18 Due 4/8

1. A plane flies at an height where the ambient temperature is -45$\POW9,{\circ}$C and the pressure 60 kPa with a true airspeed of 900 km/h. Air is flowing into an adiabatic jet engine diffuser through an entrance area of 1 m$\POW9,{2}$ with a speed of 900 km/h and slows down to 20 m/s at the end of it. What is the temperature at the end of the diffuser, and what is the maximum possible pressure there? Use table A-17 values, not table A-2 ones.

2. An isothermal compressor compresses R-134a at 0$\POW9,{\circ}$C and 200 kPa to saturated vapor. Construct the initial phase in the $Pv$ and $Ts$ diagrams. In the diagrams, list no more than is needed to construct the phase, but do list the values of the curves/points used. Also show the final state in the diagrams, and the process between the two as a fat line. Find the specific heat transfer and work. Show the areas in the $Pv$ and $Ts$ diagrams that are equal to these. (The work in a control volume is $\int v {\rm d}P$.)

3. Three kg/s of R-134a at 500 kPa flows as saturated vapor into an isobaric reversible heat exchanger where it is heated to 60$\POW9,{\circ}$C. Show the process in a $Ts$ diagram. There should be no need to construct the phases. Compute the heat that is added to the R-134a. Now assume that this heat is provided by a reversible heat pump that takes in heat from the surroundings that is at 300 K. What is the power needed by the heat pump?

   Warning: do not try to use the Carnot formula for the COP of the heat pump. It does not work since the high temperature, (the temperature of the R-134a), is not constant but varies from about 16$\POW9,{\circ}$C to 60$\POW9,{\circ}$C. Instead, write the second law for the combined system and use the fact that the generated entropy in the combined system is zero, because everything is reversible. That will give you the low heat flow. Then use the first law for the heat pump to find the work.

4. A completely reversible air heater receives a flow of 2 kg/s air at 400 K and 200 kPa and the air leaves at 600 K and 100 kPa. The heater pumps heat at a rate of 50 kW out of a reservoir at 500 K, while it pumps the remaining heat out of the environment at 300 K. What is the heat obtained from the environment and what is the work needed to keep this reversible heater running?