Modern Engineering Thermodynamics

314 CHAPTER 9: Second Law Open System Applications
46. Steam at 400. psia and 50.0% quality is heated in a steady
flow, isobaric heat exchanger until it becomes a saturated
vapor. It is then expanded adiabatically through a turbine to
1.00 psia and 98.0% quality. This is followed by isobaric
cooling to a saturated liquid in a second heat exchanger then
compression and heating to the initial state. For the turbine
alone, determine
a. The net power output per unit mass flow rate of steam.
b. The entropy production rate per unit mass flow rate of steam
flowing in the system.
47.* Through a clerical error, our purchasing department ordered a
finely crafted but mysterious device from a foreign manufacturer
(Figure 9.30). The manuals are all in a foreign language, and the
only intelligible information is in the form of some numbers
printed next to the entrance and exit ports and the rotating
shaft. The 10.0 kW rating on the shaft may mean either a work
input or a work output. Determine
a. The flow direction, a to b or b to a.
b. The mass flow rate.
c. The entropy production rate of the device.
A
0.200 MPa
200.°C
FIGURE 9.30
Problem 47.
10.0 kW
B
30.0 MPa
800.°C
Assume a steady state, adiabatic device and that the working
substance is H 2 O. Assume also that the kinetic and potential
energies of outlet and inlet flow streams are negligible.
48. An irreversible, steady state, steady flow steam turbine that has
no thermal insulation has an isothermal surface temperature of
100.°F. It operates with a steam mass flow rate of 15.0 lbm/s.
The turbine inlet is at 300. psia, 1200.°F, and the exit is at
14.7 psia, 300.°F. If the turbine’s entropy production rate is
0.500 Btu/(s · R), then determine
a. The turbine’s heat transfer rate.
b. The turbine’s work rate (power).
49.* A dog food manufacturer wishes to carry out the canning and
sterilization process of a new pet food product at 100.°C,
0.0100 MPa. After crawling around in the rafters of the plant, an
engineer finds a 1.60 MPa wet steam line. A pipe is run from
this line to the canning area, where it produces 1.40 MPa steam
with 2.00% moisture. Now, instead of just throttling down to
the 0.0100 MPa state needed and wasting all that energy, the
engineer decides to drop the pressure through a small adiabatic
steam turbine.
a. What steam mass flow rate must be used to obtain 1.00 hp
from the turbine?
b. What is the turbine’s entropy production rate under these
conditions?
50. A nuclear reactor heats a fluid for the steady flow power plant
shown in Figure 9.31. The mass flow rate is 10.0 lbm/s.
Determine
a. The horsepower input to the adiabatic pump.
Reactor
Pump
u = 100.0 Btu/lbm W pump
v = 10.0 ft 3 /lbm
p = 77.8 lbf/ft 2
s = 1.000 Btu/lbm•R
FIGURE 9.31
Problem 50.
h = 1000.0 Btu/lbm
s = 1.001 Btu/lbm•R
Condenser
h = 100.0 Btu/lbm
p = 10.0 lbf/ft 2
Turbine
W T
h = 200.0 Btu/lbm
s = 1.003 Btu/lbm•R
b. The entropy production rate in the insulated reactor.
c. The entropy production rate in the insulated turbine.
51. The sales literature for the device shown in Figure 9.32 claims
that the outlet temperature is slightly higher than the inlet
temperature due to the presence of the vortex tube (see Case
Study 9.1).
a. Assuming the vortex tube and the rest of the system are
isentropic, determine the outlet temperature (T 4 ) from the
data given in Figure 9.32.
b. Explain how the temperature rise claimed by the
manufacturer could in fact exist.
Air
100. psia
70.0°F
3
FIGURE 9.32
Problem 51.
Vortex
tube
1
2
4
92.0 psia
T 4 > 70.0°F
52.* Determine the entropy production rate as 0.0500 kg/s of air flows
through a vortex tube from an inlet pressure of 1.00 MPa. Both
hot and cold side exit pressures are 101.3 kPa, and the hot side
temperature is 50.0°C while the cold side temperature is –40.0°C.
Two thirds of the inlet mass flow rate passes through the hot side
exit. Assume constant, specific heat, ideal gas behavior and neglect
any changes in kinetic and potential energy (see Case Study 9.1).
53. Using Eqs. (9.41), (9.29), and (7.33), discuss the possibility of
having a temperature separation occur in a constant, specific
heat, incompressible liquid flowing through a vortex tube (see
Case Study 9.1).
54. A company claims to be able to manufacture a vortex tube using
air that reaches –250.°F cold side and +250.°F hot side (both at
atmospheric pressure) with an inlet pressure of 20.0 psig and a
hot side mass flow fraction of 50.0%. Does their vortex tube
violate the second law of thermodynamics? Assume constant
specific heat ideal gas behavior and neglect any changes in
kinetic and potential energy.