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Modern Engineering Thermodynamics

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314 CHAPTER 9: Second Law Open System Applications<br />

46. Steam at 400. psia and 50.0% quality is heated in a steady<br />

flow, isobaric heat exchanger until it becomes a saturated<br />

vapor. It is then expanded adiabatically through a turbine to<br />

1.00 psia and 98.0% quality. This is followed by isobaric<br />

cooling to a saturated liquid in a second heat exchanger then<br />

compression and heating to the initial state. For the turbine<br />

alone, determine<br />

a. The net power output per unit mass flow rate of steam.<br />

b. The entropy production rate per unit mass flow rate of steam<br />

flowing in the system.<br />

47.* Through a clerical error, our purchasing department ordered a<br />

finely crafted but mysterious device from a foreign manufacturer<br />

(Figure 9.30). The manuals are all in a foreign language, and the<br />

only intelligible information is in the form of some numbers<br />

printed next to the entrance and exit ports and the rotating<br />

shaft. The 10.0 kW rating on the shaft may mean either a work<br />

input or a work output. Determine<br />

a. The flow direction, a to b or b to a.<br />

b. The mass flow rate.<br />

c. The entropy production rate of the device.<br />

A<br />

0.200 MPa<br />

200.°C<br />

FIGURE 9.30<br />

Problem 47.<br />

10.0 kW<br />

B<br />

30.0 MPa<br />

800.°C<br />

Assume a steady state, adiabatic device and that the working<br />

substance is H 2 O. Assume also that the kinetic and potential<br />

energies of outlet and inlet flow streams are negligible.<br />

48. An irreversible, steady state, steady flow steam turbine that has<br />

no thermal insulation has an isothermal surface temperature of<br />

100.°F. It operates with a steam mass flow rate of 15.0 lbm/s.<br />

The turbine inlet is at 300. psia, 1200.°F, and the exit is at<br />

14.7 psia, 300.°F. If the turbine’s entropy production rate is<br />

0.500 Btu/(s · R), then determine<br />

a. The turbine’s heat transfer rate.<br />

b. The turbine’s work rate (power).<br />

49.* A dog food manufacturer wishes to carry out the canning and<br />

sterilization process of a new pet food product at 100.°C,<br />

0.0100 MPa. After crawling around in the rafters of the plant, an<br />

engineer finds a 1.60 MPa wet steam line. A pipe is run from<br />

this line to the canning area, where it produces 1.40 MPa steam<br />

with 2.00% moisture. Now, instead of just throttling down to<br />

the 0.0100 MPa state needed and wasting all that energy, the<br />

engineer decides to drop the pressure through a small adiabatic<br />

steam turbine.<br />

a. What steam mass flow rate must be used to obtain 1.00 hp<br />

from the turbine?<br />

b. What is the turbine’s entropy production rate under these<br />

conditions?<br />

50. A nuclear reactor heats a fluid for the steady flow power plant<br />

shown in Figure 9.31. The mass flow rate is 10.0 lbm/s.<br />

Determine<br />

a. The horsepower input to the adiabatic pump.<br />

Reactor<br />

Pump<br />

u = 100.0 Btu/lbm W pump<br />

v = 10.0 ft 3 /lbm<br />

p = 77.8 lbf/ft 2<br />

s = 1.000 Btu/lbm•R<br />

FIGURE 9.31<br />

Problem 50.<br />

h = 1000.0 Btu/lbm<br />

s = 1.001 Btu/lbm•R<br />

Condenser<br />

h = 100.0 Btu/lbm<br />

p = 10.0 lbf/ft 2<br />

Turbine<br />

W T<br />

h = 200.0 Btu/lbm<br />

s = 1.003 Btu/lbm•R<br />

b. The entropy production rate in the insulated reactor.<br />

c. The entropy production rate in the insulated turbine.<br />

51. The sales literature for the device shown in Figure 9.32 claims<br />

that the outlet temperature is slightly higher than the inlet<br />

temperature due to the presence of the vortex tube (see Case<br />

Study 9.1).<br />

a. Assuming the vortex tube and the rest of the system are<br />

isentropic, determine the outlet temperature (T 4 ) from the<br />

data given in Figure 9.32.<br />

b. Explain how the temperature rise claimed by the<br />

manufacturer could in fact exist.<br />

Air<br />

100. psia<br />

70.0°F<br />

3<br />

FIGURE 9.32<br />

Problem 51.<br />

Vortex<br />

tube<br />

1<br />

2<br />

4<br />

92.0 psia<br />

T 4 > 70.0°F<br />

52.* Determine the entropy production rate as 0.0500 kg/s of air flows<br />

through a vortex tube from an inlet pressure of 1.00 MPa. Both<br />

hot and cold side exit pressures are 101.3 kPa, and the hot side<br />

temperature is 50.0°C while the cold side temperature is –40.0°C.<br />

Two thirds of the inlet mass flow rate passes through the hot side<br />

exit. Assume constant, specific heat, ideal gas behavior and neglect<br />

any changes in kinetic and potential energy (see Case Study 9.1).<br />

53. Using Eqs. (9.41), (9.29), and (7.33), discuss the possibility of<br />

having a temperature separation occur in a constant, specific<br />

heat, incompressible liquid flowing through a vortex tube (see<br />

Case Study 9.1).<br />

54. A company claims to be able to manufacture a vortex tube using<br />

air that reaches –250.°F cold side and +250.°F hot side (both at<br />

atmospheric pressure) with an inlet pressure of 20.0 psig and a<br />

hot side mass flow fraction of 50.0%. Does their vortex tube<br />

violate the second law of thermodynamics? Assume constant<br />

specific heat ideal gas behavior and neglect any changes in<br />

kinetic and potential energy.

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