Modern Engineering Thermodynamics

190 CHAPTER 6: First Law Open System Applications
EXAMPLE 6.6 (Continued )
The MERB for the conditions described in the problem statement is Eq. (6.31):
_W shaft = _mðh 1 − h 2 Þ
We do not know _m here, but we do know the energy produced per kilogram of steam flowing:
W/m = _W/ _m = 2000: kJ/kg, so 2000: kJ/kg = h 1 − h 2
m
1
2
Unknown: x 2 = ?
W/m = 2000. kJ/kg
Station 1
p 1 = 2.00 MPa
T 1 = 800.°C
h 1 = 4150.4 kJ/kg
Process: Turbine
Station 2
p 2 = 1.00 kPa
h 2 = 2150.4 kJ/kg
x 2 = ?
FIGURE 6.13
Example 6.6.
From Table C.3b of Thermodynamic Tables to accompany Modern Engineering Thermodynamics, wehaveh 1 = 4150:4 kJ/kg; and
from Table C.2b, we have h f 2 = 29:30 kJ/kg, h fg2 = 2484:9 kJ/kg, and h g2 = 2514:2 kJ/kg (all at 1.0 kPa). Therefore,
h 2 = h 1 − _W/ _m = 4150:4 − 2000: = 2150: kJ/kg
These values of h 1 and h 2 have been added to our station data list in Figure 6.13. Hence, the values of h 2 = 2150: kJ/kg and
p 2 = 1:00 kPa are a pair of independent properties in the outlet state. Therefore, the outlet quality can be found from the
auxiliary formula for quality:
x 2 = h 2 − h f 2 ð1:00 kPaÞ
/hfg2 ð1:00 kPaÞ = ð2150: − 29:30Þ/2484:9 = 0:854
= 85:4% vapor at the turbine’s outlet
Exercises
15. Determine the exit steam quality in Example 6.6 if the exit pressure is atmospheric pressure (0.101 MPa) instead of
1.00 kPa and everything else remains the same. Answer: x 2 = 76.8%.
16. Determine the exit steam quality in Example 6.6 if the inlet steam temperature is 900.°C instead of 800.°C and
everything else remains the same. Answer: x 2 = 95.1%.
17. Suppose the shaft power produced by the turbine in Example 6.6 is 2000. kW and the steam mass flow rate is 2.00 kg/s.
Determine the exit steam quality if everything else remains the same. Answer: Since h 2 > h g (1 kPa) here, the exit steam
is superheated and quality is not a valid property.
6.10 OPEN SYSTEM UNSTEADY
STATE PROCESSES
There are a wide variety of open system unsteady state
processes in industry. Most are too complex to analyze
easily, but one of the simpler cases involves the filling
or emptying of a rigid tank or vessel.
Consider the tank-filling process illustrated in Figure
6.14. In this system, a rigid tank is connected through
a valve to a high-pressure supply pipe. When the valve
is opened, the rigid tank is filled from the supply pipe
until the tank pressure is equal to that of the supply
pipe. This is the filling process that we analyze.
The filling process is neither steady state nor steady flow,
since the mass of the system is continually changing.
FIGURE 6.14
Filling a rigid vessel.
High-pressure pipe
Valve
Rigid tank (vessel)
System boundary