Moran M.J., Shapiro H.N. Fundamentals of Engineering Thermodynamics
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Problems: Developing Engineering Skills 763
same temperature and pressure. If the partition is removed
is entropy produced within the container? Explain.
5. Which do you think is most closely related to human comfort,
the humidity ratio or the relative humidity? Explain.
6. How do you explain the different rates of evaporation from
a dish of water in winter and summer?
7. Can the dry-bulb and wet-bulb temperatures be equal? Explain.
8. How do you explain the water dripping from the tailpipe of
an automobile on a cold morning?
9. Would you recommend an evaporative cooling system for
use in Florida? In Arizona? Explain.
10. During winter, why do eyeglasses fog up when the wearer
enters a warm building?
11. Does operating a car’s air-conditioning system affect its
fuel economy? Explain.
12. What is a food dehydrator and when might you use one?
13. What is meant by a zero-energy building?
14. What is the difference between a steam sauna and a steam
room?
15. Your local weather report gives the temperature, relative
humidity, and dew point. When planning summertime
outdoor activities, are these equally important? Explain.
16. Under what conditions would frost accumulate on the
interior of a car’s windshield?
c PROBLEMS: DEVELOPING ENGINEERING SKILLS
Determining Mixture Composition
12.1 The analysis on a mass basis of an ideal gas mixture at 508F,
25 lbf/in.
2
is 60% CO
2
, 25% SO
2
, and 15% N
2
. Determine
(a) the analysis in terms of mole fractions.
(b) the apparent molecular weight of the mixture.
(c) the partial pressure of each component, in lbf/in.
2
(d) the volume occupied by 20 lb of the mixture, in ft
3
.
12.2 The molar analysis of a gas mixture at 30
8C, 2 bar is 40%
N
2
, 50% CO
2
, and 10% CH
4
. Determine
(a) the analysis in terms of mass fractions.
(b) the partial pressure of each component, in bar.
(c) the volume occupied by 10 kg of mixture, in m
3
.
12.3 The analysis on a molar basis of a gas mixture at 50
8F,
1 atm is 20% Ar, 35% CO
2
, and 45% O
2
. Determine
(a) the analysis in terms of mass fractions.
(b) the partial pressure of each component, in lbf/in.
2
(c) the volume occupied by 10 lb of mixture, in ft
3
.
12.4 The molar analysis of a gas mixture at 25
8C, 0.1 MPa is
60% N
2
, 30% CO
2
, and 10% O
2
. Determine
(a) the analysis in terms of mass fractions.
(b) the partial pressure of each component, in MPa.
(c) the volume occupied by 50 kg of the mixture, in m
3
.
12.5 The analysis on a mass basis of an ideal gas mixture at 30
8F,
15 lbf/in.
2
is 55% CO
2
, 30% CO, and 15% O
2
. Determine
(a) the analysis in terms of mole fractions.
(b) the apparent molecular weight of the mixture.
(c) the partial pressure of each component, in lbf/in.
2
(d) the volume occupied by 10 lb of the mixture, in ft
3
.
12.6 Natural gas at 23
8C, 1 bar enters a furnace with the
following molar analysis: 40% propane (C
3
H
8
), 40% ethane
(C
2
H
6
), 20% methane (CH
4
). Determine
(a) the analysis in terms of mass fractions.
(b) the partial pressure of each component, in bar.
(c) the mass flow rate, in kg/s, for a volumetric flow rate
of 20 m
3
/s.
12.7 A rigid vessel having a volume of 3 m
3
initially contains
a mixture at 21
8C, 1 bar consisting of 79% N
2
and 21% O
2
on a molar basis. Helium is allowed to flow into the vessel
until the pressure is 2 bar. If the final temperature of the
mixture within the vessel is 27
8C, determine the mass, in kg,
of each component present.
12.8 Nitrogen (N
2
) at 150 kPa, 408C occupies a closed, rigid
container having a volume of 1 m
3
. If 2 kg of oxygen (O
2
)
is added to the container, what is the molar analysis of the
resulting mixture? If the temperature remains constant, what
is the pressure of the mixture, in kPa?
12.9 A flue gas in which the mole fraction of H
2
S is 0.002
enters a scrubber operating at steady state at 200
8F, 1 atm
and a volumetric flow rate of 20,000 ft
3
/h. If the scrubber
removes 92% (molar basis) of the entering H
2
S, determine
the rate at which H
2
S is removed, in lb/h. Comment on why
H
2
S should be removed from the gas stream.
12.10 A gas mixture with a molar analysis of 20% C
3
H
8
(propane) and 80% air enters a control volume operating at
steady state at location 1 with a mass flow rate of 5 kg/min,
as shown in Fig. P12.10. Air enters as a separate stream at 2
and dilutes the mixture. A single stream exits with a mole
fraction of propane of 3%. Assuming air has a molar analysis
of 21% O
2
and 79% N
2
, determine
(a) the molar flow rate of the entering air at 2, in kmol/min.
(b) the mass flow rate of oxygen in the exiting stream, in
kg/min.
20% C
3
H
8
, 80% Air
m
1
= 5 kg/min
3% C
3
H
8
,
97% Air
Air
(21% O
2
, 79% N
2
)
3
1
2
·
Fig. P12.10
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764 Chapter 12
Ideal Gas Mixture and Psychrometric Applications
Considering Constant-Composition Processes
12.11 A gas mixture in a piston–cylinder assembly consists of
2 lb of N
2
and 3 lb of He. Determine
(a) the composition in terms of mass fractions.
(b) the composition in terms of mole fractions.
(c) the heat transfer, in Btu, required to increase the mixture
temperature from 70 to 150
8F, while keeping the pressure
constant.
(d) the change in entropy of the mixture for the process of
part (c), in Btu/
8R.
For parts (c) and (d), use the ideal gas model with constant
specific heats.
12.12 Two kg of a mixture having an analysis on a mass basis
of 30% N
2
, 40% CO
2
, 30% O
2
is compressed adiabatically
from 1 bar, 300 K to 4 bar, 500 K. Determine
(a) the work, in kJ.
(b) the amount of entropy produced, in kJ/K.
12.13 As illustrated in Fig. P12.13, an ideal gas mixture in a
piston–cylinder assembly has a molar analysis of 30% carbon
dioxide (CO
2
) and 70% nitrogen (N
2
). The mixture is cooled
at constant pressure from 425 to 325 K. Assuming constant
specific heats evaluated at 375 K, determine the heat transfer
and the work, each in kJ per kg of mixture.
(a) Neglecting potential energy effects, determine the power
input to the compressor, in kW.
(b) If the compression is polytropic, evaluate the polytropic
exponent n and the exit pressure, in bar.
12.17 A mixture of 5 kg of H
2
and 4 kg of O
2
is compressed in
a piston–cylinder assembly in a polytropic process for which
n
5 1.6. The temperature increases from 40 to 2508C. Using
constant values for the specific heats, determine
(a) the heat transfer, in kJ.
(b) the entropy change, in kJ/K.
12.18 A gas turbine receives a mixture having the following molar
analysis: 10% CO
2
, 19% H
2
O, 71% N
2
at 720 K, 0.35 MPa
and a volumetric flow rate of 3.2 m
3
/s. The mixture exits the
turbine at 380 K, 0.11 MPa. For adiabatic operation with
negligible kinetic and potential energy effects, determine the
power developed at steady state, in kW.
12.19 A gas mixture at 1500 K with the molar analysis 10%
CO
2
, 20% H
2
O, 70% N
2
enters a waste-heat boiler operating
at steady state, and exits the boiler at 600 K. A separate
stream of saturated liquid water enters at 25 bar and exits
as saturated vapor with a negligible pressure drop. Ignoring
stray heat transfer and kinetic and potential energy changes,
determine the mass flow rate of the exiting saturated vapor,
in kg per kmol of gas mixture.
12.20 An equimolar mixture of helium and carbon dioxide
enters an insulated nozzle at 260
8F, 5 atm, 100 ft/s and
expands isentropically to a pressure of 3.24 atm. Determine
the temperature, in
8F, and the velocity, in ft/s, at the nozzle
exit. Neglect potential energy effects.
12.21 An equimolar mixture of helium (He) and carbon
dioxide (CO
2
) enters an insulated nozzle at 2608F, 5 atm,
100 ft/s and expands isentropically to a velocity of 1110 ft/s.
Determine the temperature, in
8F, and the pressure, in atm,
at the nozzle exit. Neglect potential energy effects.
12.22 A gas mixture having a molar analysis of 60% O
2
and
40% N
2
enters an insulated compressor operating at steady
state at 1 bar, 20
8C with a mass flow rate of 0.5 kg/s and is
compressed to 5.4 bar. Kinetic and potential energy effects
are negligible. For an isentropic compressor efficiency of
78%, determine
(a) the temperature at the exit, in
8C.
(b) the power required, in kW.
(c) the rate of entropy production, in kW/K.
12.23 A mixture having a molar analysis of 60% N
2
, 17% CO
2
,
and 17% H
2
O enters a turbine at 1000 K, 8 bar, with a mass
flow rate of 2 kg/s and expands isentropically to a pressure
of 1 bar. Ignoring kinetic and potential energy effects,
determine for steady-state operation
(a) the temperature at the exit, in K.
(b) the power developed by the turbine, in kW.
12.24 A mixture having a molar analysis of 60% N
2
and 40%
CO
2
enters an insulated compressor operating at steady
state at 1 bar, 30
8C with a mass flow rate of 1 kg/s and is
compressed to 3 bar, 147
8C. Neglecting kinetic and potential
energy effects, determine
x
CO
2
= 0.3
T
1
= 425K
T
2
= 325K
x
N
2
= 0.7
p = constan
t
Fig. P12.13
12.14 A mixture consisting of 0.6 lbmol of N
2
and 0.4 lbmol of
O
2
is compressed isothermally at 10008R from 1 to 3 atm.
During the process, there is energy transfer by heat from the
mixture to the surroundings, which are at 40
8F. For the
mixture, determine
(a) the work, in Btu.
(b) the heat transfer, in Btu.
(c) the amount of entropy produced, in Btu/
8R.
For an enlarged system that includes the mixture and enough
of its immediate surroundings that heat transfer occurs at
40
8F, determine the amount of entropy produced, in Btu/8R.
Discuss.
12.15 A mixture consisting of 2.8 kg of N
2
and 3.2 kg of O
2
is
compressed from 1 bar, 300 K to 2 bar, 600 K. During the
process there is heat transfer from the mixture to the
surroundings, which are at 27
8C. The work done on the mixture
is claimed to be 2300 kJ. Can this value be correct?
12.16 A mixture having a molar analysis of 50% CO
2
, 33.3%
CO, and 16.7% O
2
enters a compressor operating at steady
state at 37
8C, 1 bar, 40 m/s with a mass flow rate of 1 kg/s
and exits at 237
8C, 30 m/s. The rate of heat transfer from the
compressor to its surroundings is 5% of the power input.
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(a) the power required, in kW.
(b) the isentropic compressor efficiency.
(c) the rate of exergy destruction, in kW, for T
0
5 300 K.
12.25 An equimolar mixture of N
2
and CO
2
enters a heat
exchanger at
2408F, 500 lbf/in.
2
and exits at 5008F, 500 lbf/in.
2
The heat exchanger operates at steady state, and kinetic and
potential energy effects are negligible.
(a) Using the ideal gas mixture concepts of the present
chapter, determine the rate of heat transfer to the mixture,
in Btu per lbmol of mixture flowing.
(b) Compare with the value of the heat transfer determined
using the generalized enthalpy chart (Fig. A-4), together with
Kay’s rule (see Sec. 11.8).
12.26 Natural gas having a molar analysis of 60% methane
(CH
4
) and 40% ethane (C
2
H
6
) enters a compressor at 340 K,
6 bar and is compressed isothermally without internal
irreversibilities to 20 bar. The compressor operates at
steady state, and kinetic and potential energy effects are
negligible.
(a) Assuming ideal gas behavior, determine for the compressor
the work and heat transfer, each in kJ per kmol of mixture
flowing.
(b) Compare with the values for work and heat transfer,
respectively, determined assuming ideal solution behavior
(Sec. 11.9.5). For the pure components at 340 K:
h (kJ/kg) s (kJ/kg ? K)
6 bar 20 bar 6 bar 20 bar
Methane 715.33 704.40 10.9763 10.3275
Ethane 462.39 439.13 7.3493 6.9680
Forming Mixtures
12.27 One kilogram of argon at 278C, 1 bar is contained in a
rigid tank connected by a valve to another rigid tank
containing 0.8 kg of O
2
at 1278C, 5 bar. The valve is opened,
and the gases are allowed to mix, achieving an equilibrium
state at 87
8C. Determine
(a) the volume of each tank, in m
3
.
(b) the final pressure, in bar.
(c) the heat transfer to or from the gases during the process,
in kJ.
(d) the entropy change of each gas, in kJ/K.
12.28 Using the ideal gas model with constant specific heats,
determine the mixture temperature, in K, for each of two
cases:
(a) Initially, 0.6 kmol of O
2
at 500 K is separated by a
partition from 0.4 kmol of H
2
at 300 K in a rigid insulated
vessel. The partition is removed and the gases mix to obtain
a final equilibrium state.
(b) Oxygen (O
2
) at 500 K and a molar flow rate of 0.6 kmol/s
enters an insulated control volume operating at steady
state and mixes with H
2
entering as a separate stream at
300 K and a molar flow rate of 0.4 kmol/s. A single mixed
stream exits. Kinetic and potential energy effects can be
ignored.
12.29 A system consists initially of n
A
moles of gas A at
pressure p and temperature T and n
B
moles of gas B separate
from gas A but at the same pressure and temperature. The
gases are allowed to mix with no heat or work interactions
with the surroundings. The final equilibrium pressure and
temperature are p and T, respectively, and the mixing occurs
with no change in total volume.
(a) Assuming ideal gas behavior, obtain an expression for
the entropy produced in terms of
R, n
A
, and n
B
.
(b) Using the result of part (a), demonstrate that the entropy
produced has a positive value.
(c) Would entropy be produced when samples of the same
gas at the same temperature and pressure mix? Explain.
12.30 Determine the amount of entropy produced, in Btu/
8R,
when 1 lb of H
2
at 708F, 1 atm is allowed to mix adiabatically
to a final equilibrium state with 20 lb of (a) CO
2
and (b) H
2
,
initially at the same temperature and pressure.
12.31 Two kg of N
2
at 450 K, 7 bar is contained in a rigid tank
connected by a valve to another rigid tank holding 1 kg of
O
2
at 300 K, 3 bar. The valve is opened and gases are
allowed to mix, achieving an equilibrium state at 370 K.
Determine
(a) the volume of each tank, in m
3
.
(b) the final pressure, in bar.
(c) the heat transfer to or from the gases during the process,
in kJ.
(d) the entropy change of each gas, in kJ/K.
12.32 An insulated tank having a total volume of 60 ft
3
is
divided into two compartments. Initially one compartment
having a volume of 20 ft
3
contains 4 lb of carbon monoxide
(CO) at 500
8F and the other contains 0.8 lb of helium (He)
at 60
8F. The gases are allowed to mix until an equilibrium
state is attained. Determine
(a) the final temperature, in
8F.
(b) the final pressure, in lbf/in.
2
(c) the exergy destruction, in Btu, for T
0
5 608F.
12.33 A rigid insulated tank has two compartments. Initially
one compartment is filled with 2.0 lbmol of argon at 150
8F,
50 lbf/in.
2
and the other is filled with 0.7 lbmol of helium at
0
8F, 15 lbf/in.
2
The gases are allowed to mix until an equilibrium
state is attained. Determine
(a) the final temperature, in
8F.
(b) the final pressure, in atm.
(c) the amount of entropy produced, in Btu/
8R.
12.34 A rigid insulated tank has two compartments. Initially
one contains 0.5 kmol of carbon dioxide (CO
2
) at 278C,
2 bar and the other contains 1 kmol of oxygen (O
2
) at 1528C,
5 bar. The gases are allowed to mix while 500 kJ of energy
are added by electrical work. Determine
(a) the final temperature, in
8C.
(b) the final pressure, in bar.
(c) the change in exergy, in kJ, for T
0
5 208C.
(d) the exergy destruction, in kJ.
12.35 Air at 40
8C, 1 atm and a volumetric flow rate of 50 m
3
/min
enters an insulated control volume operating at steady state
and mixes with helium entering as a separate stream at 100
8C,
1 atm and a volumetric flow rate of 20 m
3
/min. A single mixed
Problems: Developing Engineering Skills 765
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766 Chapter 12
Ideal Gas Mixture and Psychrometric Applications
stream exits at 1 atm. Ignoring kinetic and potential energy
effects, determine for the control volume
(a) the temperature of the exiting mixture, in 8C.
(b) the rate of entropy production, in kW/K.
12.36 Argon (Ar), at 300 K, 1 bar with a mass flow rate of
1 kg/s enters the insulated mixing chamber shown in Fig.
P12.36 and mixes with carbon dioxide (CO
2
) entering as a
separate stream at 575 K, 1 bar with a mass flow rate of
0.5 kg/s. The mixture exits at 1 bar. Assume ideal gas behavior
with k
5 1.67 for Ar and k 5 1.25 for CO
2
. For steady-state
operation, determine
(a) the molar analysis of the exiting mixture.
(b) the temperature of the exiting mixture, in K.
(c) the rate of entropy production, in kW/K.
(a) the mass and molar analyses of the mixture.
(b) the temperature of the mixture at the exit of the valve, in
8F.
(c) the rates of exergy destruction for the mixing chamber
and the valve, each in Btu per lb of mixture, for T
0
5 408F.
Kinetic and potential energy effects can be ignored.
12.40 Helium at 400 K, 1 bar enters an insulated mixing
chamber operating at steady state, where it mixes with argon
entering at 300 K, 1 bar. The mixture exits at a pressure of
1 bar. If the argon mass flow rate is x times that of helium,
plot versus x
(a) the exit temperature, in K.
(b) the rate of exergy destruction within the chamber, in kJ
per kg of helium entering.
Kinetic and potential energy effects can be ignored. Let
T
0
5
300
K.
12.41 Hydrogen (H
2
) at 778C, 4 bar enters an insulated
chamber at steady state, where it mixes with nitrogen (N
2
)
entering as a separate stream at 277
8C, 4 bar. The mixture exits
at 3.8 bar with the molar analysis 75% H
2
, 25% N
2
. Kinetic
and potential energy effects can be ignored. Determine
(a) the temperature of the exiting mixture, in 8C.
(b) the rate at which entropy is produced, in kJ/K per kmol
of mixture exiting.
12.42 An insulated, rigid tank initially contains 1 kmol of
argon (Ar) at 300 K, 1 bar. The tank is connected by a valve
to a large vessel containing nitrogen (N
2
) at 500 K, 4 bar. A
quantity of nitrogen flows into the tank, forming an argon-
nitrogen mixture at temperature T and pressure p. Plot T, in
K, and p, in bar, versus the amount of N
2
within the tank, in
kmol.
12.43 A stream of oxygen (O
2
) at 1008F, 2 atm enters an
insulated chamber at steady state with a mass flow rate of
1 lb/min and mixes with a stream of air entering separately at
200
8F, 1.5 atm with a mass flow rate of 2 lb/min. The mixture
exits at a pressure of 1 atm. Kinetic and potential energy
effects can be ignored. On the basis of constant specific heats,
determine
(a) the temperature of the exiting mixture, in
8F.
(b) the rate of exergy destruction, in Btu/min, for T
0
5 408F.
12.44 A device is being designed to separate into components
a natural gas consisting of CH
4
and C
2
H
6
in which the mole
fraction of C
2
H
6
, denoted by y, may vary from 0.05 to 0.50.
The device will receive natural gas at 20
8C, 1 atm with a
volumetric flow rate of 100 m
3
/s. Separate streams of CH
4
and C
2
H
6
will exit, each at 208C, 1 atm. Heat transfer
between the device and its surroundings occurs at 20
8C.
Ignoring kinetic and potential energy effects, plot versus y
the minimum theoretical work input required at steady
state, in kW.
Exploring Psychrometric Principles
12.45 A water pipe at 58C runs above ground between two
buildings. The surrounding air is at 35
8C. What is the maximum
relative humidity the air can have before condensation occurs
on the pipe?
Carbon dioxide (CO
2
)
T
2
= 575 K
p
2
= 1 bar
m
2
= 0.5 kg/s
Argon (Ar)
T
1
= 300 K
p
1
= 1 bar
m
1
= 1 kg/s
insulation
mixture
exiting
p
3
= 1 bar
2
31
·
·
Fig. P12.36
12.37 Nitrogen (N
2
) at 1208F, 20 lbf/in.
2
and a volumetric flow
rate of 300 ft
3
/min enters an insulated control volume
operating at steady state and mixes with oxygen (O
2
) entering
as a separate stream at 200
8F, 20 lbf/in.
2
and a mass flow rate
of 50 lb/min. A single mixed stream exits at 17 lbf/in.
2
Kinetic
and potential energy effects can be ignored. Using the ideal
gas model with constant specific heats, determine for the
control volume
(a) the temperature of the exiting mixture, in
8F.
(b) the rate of exergy destruction, in Btu/min, for T
0
5 408F.
12.38 Air at 77
8C, 1 bar, and a molar flow rate of 0.1 kmol/s
enters an insulated mixing chamber operating at steady state
and mixes with water vapor entering at 277
8C, 1 bar, and a
molar flow rate of 0.3 kmol/s. The mixture exits at 1 bar.
Kinetic and potential energy effects can be ignored. For the
chamber, determine
(a) the temperature of the exiting mixture, in
8C.
(b) the rate of entropy production, in kW/K.
12.39 A gas mixture required in an industrial process is prepared
by first allowing carbon monoxide (CO) at 80
8F, 18 lbf/in.
2
to
enter an insulated mixing chamber operating at steady state
and mix with argon (Ar) entering at 380
8F, 18 lbf/in.
2
The
mixture exits the chamber at 140
8F, 16 lbf/in.
2
and is then
allowed to expand in a throttling process through a valve to
14.7 lbf/in.
2
Determine
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12.46 The inside temperature of a wall in a dwelling is 168C. If
the air in the room is at 218C, what is the maximum relative
humidity the air can have before condensation occurs on the
wall?
12.47 A lecture hall having a volume of 10
6
ft
3
contains air at
808F, 1 atm, and a humidity ratio of 0.01 lb of water vapor
per lb of dry air. Determine
(a) the relative humidity.
(b) the dew point temperature, in 8F.
(c) the mass of water vapor contained in the room, in lb.
12.48 A large room contains moist air at 308C, 102 kPa. The
partial pressure of water vapor is 1.5 kPa. Determine
(a) the relative humidity.
(b) the humidity ratio, in kg(vapor) per kg(dry air).
(c) the dew point temperature, in 8C.
(d) the mass of dry air, in kg, if the mass of water vapor is
10 kg.
12.49 To what temperature, in 8C, must moist air with a humidity
ratio of 5 3 10
23
kg(vapor) per kg(dry air) be cooled at a
constant pressure of 2 bar to become saturated moist air?
12.50 A fixed amount of moist air initially at 1 bar and a
relative humidity of 60% is compressed isothermally until
condensation of water begins. Determine the pressure of the
mixture at the onset of condensation, in bar. Repeat if the
initial relative humidity is 90%.
12.51 As shown in Fig. P12.51, moist air at 308C, 2 bar, and
50% relative humidity enters a heat exchanger operating at
steady state with a mass flow rate of 600 kg/h and is cooled
at constant pressure to 208C. Ignoring kinetic and potential
energy effects, determine the rate of heat transfer from the
moist air stream, in kJ/h.
Fig. P12.47
m
1
= 600 kg/h
·
T
1
= 30°C
p
1
= 2 bar
f
1
= 50%
T
2
= 20°C
p
2
= 2 bar
1
2
Fig. P12.51
12.52 One pound of moist air initially at 808F, 1 atm, 50% relative
humidity is compressed isothermally to 3 atm. If condensation
occurs, determine the amount of water condensed, in lb. If
there is no condensation, determine the final relative humidity.
12.53 A vessel whose volume is 0.5 m
3
initially contains dry
air at 0.2 MPa and 208C. Water is added to the vessel until
the air is saturated at 208C. Determine the
(a) mass of water added, in kg.
(b) final pressure in the vessel, in bar.
12.54 Wet grain at 208C containing 40% moisture by mass
enters a dryer operating at steady state. Dry air enters the
dryer at 908C, 1 atm at a rate of 15 kg per kg of wet grain
entering. Moist air exits the dryer at 388C, 1 atm, and 52%
relative humidity. For the grain exiting the dryer, determine
the percent moisture by mass.
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768 Chapter 12
Ideal Gas Mixture and Psychrometric Applications
12.55 Figure P12.55 shows a spray dryer operating at steady
state. The mixture of liquid water and suspended solid
particles entering through the spray head contains 30% solid
matter by mass. Dry air enters at 1778C, 1 atm, and moist air
exits at 858C, 1 atm, and 21% relative humidity with a
volumetric flow rate of 310 m
3
/min. The dried particles exit
separately. Determine
(a) the volumetric flow rate of the entering dry air, in m
3
/min.
(b) the rate that dried particles exit, in kg/min.
is compressed to 100 lbf/in.
2
The isentropic compressor
efficiency is h
c
.
(a) For h
c
5 0.8, determine the temperature, in 8R, of the
exiting air, and the work input required and the exergy destruction,
each in Btu per lb of dry air flowing. Let T
0
5 5208R.
(b) Plot each of the quantities determined in part (a) versus
h
c
ranging from 0.7 to 1.0.
12.63 Air at 358C, 3 bar, 30% relative humidity, and a velocity
of 50 m/s expands isentropically through a nozzle. Determine
the lowest exit pressure, in bar, that can be attained without
condensation. For this exit pressure, determine the exit
velocity, in m/s. The nozzle operates at steady state and
without significant potential energy effects.
12.64 A closed, rigid tank having a volume of 1 m
3
contains a
mixture of carbon dioxide (CO
2
) and water vapor at 758C. The
respective masses are 12.3 kg of carbon dioxide and 0.05 kg of
water vapor. If the tank contents are cooled to 208C, determine
the heat transfer, in kJ, assuming ideal gas behavior.
12.65 Gaseous combustion products at 8008F, 1 atm and a
volumetric flow rate of 5 ft
3
/s enter a counterflow heat
exchanger operating at steady state and exit at 2008F. The
molar analysis of the products is 7.1% CO
2
, 4.3% O
2
, 14.3%
H
2
O, 74.3% N
2
. A separate moist-air stream enters the heat
exchanger at 608F, 1 atm, and 30% relative humidity and
exits at 1008F. Determine the mass flow rate of the entering
moist-air stream, in lb/s. The pressure drops of the two
streams can be ignored, as can stray heat transfer and kinetic
and potential energy effects.
12.66 Air enters a compressor operating at steady state at 508C,
0.9 bar, 70% relative humidity with a volumetric flow rate of
0.8 m
3
/s. The moist air exits the compressor at 1958C, 1.5 bar.
Assuming the compressor is well insulated, determine
(a) the relative humidity at the exit.
(b) the power input, in kW.
(c) the rate of entropy production, in kW/K.
12.67 Moist air enters a control volume operating at steady
state with a volumetric flow rate of 3500 ft
3
/min. The moist
air enters at 1208F, 1.2 atm, and 75% relative humidity. Heat
transfer occurs through a surface maintained at 508F.
Saturated moist air and condensate exit the control volume,
each at 688F. Assuming W
#
cv
5 0, and kinetic and potential
energy effects are negligible, determine
(a) the mass flow rate of condensate, in lb/min.
(b) the rate of heat transfer, in Btu/min.
(c) the rate of entropy production, in Btu/8R ? min.
(d) the rate of exergy destruction, in Btu/min, for T
0
5 508F.
12.68 Moist air at 158C, 1.3 atm, 63% relative humidity and a
volumetric flow rate of 770 m
3
/h enters a control volume at
steady state and flows along a surface maintained at 1878C,
through which heat transfer occurs. Liquid water at 158C is
injected at a rate of 7 kg/h and evaporates into the flowing
stream. For the control volume, W
#
cv
5 0, and kinetic and
potential energy effects are negligible. If moist air exits at
458C, 1.3 atm, determine
(a) the rate of heat transfer, in kW.
(b) the rate of entropy production, in kW/K.
Solid–liquid
mixture
70% liquid
30% solid
Dry air,
177°C,
1 atm
Dried
particles
φ
Moist air
310 m
3
/min,
85°C,
1 atm,
= 21%
Fig. P12.55
12.56 A mixture of nitrogen and water vapor at 2008F, 1 atm has
the molar analysis 80% N
2
, 20% water vapor. If the mixture
is cooled at constant pressure, determine the temperature, in
8F, at which water vapor begins to condense.
12.57 A system consisting initially of 0.5 m
3
of air at 358C, 1 bar,
and 70% relative humidity is cooled at constant pressure to
298C. Determine the work and heat transfer for the process,
each in kJ.
12.58 Moist air initially at 1258C, 4 bar, and 50% relative
humidity is contained in a 2.5-m
3
closed, rigid tank. The tank
contents are cooled. Determine the heat transfer, in kJ, if the
final temperature in the tank is (a) 1108C, (b) 308C.
12.59 A closed, rigid tank initially contains 0.5 m
3
of moist air
in equilibrium with 0.1 m
3
of liquid water at 808C and 0.1 MPa.
If the tank contents are heated to 2008C, determine
(a) the final pressure, in MPa.
(b) the heat transfer, in kJ.
12.60 A closed, rigid cylindrical tank having a height of 6 ft and
a diameter of 2 ft initially contains air at 3008F, 80 lbf/in.
2
,
and 10% relative humidity. If the tank contents are cooled
to 1708F, determine
(a) if condensation occurs.
(b) the final pressure, in lbf/in.
2
(c) the heat transfer, in Btu.
(d) the change in entropy, in Btu/8R.
12.61 Gaseous combustion products with the molar analysis of
15% CO
2
, 25% H
2
O, 60% N
2
enter an engine’s exhaust pipe
at 11008F, 1 atm and are cooled as they pass through the
pipe, to 1258F, 1 atm. Determine the heat transfer at steady
state, in Btu per lb of entering mixture.
12.62 Air at 608F, 14.7 lbf/in.
2
, and 75% relative humidity
enters an insulated compressor operating at steady state and
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12.69 Using Eq. 12.48, determine the humidity ratio and
relative humidity for each case below.
(a) The dry-bulb and wet-bulb temperatures in a conference
room at 1 atm are 24 and 168C, respectively.
(b) The dry-bulb and wet-bulb temperatures in a factory
space at 1 atm are 75 and 608F, respectively.
(c) Repeat parts (a) and (b) using the psychrometric chart.
(d) Repeat parts (a) and (b) using Interactive Thermody-
namics: IT.
12.70 Using the psychrometric chart, Fig. A-9, determine
(a) the relative humidity, the humidity ratio, and the specific
enthalpy of the mixture, in kJ per kg of dry air, corresponding
to dry-bulb and wet-bulb temperatures of 30 and 258C,
respectively.
(b) the humidity ratio, mixture specific enthalpy, and wet-
bulb temperature corresponding to a dry-bulb temperature
of 308C and 60% relative humidity.
(c) the dew point temperature corresponding to dry-bulb
and wet-bulb temperatures of 30 and 208C, respectively.
(d) Repeat parts (a)–(c) using Interactive Thermodynamics: IT.
12.71 Using the psychrometric chart, Fig. A-9E, determine
(a) the dew point temperature corresponding to dry-bulb
and wet-bulb temperatures of 80 and 708F, respectively.
(b) the humidity ratio, the specific enthalpy of the mixture, in
Btu per lb of dry air, and the wet-bulb temperature corres-
ponding to a dry-bulb temperature of 808F and 70% relative
humidity.
(c) the relative humidity, humidity ratio, and mixture specific
enthalpy corresponding to dry-bulb and wet-bulb temperatures
of 80 and 658F, respectively.
(d) Repeat parts (a)–(c) using Interactive Thermodynamics: IT.
12.72 A fixed amount of air initially at 528C, 1 atm, and 10%
relative humidity is cooled at constant pressure to 158C. Using
the psychrometric chart, determine whether condensation
occurs. If so, evaluate the amount of water condensed, in kg
per kg of dry air. If there is no condensation, determine the
relative humidity at the final state.
12.73 A fan within an insulated duct delivers moist air at the
duct exit at 358C, 50% relative humidity, and a volumetric
flow rate of 0.4 m
3
/s. At steady state, the power input to the
fan is 1.7 kW. The pressure in the duct is nearly 1 atm
throughout. Using the psychrometric chart, determine the
temperature, in 8C, and relative humidity at the duct inlet.
12.74 The mixture enthalpy per unit mass of dry air, in kJ/kg(a),
represented on Fig. A-9 can be approximated closely from
the expression
H
m
a
5 1.005 T18C21 v32501.7 1 1.82 T18C24
When using Fig. A-9E, the corresponding expression, in
Btu/lb(a), is
H
m
a
5 0.24 T18F21 v31061 1 0.444 T18F24
Noting all significant assumptions, develop the above
expressions.
Considering Air-Conditioning Applications
12.75 Each case listed gives the dry-bulb temperature and
relative humidity of the moist-air stream entering an air-
conditioning system: (a) 308C, 40%, (b) 178C, 60%, (c) 258C,
70%, (d) 158C, 40%, (e) 278C, 30%. The condition of the
moist-air stream exiting the system must satisfy these
constraints: 22 # T
db
# 278C, 40 # f # 60%. In each case,
develop a schematic of equipment and processes from Sec.
12.8 that would achieve the desired result. Sketch the
processes on a psychrometric chart.
12.76 Moist air enters an air-conditioning system as shown in
Fig. 12.11 at 268C, f 5 80% and a volumetric flow rate of
0.47 m
3
/s. At the exit of the heating section the moist air is at
268C, f 5 50%. For operation at steady state, and neglecting
kinetic and potential energy effects, determine
(a) the rate energy is removed by heat transfer in the
dehumidifier section, in tons.
(b) the rate energy is added by heat transfer in the heating
section, in kW.
12.77 Air at 1 atm with dry-bulb and wet-bulb temperatures
of 82 and 688F, respectively, enters a duct with a mass flow
rate of 10 lb/min and is cooled at essentially constant pressure
to 628F. For steady-state operation and negligible kinetic and
potential energy effects, determine
(a) the relative humidity at the duct inlet.
(b) the rate of heat transfer, in Btu/min.
(c) Check your answers using data from the psychrometric
chart.
(d) Check your answers using Interactive Thermodynamics: IT.
12.78 Air at 358C, 1 atm, and 50% relative humidity enters a
dehumidifier operating at steady state. Saturated moist air
and condensate exit in separate streams, each at 158C.
Neglecting kinetic and potential energy effects, determine
(a) the heat transfer from the moist air, in kJ per kg of dry air.
(b) the amount of water condensed, in kg per kg of dry air.
(c) Check your answers using data from the psychrometric
chart.
(d) Check your answers using Interactive Thermodynamics: IT.
12.79 Air at 808F, 1 atm, and 70% relative humidity enters a
dehumidifier operating at steady state with a mass flow rate
of 1 lb/s. Saturated moist air and condensate exit in separate
streams, each at 508F. Neglecting kinetic and potential energy
effects, determine
(a) the rate of heat transfer from the moist air, in tons.
(b) the rate water is condensed, in lb/s.
(c) Check your answers using data from the psychrometric
chart.
(d) Check your answers using Interactive Thermodynamics: IT.
12.80 Moist air at 288C, 1 bar, and 50% relative humidity flows
through a duct operating at steady state. The air is cooled at
essentially constant pressure and exits at 208C. Determine
the heat transfer rate, in kJ per kg of dry air flowing, and
the relative humidity at the exit.
12.81 An air conditioner operating at steady state takes in
moist air at 288C, 1 bar, and 70% relative humidity. The moist
air first passes over a cooling coil in the dehumidifier unit and
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770 Chapter 12
Ideal Gas Mixture and Psychrometric Applications
some water vapor is condensed. The rate of heat transfer
between the moist air and the cooling coil is 11 tons. Saturated
moist air and condensate streams exit the dehumidifier unit
at the same temperature. The moist air then passes through a
heating unit, exiting at 248C, 1 bar, and 40% relative humidity.
Neglecting kinetic and potential energy effects, determine
(a) the temperature of the moist air exiting the dehumidifier
unit, in 8C.
(b) the volumetric flow rate of the air entering the air
conditioner, in m
3
/min.
(c) the rate water is condensed, in kg/min.
(d) the rate of heat transfer to the air passing through the
heating unit, in kW.
12.82 Figure P12.82 shows a compressor followed by an
aftercooler. Atmospheric air at 14.7 lbf/in.
2
, 908F, and 75%
relative humidity enters the compressor with a volumetric
flow rate of 100 ft
3
/min. The compressor power input is 15 hp.
The moist air exiting the compressor at 100 lbf/in.
2
, 4008F
flows through the aftercooler, where it is cooled at constant
pressure, exiting saturated at 1008F. Condensate also exits
the aftercooler at 1008F. For steady-state operation and
negligible kinetic and potential energy effects, determine
(a) the rate of heat transfer from the compressor to its
surroundings, in Btu/min.
(b) the mass flow rate of the condensate, in lb/min.
(c) the rate of heat transfer from the moist air to the refrigerant
circulating in the cooling coil, in tons of refrigeration.
12.84 An air-conditioning system consists of a spray section
followed by a reheater. Moist air at 328C and f 5 77% enters
the system and passes through a water spray, leaving the spray
section cooled and saturated with water. The moist air is then
heated to 258C and f 5 45% with no change in the amount of
water vapor present. For operation at steady state, determine
(a) the temperature of the moist air leaving the spray section,
in 8C.
(b) the change
m
#
the amount of water vapor contained in the
moist air passing through the system, in kg per kg of dry air.
Locate the principal states on a psychrometric chart.
12.85 Moist air at 958F, 1 atm, and a relative humidity of 30%
enters a steam-spray humidification device operating at steady
state with a volumetric flow rate of 5700 ft
3
/min. Saturated
water vapor at 2308F is sprayed into the moist air, which then
exits the device at a relative humidity of 50%. Heat transfer
between the device and its surroundings can be ignored, as
can kinetic and potential energy effects. Determine
(a) the temperature of the exiting moist air stream, in 8F.
(b) the rate at which steam is injected, in lb/min.
12.86 For the steam-spray humidifier in Problem 12.85, determine
the exergy destruction rate, in Btu/min. Let T
0
5 958F.
12.87 Outside air at 508F, 1 atm, and 40% relative humidity
enters an air conditioner operating at steady state with a mass
flow rate of 3.3 lb/s. The air is first heated at essentially constant
pressure to 908F. Liquid water at 608F is then injected, bringing
the air to 708F, 1 atm. Determine
(a) the rate of heat transfer to the air passing through the
heating section, in Btu/s.
(b) the rate water is injected, in lb/s.
(c) the relative humidity at the exit of the humidification
section.
Kinetic and potential energy effects can be ignored.
12.88 Moist air at 278C, 1 atm, and 50% relative humidity enters
an evaporative cooling unit operating at steady state consisting
of a heating section followed by a soaked pad evaporative
cooler operating adiabatically. The air passing through the
heating section is heated to 458C. Next, the air passes through
a soaked pad exiting with 50% relative humidity. Using data
from the psychrometric chart, determine
(a) the humidity ratio of the entering moist air mixture, in
kg(vapor) per kg(dry air).
(b) the rate of heat transfer to the moist air passing through
the heating section, in kJ per kg of mixture.
(c) the humidity ratio and temperature, in 8C, at the exit of
the evaporative cooling section.
12.89 In an industrial dryer operating at steady state, atmospheric
air at 808F, 1 atm, and 65% relative humidity is first heated to
2808F at constant pressure. The heated air is then allowed to
pass over the materials being dried, exiting the dryer at 1508F,
1 atm, and 30% relative humidity. If moisture is to be removed
from the materials at a rate of 2700 lb/h, determine
(a) the mass flow rate of dry air required, in lb/h.
(b) the rate of heat transfer to the air as it passes through
the heating section, in Btu/h.
Neglect kinetic and potential energy effects.
Compressor
Aftercooler
Refrigerant circulating
in a cooling coil
3
2
1
Air-water vapor
mixture
Saturated
liquid at 100°F
Power in
15 hp
Heat
transfer to
the surroundings
φ
T
3
= 100°F
3
= 100%
p
3
= 100 lbf/in.
2
T
2
= 400°F
p
3
= 100 lbf/in.
2
Atmospheric air,
100 ft
3
/min at T
1
= 90°F,
1
= 75%, p
1
= 14.7 lbf/in.
2
φ
Fig. P12.82
12.83 Outside air at 508F, 1 atm, and 40% relative humidity
enters an air-conditioning device operating at steady state.
Liquid water is injected at 458F and a moist air stream exits
with a volumetric flow rate of 1000 ft
3
/min at 908F, 1 atm and
a relative humidity of 40%. Neglecting kinetic and potential
energy effects, determine
(a) the rate water is injected, in lb/min.
(b) the rate of heat transfer to the moist air, in Btu/h.
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12.90 At steady state, moist air is to be supplied to a classroom
at a specified volumetric flow rate and temperature T. Air
is removed from the classroom in a separate stream at a
temperature of 278C and 50% relative humidity. Moisture is
added to the air in the room from the occupants at a rate
of 4.5 kg/h. The moisture can be regarded as saturated vapor
at 338C. Heat transfer into the occupied space from all
sources is estimated to occur at a rate of 34,000 kJ/h. The
pressure remains uniform at 1 atm.
(a) For a supply air volumetric flow rate of 40 m
3
/min, determine
the supply air temperature T, in 8C, and the relative humidity.
(b) Plot the supply air temperature, in 8C, and relative
humidity, each versus the supply air volumetric flow rate
ranging from 35 to 90 m
3
/min.
12.91 At steady state, a device for heating and humidifying air
has 250 ft
3
/min of air at 408F, 1 atm, and 80% relative humidity
entering at one location, 1000 ft
3
/min of air at 608F, 1 atm,
and 80% relative humidity entering at another location, and
liquid water injected at 558F. A single moist air stream exits
at 858F, 1 atm, and 35% relative humidity. Determine
(a) the rate of heat transfer to the device, in Btu/min.
(b) the rate at which liquid water is injected, in lb/min.
Neglect kinetic and potential energy effects.
12.92 Air at 358C, 1 bar, and 10% relative humidity enters an
evaporative cooler operating at steady state. The volumetric
flow rate of the incoming air is 50 m
3
/min. Liquid water at
208C enters the cooler and fully evaporates. Moist air exits
the cooler at 258C, 1 bar. If there is no significant heat transfer
between the device and its surroundings, determine
(a) the rate at which liquid enters, in kg/min.
(b) the relative humidity at the exit.
(c) the rate of exergy destruction, in kJ/min, for T
0
5 208C.
Neglect kinetic and potential energy effects.
12.93 Using Eqs. 12.56, show that
m
#
a1
m
#
a2
5
v
3
2 v
2
v
1
2 v
3
5
1h
a3
1 v
3
h
g3
22 1h
a2
1 v
2
h
g2
2
1h
a1
1 v
1
h
g1
22 1h
a3
1 v
3
h
g3
2
Employ this relation to demonstrate on a psychrometric chart
that state 3 of the mixture lies on a straight line connecting
the initial states of the two streams before mixing.
12.94 For the adiabatic mixing process in Example 12.14, plot
the exit temperature, in 8C, versus the volumetric flow rate
of stream 2 ranging from 0 to 1400 m
3
/min. Discuss the plot
as (AV)
2
goes to zero and as (AV)
2
becomes large.
12.95 A stream consisting of 35 m
3
/min of moist air at 148C, 1
atm, 80% relative humidity mixes adiabatically with a stream
consisting of 80 m
3
/min of moist air at 408C, 1 atm, 40%
relative humidity, giving a single mixed stream at 1 atm.
Using the psychrometric chart together with the procedure of
Problem 12.93, determine the relative humidity and temperature,
in 8C, of the exiting stream.
12.96 At steady state, a stream of air at 608F, 1 atm, 30%
relative humidity is mixed adiabatically with a stream of air at
908F, 1 atm, 70% relative humidity. The mass flow rate of the
higher-temperature stream is twice that of the other stream. A
single mixed stream exits at 1 atm. Using the result of Problem
12.74, determine for the exiting stream
(a) the temperature, in 8F.
(b) the relative humidity.
Neglect kinetic and potential energy effects.
12.97 At steady state, moist air at 428C, 1 atm, 30% relative
humidity is mixed adiabatically with a second moist air
stream entering at 1 atm. The mass flow rates of the two
streams are the same. A single mixed stream exits at 298C,
1 atm, 40% relative humidity with a mass flow rate of 2 kg/s.
Kinetic and potential energy effects are negligible. For the
second entering moist air stream, determine, using data from
the psychrometric chart,
(a) the relative humidity.
(b) the temperature, in 8C.
12.98 Figure P12.98 shows two options for conditioning
atmospheric air at steady state. In each case, air enters at
158C, 1 atm, and 20% relative humidity with a volumetric
flow rate of 150 m
3
/min and exits at 308C, 1 atm, and 40%
Electric resistor
+–
Air
T
1
= 15°C = 288 K
p
1
= 1 atm
f
1
= 20%
(AV)
1
= 150 m
3
/min
T
2
= 30°C
p
2
= 1 atm
f
2
= 40%
12
Option A
Saturated water vapor at 1 atm
3
Air
T
1
= 15°C = 288 K
p
1
= 1 atm
f
1
= 20%
(AV)
1
= 150 m
3
/min
T
2
= 30°C
p
2
= 1 atm
f
2
= 40%
12
Option B
Liquid water at 20°C
3
Fig. P12.98
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772 Chapter 12 Ideal Gas Mixture and Psychrometric Applications
relative humidity. One method conditions the air by injecting
saturated water vapor at 1 atm. The other method allows the
entering air to pass through a soaked pad replenished by liquid
water entering at 208C. The moist air stream is then heated
by an electric resistor. For T
0
5 288 K, which of the two
options is preferable from the standpoint of having less exergy
destruction? Discuss.
12.99 Air at 308C, 1 bar, 50% relative humidity enters an
insulated chamber operating at steady state with a mass flow
rate of 3 kg/min and mixes with a saturated moist air stream
entering at 58C, 1 bar with a mass flow rate of 5 kg/min. A
single mixed stream exits at 1 bar. Determine
(a) the relative humidity and temperature, in 8C, of the exiting
stream.
(b) the rate of exergy destruction, in kW, for T
0
5 208C.
Neglect kinetic and potential energy effects.
12.100 Moist air enters a dehumidifier at 808F, 1 atm, and f 5 60%
and exits at 588F, 1 atm, and f 5 90% with a volumetric flow rate
of 10,000 ft
3
/min. The stream then mixes adiabatically with a
moist air stream at 958F, 1 atm, and f 5 47% having a volumetric
flow rate of 2000 ft
3
/min. A single moist-air stream exits the
mixing chamber. Stray heat transfer and kinetic and potential
energy effects can be ignored. Determine at steady state
(a) the rate water is removed from the moist air passing
through the dehumidifier, in lb/h.
(b) the temperature, in 8F, and the relative humidity of the
moist air at the mixing chamber exit.
12.101 A stream of air (stream 1) at 608F, 1 atm, 30% relative
humidity is mixed adiabatically with a stream of air (stream 2) at
908F, 1 atm, 80% relative humidity. A single stream (stream 3)
exits the mixing chamber at temperature T
3
and 1 atm.
Assume steady state and ignore kinetic and potential energy
effects. Letting r denote the ratio of dry air mass flow rates
m
#
a1
/
m
#
a2
(a) determine T
3
, in 8F, for r 5 2.
(b) plot T
3
, in 8F, versus r ranging from 0 to 10.
12.102 Figure P12.102 shows the adiabatic mixing of two
moist-air streams at steady state. Kinetic and potential
energy effects are negligible. Determine the rate of exergy
destruction, in Btu/min, for T
0
5 958F.
Analyzing Cooling Towers
12.103 In the condenser of a power plant, energy is discharged
by heat transfer at a rate of 836 MW to cooling water that
exits the condenser at 408C into a cooling tower. Cooled
water at 208C is returned to the condenser. Atmospheric air
enters the tower at 258C, 1 atm, 35% relative humidity. Moist
air exits at 358C, 1 atm, 90% relative humidity. Makeup
water is supplied at 208C. For operation at steady state,
determine the mass flow rate, in kg/s, of
(a) the entering atmospheric air.
(b) the makeup water.
Ignore kinetic and potential energy effects.
12.104 Liquid water at 1008F enters a cooling tower operating
at steady state, and cooled water exits the tower at 808F.
Data for the various streams entering and exiting the tower
are shown in Fig. P12.104. No makeup water is provided.
Determine
(a) the mass flow rate of the entering atmospheric air, in lb/h.
(b) the rate at which water evaporates, in lb/h.
(c) the mass flow rate of the exiting liquid stream, in lb/h.
3
1
2
p
= 1 atm
(AV)
T
p
= 2770 ft
3
/min
= 80°F
= 1 atm
= 50%
φ
(AV)
T
p
T
wb
= 3000 ft
3
/min
= 120°F
= 1 atm
= 85°F
Fig. P12.102
2
4
3
1
Liquid water at
T
2
= 100°F
m
·
2
= 10,000 lb/h
Liquid water at
T
4
= 80°F
Atmospheric air
T
1
= 70°F
p
1
= 1 atm
f
1
= 40%
T
3
= 85°F
p
3
= 1 atm
f
3
= 90%
Fig. P12.104
12.105 Liquid water at 1308F and a mass flow rate of 10
5
lb/h
enters a cooling tower operating at steady state. Liquid
water exits the tower at 708F. No makeup water is provided.
Atmospheric air enters at 1 atm with a dry-bulb temperature
of 508F and a wet-bulb temperature of 358F. Saturated air
exits at 1208F, 1 atm. Ignoring kinetic and potential energy
effects, determine the mass flow rate of the cooled water
stream exiting the tower, in lb/h.
12.106 Liquid water at 1008F and a volumetric flow rate of
200 gal/min enters a cooling tower operating at steady state.
Atmospheric air enters at 1 atm with a dry-bulb temperature
of 808F and a wet-bulb temperature of 608F. Moist air exits
the cooling tower at 908F and 90% relative humidity.
Makeup water is provided at 808F. Plot the mass flow rates
of the dry air and makeup water, each in lb/min, versus
return water temperature ranging from 80 to 1008F. Ignore
kinetic and potential energy effects.
12.107 Liquid water enters a cooling tower operating at steady
state at 408C with a mass flow rate of 10
5
kg/h. Cooled water
at 258C exits the cooling tower at the same mass flow rate.
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