Modern Engineering Thermodynamics

Problems 311
entropy production rate density of any new technology. This
becomes known simply as the EPRD number, determined by
dividing the entire mass of the system generating the entropy
into its total entropy production rate. Determine the steady state
EPRD of an insulated steam turbine that has a total mass of
2000. kg, takes in steam at 3.50 MPa, 400.°C at a rate of
2.00 kg/s and exhausts it at 5.00 kPa, 90.0% quality.
12. Determine the entropy production rate as 5.00 lbm/s of
saturated water vapor at 14.696 psia is condensed isothermally
and aergonically in a steady flow, steady state process to a
saturated liquid. Ignore all kinetic and potential energy changes.
Explain the significance of your answer.
13.* Air is throttled from 1.00 MPa and 30.0°C to 0.100 MPa in a
steady flow, adiabatic process. Assuming constant specific heat
ideal gas behavior and ignoring any changes in kinetic and
potential energy, determine
a. The change in flow stream entropy.
b. The entropy produced per kg of air flowing.
14. Determine the nozzle outlet diameter in Example 9.2 required
to increase the nozzle efficiency by decreasing the entropy
production rate by 25.0%.
15.* Determine the final temperature and the entropy production per
unit mass of air at 1.00 MPa, 25.0°C, and 2.00 m/s that expands
adiabatically through a horizontal nozzle to 0.100 MPa and
100. m/s. Assume constant specific heat ideal gas behavior, and
ignore any changes in kinetic and potential energy.
16. Refrigerant-134a enters an insulated nozzle at 25.0 psia, 80.0°F,
and 10.0 ft/s. The flow accelerates and reaches 15.0 psia and
60.0°F just before it exits the nozzle. The process is adiabatic
and steady flow.
a. What is the exit velocity?
b. Is the flow reversible or irreversible?
17. Air is expanded in an insulated horizontal nozzle from
100. psia, 100.°F to 26.0 psia, 70.0°F. Neglecting the inlet
velocity and any change in potential energy, determine (a) the
outlet velocity and (b) the entropy production rate per unit
mass flowing. Assume the air behaves as an ideal gas with
constant specific heats.
18.* Steam at 40.0 MPa, 800.°C expands through a heated nozzle to
0.100 MPa and 90.0% quality at a rate of 100. kg/h. Neglect the
inlet velocity and any change in potential energy, and take the
entropy production rate to be 10.0% of the magnitude of the
entropy transport rate due to heat transfer. Determine
a. The entropy production rate if the surface temperature of the
nozzle is 450.°C.
b. The exit velocity.
c. The exit area of the nozzle.
19. Refrigerant-134a flows steadily through an adiabatic throttling
valve. At the inlet to the valve, the fluid is a saturated liquid at
110.°F. At the valve outlet, the pressure is 20.0 psia. Neglecting
any changes in kinetic and potential energy, determine
a. The quality of the fluid at the valve outlet.
b. The entropy production per pound of R-134a flowing
through the valve.
20.* Carbon dioxide (CO 2 ) at 50 MPa and 207°C is expanded
isothermally through an uninsulated nozzle to 1.50 MPa in a
steady state, steady flow process. There is no change in potential
energy across the nozzle, and the surface temperature of the
nozzle is 307°C. The entropy production rate magnitude in this
problem can be taken to be 10% of the absolute value of the
heat transfer rate. Assuming the CO 2 to be a constant specific
heat ideal gas, determine
a. The heat transfer rate of the nozzle per kg of CO 2 flowing.
b. The change in kinetic energy of the CO 2 across the nozzle
per kg of CO 2 flowing.
21. Refrigerant-134a is throttled irreversibly through an insulated,
horizontal, constant diameter tube. Saturated liquid R-134a
enters the tube at 80.0°F and exits the tube at 10.0°F.
a. What is the increase in entropy per lbm of R-134a flowing
through the tube?
b. What is the entropy production rate per unit mass flow rate
of R-134a?
c. Show the initial and final states on a T-s diagram.
d. Determine the average Joule-Thomson coefficient for this
process.
22. Saturated liquid Refrigerant-134a is expanded irreversibly in a
refrigerator expansion valve from 100.°F to 0.00°F. Determine
(a) the entropy of the R-134a after the expansion and (b) the
entropy production rate of the expansion process per unit mass
flow rate. Assume the process is adiabatic and aergonic, and
neglect any changes in kinetic and potential energy.
23.* A steady state desuperheater (a type of mixing heat exchanger)
adiabatically mixes superheated vapor and liquid with the
properties shown in Figure 9.24. Complete vaporization of the
liquid reduces the enthalpy of the vapor to h=1390 kJ/kg at the
exit of the desuperheater. Compute the rate of entropy
production in the desuperheater.
Vapor
inlet
m = 1000. kg/h
h = 1500. kJ/kg
s = 1.650 kJ/kg •K
FIGURE 9.24
Problem 23.
h = 180.0 kJ/kg
s = 0.3000 kJ/kg •K
Liquid
inlet
Mixture
outlet
h = 139.0 kJ/kg
s = 1.560 kJ/kg •K
24. A solar concentrating heat exchanger system directs sunlight
onto a long, straight pipe. The pipe receives 153.616 Btu/h per
foot of length. If water enters the pipe at 50.0 lbm/h as
saturated liquid at 300.°F and is heated isothermally so that it
leaves as vapor at 20.0 psia, then
a. How long is the pipe for steady state, steady flow conditions.
b. What is the rate of entropy production.
c. Show whether this system violates the second law of
thermodynamics.
25.* Consider a simple constant pressure boiler that converts 3.00 kg/
min of saturated liquid water at 1.00 atm pressure into saturated
vapor at 1.00 atm in a steady state, steady flow, single-inlet,
single-outlet process.
a. What is the heat transfer rate into the boiler?
b. What is the entropy production rate inside the boiler?
26.* A brilliant young engineering student just invented a new
chrome-plated digital heat exchanger that has water flowing
through it at 14.41 kg/s. At the inlet, the water is a saturated
vapor at 200.°C. The water passes isothermally through the