21 listed incorrectly as 2045.21. Please correct.
   3. Now you need to construct the phase of state 2. Do $s_2$ first. So in the $Ts$-diagram that you already made, line 1 will be a vertical line. You are then interested in where this line hits the two phase region, which will be at the point on the saturated vapor line where $s_g=s_2$. Use table B.1.2, not B.1.1 to do so, because then you find $s_2$ to 4 digits accurate already in the table (it is actually 5 significant digits, because a single tick does not make a digit insignificant), so you do not have to interpolate. Now check the value of the second variable at that point. If you overshot the desired value going down from state 1, then obviously state 2 is before the line hits the saturated vapor curve, and state 2 must still be in the SUV region. On the other hand, if you have not yet reached the target value of the second variable, then obviously state 2 will be still lower down, and inside the two phase region. In the unlikely case that you hit exactly the value of the second variable, then obviously state 2 is saturated vapor.
   4. Show the final state, and the process line as a fat curve, in the two diagrams you made earlier.
   5. Find the final pressure and temperature.