Modern Engineering Thermodynamics

9.9 Unsteady State Processes in Open Systems 303
EXAMPLE 9.9
The Vortec Corporation manufactures a vortex tube to provide hot and cold air from a standard compressed air system. For an
equally split mass flow rate (y = 0.500), Table 9.2 lists the hot and cold outlet temperatures for various inlet pressures when
the inlet temperature is 70.0°F. Assuming the exit pressure is atmospheric, determine the entropy production rate per unit
mass flow rate for each pressure shown and plot the results.
Table 9.2 Hot and Cold Outlet Temperatures
Inlet pressure Outlet temperatures T H ð°FÞ + 460
(psig) (psia) T hot (°F) T coldt (°F)
T C ð°FÞ + 460
0.000 14.7 70.0 70.0 1.000
20.00 34.7 119.0 19.5 1.209
40.00 54.7 141.0 –3.00 1.315
60.00 74.7 150.0 –14.0 1.368
80.00 94.7 156.0 –22.0 1.406
100.0 114.7 161.0 –29.0 1.441
120.0 134.7 164.0 –34.0 1.465
140.0 154.7 166.0 –39.0 1.487
Solution
First, draw a sketch of the system (Figure 9.19).
T inlet = 70.0°F
Hot outlet
Inlet
m
y = H
m
= 0.500
C
Cold outlet
FIGURE 9.19
Example 9.9, system.
The unknowns are the entropy production rate per unit mass flow rate for each pressure shown; plot the results. The
material is air.
Table 9.3 Remaining Results for Example 9.9
Inlet pressure psig T 1 /T 2 SP
_ / _m 3 Btu/ ðlbm ⋅ RÞ
0.000 1.000 0.0000
20.00 1.209 0.0577
40.00 1.315 0.0878
60.00 1.368 0.1084
80.00 1.406 0.1241
100.0 1.441 0.1367
120.0 1.465 0.1474
140.0 1.487 0.1565
(Continued )