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. |
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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. |
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Given: |
T1 |
-20 |
oC |
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Find: |
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WS |
??? |
kJ/kg |
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x1 |
1 |
kg vap/kg |
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P2 |
700 |
kPa |
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Diagram: |
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Assumptions: |
1 - |
The compressor is isentropic. |
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2 - |
The compressor operates at steady-state. |
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3 - |
Changes in kinetic and potential energies are negligible. |
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4 - |
Shaft
work and flow work are the only types of work that cross the system boundary. |
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Equations
/ Data / Solve: |
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Apply the 1st Law to the compressor to determine the shaft work requirement. |
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For a steady-state, single-inlet, single outlet system with no heat
transfer and negligible kinetic
and potential energy changes, the 1st Law is: |
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Eqn 1 |
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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: |
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H1 |
386.6 |
kJ/kg |
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The compressor is isentropic, so S2 = S1 and we can get S1 from the R-134a tables or the NIST Webbook. |
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S1 |
1.7413 |
kJ/kg-K |
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S2 |
1.7413 |
kJ/kg-K |
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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. |
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At P
= 700 kPa: |
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T (oC) |
H (kJ/kg) |
So
(kJ/kg-K) |
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30 |
416.60 |
1.7269 |
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T2 |
H2 |
1.7413 |
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T2 |
34.39 |
oC |
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40 |
426.72 |
1.7598 |
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H2 |
421.0 |
kJ/kg |
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Now, we can plug
values back into Eqn 1 : |
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WS |
-34.49 |
kJ/kg |
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Verify: |
The assumptions made
in the solution of this problem cannot be verified with the given
information. |
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Answers : |
WS |
-34.5 |
kJ/kg |
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