Modern Engineering Thermodynamics

9.9 Unsteady State Processes in Open Systems 297
The work transport energy efficiency η W is defined in Chapter 4 for a work producing system (e.g., an engine or
motor) by Eq. (4.72) as
Inserting Eqs. (9.35) and (9.37) gives
ðη W Þ work
producing
W
ðη W Þ work
= _ act
(4.72)
producing
_W rev
= _m½ðh 1 − T b s 1 Þ − ðh 2 − T b s 2 Þ + ðV 1 2 − V 2 2 Þ/ð2g c Þ + ðg/g c ÞðZ 1 − Z 2 ÞŠ − T b
_S P
_m½ðh 1 − T b s 1 Þ − ðh 2 − T b s 2 Þ + ðV 12 − V 22 Þ/ð2g c Þ + ðg/g c ÞðZ 1 − Z 2 ÞŠ
= 1 −
T b
_S P
_m½ðh 1 − T b s 1 Þ − ðh 2 − T b s 2 Þ + ðV 12 − V 22 Þ/ð2g c Þ + ðg/g c ÞðZ 1 − Z 2 ÞŠ
and, for a work absorbing system (pump, compressor, etc.), Eq. (4.71) gives
ðη W Þ work
absorbing
=
(9.38)
_m½ðh 1 − T b s 1 Þ − ðh 2 − T b s 2 Þ + ðV 1 2 − V 2 2 Þ/ð2g c Þ + ðg/g c ÞðZ 1 − Z 2 ÞŠ
_m½ðh 1 − T b s 1 Þ − ðh 2 − T b s 2 Þ + ðV 12 − V 22 Þ/ð2g c Þ + ðg/g c ÞðZ 1 − Z 2 ÞŠ − T b
_S P
(9.39)
EXAMPLE 9.7
Determine the maximum (reversible) power that could be produced by expanding 0.500 kg/s of steam in a shaft work
machine from 8.00 MPa, 300.°C to a saturated vapor at 100.°C. Neglect any kinetic and potential energy effects. The temperature
of the system boundary is T b = 20.0°C
Solution
First, draw a sketch of the system (Figure 9.14).
The unknown is the maximum (reversible) power for this
system. For this open system, we have the following thermodynamic
station data:
Expansion
Station 1 ƒƒƒ ƒ!
p 1 = 8:00 MPa
T 1 = 300:°F
Station 2
x 2 = 1:00
T 2 = 100:°C
m = 0.500 kg/s
1
T b = 20.0°C
2
Station 1 Station 2
p 1 = 8.00 MPa x 2 = 1.00
T 1 = 300.°C T 2 = 100.°C
W max = W rev = ?
Neglecting all kinetic and potential energy effects, Eq. (9.37)
reduces to
_W max = _W rev = _m ½ðh 1 − T b s 1 Þ − ðh 2 − T b s 2 ÞŠ
FIGURE 9.14
Example 9.7.
and, using the values just given, we get
_W max = ð0:50 kg=sÞf½2785:0 − ð20:0 + 273:15Þð5:7914ÞŠ−½2676:0 − ð20 + 273:15Þð7:3557ÞŠg
= 284 kW
Exercises
19. If the mass flow rate of steam in Example 9.7 is increased from 0.500 kg/s to 0.850 kg/s with all the inlet and exit steam
properties remaining constant, what is the maximum (reversible) power output? Answer: _W max = _W rev = 482 kW.
20. Determine the maximum (reversible) power output in Example 9.7 when the steam exits with a quality of 90.0% rather
than 100.%. Answer: _W max = _W rev = 308 kW.
21. Suppose the inlet steam pressure and temperature in Example 9.7 is increased to 10.0 MPa and 800.°C. Determine the
maximum (reversible) power output. Answer: _W max = _W rev = 712 kW.
9.9 UNSTEADY STATE PROCESSES IN OPEN SYSTEMS
In Chapter 6, we analyze the energy transport requirements in the emptying and filling of a rigid container. In
this section, we carry out an entropy analysis of the filling of a rigid container and determine whether it is more
efficient to fill it adiabatically or isothermally.