Example Problem with Complete Solution

7E-1 : Minimum Work for Compression of R-134a 4 pts
R-134a vapor enters an adiabatic compressor at -20oC and leaves at 700 kPa. If the R-134a is saturated when it enters the compressor, determine the minimum shaft work required by the compressor in kJ/kg.
Read : We must apply the 1st Law to the compressor.  We can get H1 from the R-134a tables or the NIST Webbook, but we do not know H2.  The key to solving this problem is that a process that requires the minimum shaft work is an isentropic process.  Knowing that S2 = S1 gives us the value of a 2nd intensive variable for state 2.  This allows us to use the R-134a tables or NIST Webbook to detemine H2.  We can then plug H2 into the 1st Law to determine the work requirement per kg of R-134a.
Given: T1 -20 oC Find: WS ??? kJ/kg
x1 1 kg vap/kg
P2 700 kPa
Assumptions: 1 - The compressor is isentropic.
2 - The compressor operates at steady-state.
3 - Changes in kinetic and potential energies are negligible.
4 - Shaft work and flow work are the only types of work that cross the system boundary.
Equations / Data / Solve:
Apply the 1st Law to the compressor to determine the shaft work requirement.
For a steady-state, single-inlet, single outlet system with no heat transfer and negligible kinetic and potential energy changes, the 1st Law is:
Eqn 1
We can get H1 from the R-134a tables or the NIST Webbook because we know the temperature and we know it is a saturated vapor:
H1 386.6 kJ/kg
The compressor is isentropic, so S2 = S1 and we can get S1 from the R-134a tables or the NIST Webbook.
S1 1.7413 kJ/kg-K S2 1.7413 kJ/kg-K
Now, we know the values of two intensive properties at state 2, so we can use the R-134a tables or the NIST Webbook to evaluate any other properties by interpolation.  Here, we are interested in H2.
At P = 700 kPa:
T (oC) H (kJ/kg) So (kJ/kg-K)
30 416.60 1.7269
T2 H2 1.7413 T2 34.39 oC
40 426.72 1.7598 H2 421.0 kJ/kg
Now, we can plug values back into Eqn 1 : WS -34.49 kJ/kg
Verify: The assumptions made in the solution of this problem cannot be verified with the given information.
Answers : WS -34.5 kJ/kg