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Modern Engineering Thermodynamics

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9.9 Unsteady State Processes in Open Systems 303<br />

EXAMPLE 9.9<br />

The Vortec Corporation manufactures a vortex tube to provide hot and cold air from a standard compressed air system. For an<br />

equally split mass flow rate (y = 0.500), Table 9.2 lists the hot and cold outlet temperatures for various inlet pressures when<br />

the inlet temperature is 70.0°F. Assuming the exit pressure is atmospheric, determine the entropy production rate per unit<br />

mass flow rate for each pressure shown and plot the results.<br />

Table 9.2 Hot and Cold Outlet Temperatures<br />

Inlet pressure Outlet temperatures T H ð°FÞ + 460<br />

(psig) (psia) T hot (°F) T coldt (°F)<br />

T C ð°FÞ + 460<br />

0.000 14.7 70.0 70.0 1.000<br />

20.00 34.7 119.0 19.5 1.209<br />

40.00 54.7 141.0 –3.00 1.315<br />

60.00 74.7 150.0 –14.0 1.368<br />

80.00 94.7 156.0 –22.0 1.406<br />

100.0 114.7 161.0 –29.0 1.441<br />

120.0 134.7 164.0 –34.0 1.465<br />

140.0 154.7 166.0 –39.0 1.487<br />

Solution<br />

First, draw a sketch of the system (Figure 9.19).<br />

T inlet = 70.0°F<br />

Hot outlet<br />

Inlet<br />

m<br />

y = H<br />

m<br />

= 0.500<br />

C<br />

Cold outlet<br />

FIGURE 9.19<br />

Example 9.9, system.<br />

The unknowns are the entropy production rate per unit mass flow rate for each pressure shown; plot the results. The<br />

material is air.<br />

Table 9.3 Remaining Results for Example 9.9<br />

Inlet pressure psig T 1 /T 2 SP<br />

_ / _m 3 Btu/ ðlbm ⋅ RÞ<br />

0.000 1.000 0.0000<br />

20.00 1.209 0.0577<br />

40.00 1.315 0.0878<br />

60.00 1.368 0.1084<br />

80.00 1.406 0.1241<br />

100.0 1.441 0.1367<br />

120.0 1.465 0.1474<br />

140.0 1.487 0.1565<br />

(Continued )

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