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Modern Engineering Thermodynamics

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Problems 311<br />

entropy production rate density of any new technology. This<br />

becomes known simply as the EPRD number, determined by<br />

dividing the entire mass of the system generating the entropy<br />

into its total entropy production rate. Determine the steady state<br />

EPRD of an insulated steam turbine that has a total mass of<br />

2000. kg, takes in steam at 3.50 MPa, 400.°C at a rate of<br />

2.00 kg/s and exhausts it at 5.00 kPa, 90.0% quality.<br />

12. Determine the entropy production rate as 5.00 lbm/s of<br />

saturated water vapor at 14.696 psia is condensed isothermally<br />

and aergonically in a steady flow, steady state process to a<br />

saturated liquid. Ignore all kinetic and potential energy changes.<br />

Explain the significance of your answer.<br />

13.* Air is throttled from 1.00 MPa and 30.0°C to 0.100 MPa in a<br />

steady flow, adiabatic process. Assuming constant specific heat<br />

ideal gas behavior and ignoring any changes in kinetic and<br />

potential energy, determine<br />

a. The change in flow stream entropy.<br />

b. The entropy produced per kg of air flowing.<br />

14. Determine the nozzle outlet diameter in Example 9.2 required<br />

to increase the nozzle efficiency by decreasing the entropy<br />

production rate by 25.0%.<br />

15.* Determine the final temperature and the entropy production per<br />

unit mass of air at 1.00 MPa, 25.0°C, and 2.00 m/s that expands<br />

adiabatically through a horizontal nozzle to 0.100 MPa and<br />

100. m/s. Assume constant specific heat ideal gas behavior, and<br />

ignore any changes in kinetic and potential energy.<br />

16. Refrigerant-134a enters an insulated nozzle at 25.0 psia, 80.0°F,<br />

and 10.0 ft/s. The flow accelerates and reaches 15.0 psia and<br />

60.0°F just before it exits the nozzle. The process is adiabatic<br />

and steady flow.<br />

a. What is the exit velocity?<br />

b. Is the flow reversible or irreversible?<br />

17. Air is expanded in an insulated horizontal nozzle from<br />

100. psia, 100.°F to 26.0 psia, 70.0°F. Neglecting the inlet<br />

velocity and any change in potential energy, determine (a) the<br />

outlet velocity and (b) the entropy production rate per unit<br />

mass flowing. Assume the air behaves as an ideal gas with<br />

constant specific heats.<br />

18.* Steam at 40.0 MPa, 800.°C expands through a heated nozzle to<br />

0.100 MPa and 90.0% quality at a rate of 100. kg/h. Neglect the<br />

inlet velocity and any change in potential energy, and take the<br />

entropy production rate to be 10.0% of the magnitude of the<br />

entropy transport rate due to heat transfer. Determine<br />

a. The entropy production rate if the surface temperature of the<br />

nozzle is 450.°C.<br />

b. The exit velocity.<br />

c. The exit area of the nozzle.<br />

19. Refrigerant-134a flows steadily through an adiabatic throttling<br />

valve. At the inlet to the valve, the fluid is a saturated liquid at<br />

110.°F. At the valve outlet, the pressure is 20.0 psia. Neglecting<br />

any changes in kinetic and potential energy, determine<br />

a. The quality of the fluid at the valve outlet.<br />

b. The entropy production per pound of R-134a flowing<br />

through the valve.<br />

20.* Carbon dioxide (CO 2 ) at 50 MPa and 207°C is expanded<br />

isothermally through an uninsulated nozzle to 1.50 MPa in a<br />

steady state, steady flow process. There is no change in potential<br />

energy across the nozzle, and the surface temperature of the<br />

nozzle is 307°C. The entropy production rate magnitude in this<br />

problem can be taken to be 10% of the absolute value of the<br />

heat transfer rate. Assuming the CO 2 to be a constant specific<br />

heat ideal gas, determine<br />

a. The heat transfer rate of the nozzle per kg of CO 2 flowing.<br />

b. The change in kinetic energy of the CO 2 across the nozzle<br />

per kg of CO 2 flowing.<br />

21. Refrigerant-134a is throttled irreversibly through an insulated,<br />

horizontal, constant diameter tube. Saturated liquid R-134a<br />

enters the tube at 80.0°F and exits the tube at 10.0°F.<br />

a. What is the increase in entropy per lbm of R-134a flowing<br />

through the tube?<br />

b. What is the entropy production rate per unit mass flow rate<br />

of R-134a?<br />

c. Show the initial and final states on a T-s diagram.<br />

d. Determine the average Joule-Thomson coefficient for this<br />

process.<br />

22. Saturated liquid Refrigerant-134a is expanded irreversibly in a<br />

refrigerator expansion valve from 100.°F to 0.00°F. Determine<br />

(a) the entropy of the R-134a after the expansion and (b) the<br />

entropy production rate of the expansion process per unit mass<br />

flow rate. Assume the process is adiabatic and aergonic, and<br />

neglect any changes in kinetic and potential energy.<br />

23.* A steady state desuperheater (a type of mixing heat exchanger)<br />

adiabatically mixes superheated vapor and liquid with the<br />

properties shown in Figure 9.24. Complete vaporization of the<br />

liquid reduces the enthalpy of the vapor to h=1390 kJ/kg at the<br />

exit of the desuperheater. Compute the rate of entropy<br />

production in the desuperheater.<br />

Vapor<br />

inlet<br />

m = 1000. kg/h<br />

h = 1500. kJ/kg<br />

s = 1.650 kJ/kg •K<br />

FIGURE 9.24<br />

Problem 23.<br />

h = 180.0 kJ/kg<br />

s = 0.3000 kJ/kg •K<br />

Liquid<br />

inlet<br />

Mixture<br />

outlet<br />

h = 139.0 kJ/kg<br />

s = 1.560 kJ/kg •K<br />

24. A solar concentrating heat exchanger system directs sunlight<br />

onto a long, straight pipe. The pipe receives 153.616 Btu/h per<br />

foot of length. If water enters the pipe at 50.0 lbm/h as<br />

saturated liquid at 300.°F and is heated isothermally so that it<br />

leaves as vapor at 20.0 psia, then<br />

a. How long is the pipe for steady state, steady flow conditions.<br />

b. What is the rate of entropy production.<br />

c. Show whether this system violates the second law of<br />

thermodynamics.<br />

25.* Consider a simple constant pressure boiler that converts 3.00 kg/<br />

min of saturated liquid water at 1.00 atm pressure into saturated<br />

vapor at 1.00 atm in a steady state, steady flow, single-inlet,<br />

single-outlet process.<br />

a. What is the heat transfer rate into the boiler?<br />

b. What is the entropy production rate inside the boiler?<br />

26.* A brilliant young engineering student just invented a new<br />

chrome-plated digital heat exchanger that has water flowing<br />

through it at 14.41 kg/s. At the inlet, the water is a saturated<br />

vapor at 200.°C. The water passes isothermally through the

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