Homework Problems
7E-1 :
Slow, Adiabatic Expansion of Steam
2 pts
Water is held in an
insulated piston-and-cylinder device at
300°C and
700 kPa. Grains of sand are removed one at a time from the back of the piston so that the
water expands slowly until the
pressure inside the
cylinder reaches
120 kPa. Determine the
final temperature of the
water in
°C.
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7E-2 :
Slow, Adiabatic Compression of R-134a
2 pts
R-134a is held in an
insulated piston-and-cylinder device at
100°F and
60 psia. Grains of sand are added one at a time to the back of the piston so that the
R-134a is
compressed reversibly until the
pressure inside the
cylinder reaches
200 psia. Determine the
final temperature of the
R-134a in
°F.
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7E-3 :
Ammonia Compression in a Piston-and-Cylinder Device
4 pts
Ammonia is
compressed reversibly in an
insulated piston-and-cylinder device from
500 kPa and a
quality of
0.8 kg vap/kg to a
pressure of
4.0 MPa. Determine the
final specific enthalpy of the
ammonia.
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7E-4 :
Shaft Work From a Reversible, Adiabatic Steam Turbine
3 pts
Superheated steam leaves the
boiler in a
power cycle and enters an
adiabatic turbine at
5.0 MPa and
400°C. The
steam expands to a
pressure of
180 kPa in the
turbine. If the
turbine is
internally reversible, determine the
shaft work of the
turbine in
kJ/kg?
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7E-5 :
Power Requirement of an Adiabatic, Internally Reversible Ammonia Compressor
4 pts
An
internally reversible ammonia compressor has a
compression ratio of
7:1. The
compressor effluent is at
600 psia and
200°F. Determine:
a.) The
temperature and
pressure of the
compressor feed and the
quality, if applicable.
b.) The
power requirement of the
compressor in
hP if the
mass flow rate of
ammonia is
4.8 lbm/s.
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7E-6 :
Slow, Adiabatic Compression of Carbon Monoxide
4 pts
Carbon monxide is
compressed in an
insulated piston-and-cylinder device from
25°F and
15 psia to
150 psia. Grains of sand are added one at a time to the back of the piston so that the
carbon monxide is
compressed reversibly. Determine the
final temperature of the
carbon monxide in
°C.
CP,CO = 6.72 Btu/lbmol-°R.
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7E-7 :
Adiabatic Expansion of Air in an Insulated Piston-and-Cylinder Device
4 pts
Air is held in an
insulated piston-and-cylinder device at
500°C and
1.5 MPa. Grains of sand are removed one at a time from the back of the piston so that the
air expands
reversibly and
adiabatically until the
pressure inside the
cylinder reaches
120 kPa. Determine the
final temperature of the
air in
°C using:
a.) The
2nd Gibbs Equationb.) A
polytropic path relationship}
Data: CP,air = (7/2) R.
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7E-8 :
Compare the Compression of Oxygen and Argon
4 pts
An
insulated piston-and-cylinder device is used to
reversibly compress gas from
100 kPa and
20°C up to
2 MPa. This
compression has been carried out
twice, once using
oxygen as the
working fluid and once using
argon.
Without doing any calculations, determine
which gas exhibits the
higher final temperature.
Explain your
reasoning.
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7E-9 :
Compare the Compression of Neon and Air
4 pts
An
insulated piston-and-cylinder device is used to
reversibly expand gas from
200 psia and
75°F down to a
pressure of
20 psia. This
expansion process was carried out
twice, once using
neon as the
working fluid and once using
air.
Without doing any calculations, determine
which gas exhibits the
lower final temperature.
Explain your
reasoning.
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7E-10 :
Nitrogen Compression with Different Heat Capacity Relationships
8 pts
Nitrogen is held in an
insulated piston-and-cylinder device at
350 K and
110 kPa. Grains of sand are added one at a time to the back of the piston so that the
nitrogen is
compressed reversibly until the
pressure inside the cylinder reaches
800 kPa. Determine the
final temperature of the
nitrogen in
°C and the
boundary work required for the
compression assuming:
a.) CP,N2 = (7/2) Rb.) The
Shomate Equation describes the relationship between
CP and
temperature (
numerical solution required)
c.) The
Ideal Gas Property Table for
nitrogen is applicable.
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7E-11 :
Analysis of Reversible, Adiabatic Compression of Air by Different Methods
8 pts
Air held in an
adiabatic piston-and-cylinder device
expands reversibly from
2.4 MPa and
1000 K until the
pressure reaches
400 kPa. Determine the
final temperature using:
a.) The
Ideal Gas Entropy Functionb.) Relative pressurec.) The
Shomate Equation
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7E-12 :
Analysis of Reversible, Adiabatic Compression of CO2 by Different Methods
8 pts
The
pressure of a
carbon dioxide stream at
350 K is increased by a
factor of
15 in a
reversible,
adiabatic compressor. Determine the
effluent temperature using:
a.) The
Ideal Gas Entropy Functionb.) Relative pressurec.) The
Shomate Equation
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7E-13 :
Compression of an Ideal Gas with Constant Heat Capacities
4 pts
An
ideal gas with
CP = 23 J/mol is slowly
compressed in an insulated
piston-and-cylinder device from
100 kPa to
1.4 MPa. Determine:
a.) The
factor by which the
temperature of the gas
increasesb.) The
ratio of the
initial volume to the
final volume of the gas.
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7E-14 :
Boundary Work for the Polytropic Compression of a Real Gas
3 pts
A
real gas in a
piston-and-cylinder device
expands in an
internally reversible process from
8 MPa to
200 kPa. The process path is
polytropic with
δ = 1.24. The
molar volume of the gas in the
final state is
5.7 L/mol. Determine the
boundary work for this process.
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7E-15 :
Boundary Work for Polytropic Compression of a Real Gas (AE)
3 pts
A
real gas in a
piston-and-cylinder device is
compressed in an
internally reversible process from
20 psia to
150 psia. The process path is
polytropic with
δ = 1.17. The
molar volume of the gas in the
final state is
0.78 ft3/lbmol. Determine the
boundary work for this process.
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7E-16 :
Boundary Work for the Polytropic Compression of Ammonia
5 pts
Ammonia is
compressed in a
piston-and-cylinder device from
-25°C and a
quality of
90% to a
final state in which
Pfinal = 5 Pinit.
a.) Determine
Q and
Wb for this process if it is
internally reversible and follows a
polytropic path with
δ = 1.38.
b.) Sketch the
process path on a
PV Diagram. Include the
two-phase envelope and relevant
isotherms. Think about the
shape of this
polytropic process path in terms of
concavity and
convexity.
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7E-17 :
Boundary Work for the Polytropic Expansion of Steam (AE)
5 pts
Water with a
quality of
0.75 lbm vap/lbm expands in a
piston-and-cylinder device from
350°F to a
final state in which
Vfinal = 18 Vinit.
a.) Determine
Q and
Wb for this process if it is
internally reversible and follows a
polytropic path with
δ = 0.86.
b.) Sketch the
process path on a
PV Diagram. Include the
two-phase envelope and relevant
isotherms. Think about the
shape of this
polytropic process path in terms of
concavity and
convexity.
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7E-18 :
Boundary Work for the Polytropic Compression of R-134a
5 pts
R-134a is
compressed in a
piston-and-cylinder device from
200 kPa and
45°C until the
pressure reaches
800 kPa.
a.) Determine
Q and
Wb for this process if it is
internally reversible and follows a
polytropic path with
δ = 1.
b.) Sketch the
process path on a
PV Diagram. Include the
two-phase envelope and relevant
isotherms. Think about the
shape of this
polytropic process path in terms of
concavity and
convexity.
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7E-19 :
Boundary Work for the Polytropic Expansion of Ammonia
5 pts
Ammonia expands in a
piston-and-cylinder device from
5.0 MPa doing
180 kJ/kg of
boundary work on the
surroundings. The
volume of the
ammonia increases by a factor of
65 during the expansion.
a.) Determine the
final Pressure and
Q for this process if it is
internally reversible and follows a
polytropic path with
δ = 1.
b.) Sketch the
process path on a
PV Diagram. Include the
two-phase envelope and relevant
isotherms. Think about the
shape of this
polytropic process path in terms of
concavity and
convexity.
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7E-20 :
Boundary Work for the Polytropic Expansion of an Ideal Gas
3 pts
An
ideal gas with
γ = 1.21 is
compressed slowly in an
insulated piston-and-cylinder device. Initially, the gas is at a
pressure of
140 kPa and a
volume of
12.6 L/mol. The
volume of the gas at the
end of the compression was
reduced by a
factor of
6. Determine the
boundary work for this process in
J/mol.
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7E-21 :
Boundary Work for the Polytropic Expansion of an Ideal Gas (AE)
4 pts
An
ideal gas is held within an
insulated piston-and-cylinder device at
300 psia and
500°F. The gas
expands slowly until the
volume occupied by the gas is
2.7 ft3. Determine the
final temperature in
°F and the
boundary work for this process in
Btu.
Data:
γ = 1.42,
m = 0.19 lbm,
MW = 44 lbm/lbmol
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7E-22 :
Heat Capacity Ratio From An Ideal Gas Compression Experiment
6 pts
An
ideal gas is
slowly compressed in an
insulated piston-and-cylinder device from
140 kPa to
750 kPa. The
initial volume of the gas is
21 L and the
initial temperature is
28.5°C. The
boundary work for this process was determined to be
4.0 kJ/mol. Determine the
heat capacity ratio for this gas,
assuming it is
constant, and the final
temperature in
°C.
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7E-23 :
Boundary Work in the Expansion of an Ideal Gas
4 pts
An
insulated piston-and-cylinder device contains
50 g of an
ideal gas at
500°C.
Initially, the gas occupies a
volume of
4.2 L. The gas is allowed to
slowly expand until the
volume of the gas has increased by a
factor of
4. Determine the
boundary work for this process in
J/mol.
Data:
CP = 18.6 J/mol-K
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7E-24 :
Air Carnot Power Cycle in a Piston-and-Cylinder Device
7 pts
Air is the
working fluid in a
Carnot power cycle carried out in a
piston-and-cylinder device. The
maximum and
minimum pressures in the cycle are
980 kPa and
110 kPa, respectively. The
maximum temperature in the cycle is
850 K. The
heat input in the
isothermal expansion is
200 kJ/kg. Determine the
pressure at the end of the
isothermal compression, the
boundary work and the
thermal efficiency for the cycle using:
a.) CP,air = 1.01 kJ/kg-Kb.) Variable CP for
air and the
Ideal Gas Property Tablesc.) Sketch the
path for this
cycle on both
PV and
TS Diagrams.
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7E-25 :
Nitrogen Carnot Power Cycle in a Piston-and-Cylinder Device (AE)
7 pts
Nitrogen is the
working fluid in a
Carnot power cycle carried out in a
piston-and-cylinder device. The
maximum and
minimum pressures in the cycle are
200 psia and
15 psia, respectively. The
maximum temperature in the cycle is
1800°R. The
boundary work in the
isothermal expansion is
150 Btu/lbm. Determine the
pressure at the end of the
isothermal compression, the
boundary work and the
thermal efficiency for the
cycle using:
a.) CP,air = 0.24 Btu/lbm-°Rb.) Variable CP for
nitrogen and the
Ideal Gas Property Tablesc.) Sketch the
path for this
cycle on both
PV and
TS Diagrams.
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7E-26 :
Carnot Heat Pump Cycle Using An Ideal Gas in a Piston-and-Cylinder Device
4 pts
The
working fluid in the
Carnot heat pump cycle, shown below, is an
ideal gas with a
heat capacity ratio of
1.44. The cycle is carried out in a
piston-and-cylinder device and has a
coefficient of performance of
1.8.
The
maximum and
minimum volumes in the cycle are
75 L and
1.2 L, respectively. The
minimum pressure in the cycle is
50 kPa. If the
cylinder contains
1.75 mol of gas, determine the
heat and
work for
each step in the
cycle and the
heat and
work for the
entire cycle, all in
kJ.
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7E-27 :
Carnot Vapor Refrigeration Cycle in a Piston-and-Cylinder Device
6 pts
A
Carnot refrigeration cycle is executed using a
piston-and-cylinder device that contains
R-134a. During the cycle, the
maximum and
minimum temperatures are
50°C and
-10°C, respectively.The
capacity of this
refrigeration cycle is
QC = 115 kJ/kg. The
quality at the beginning of the
adiabatic expansion is
0.05 kg vap/kg. Determine
QH and
Wb for each
step in the
cycle and
COPR.
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7E-28 :
Carnot Steam Power Cycle (SI)
5 pts
Consider the
Carnot steam power cycle, shown below.
The
boiler operates at
10 MPa and converts
saturated liquid to
saturated vapor. The
condenser operates at
200 kPa. Determine
QH,
QC,
Wcycle and the
thermal efficiency of the
power cycle.
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7E-29 :
R-134a Carnot Vapor Refrigeration Cycle (AE)
6 pts
The
Carnot Vapor Refrigeration Cycle shown below uses
R-134a as the
working fluid. The
condenser effluent is a
saturated liquid.
a.) Determine
QH,
Wcomp and
Wturb in
Btu/lbmb.) Sketch the process path for the cycle on a
PV Diagram and a
TS Diagram.
Data:
P2 = 18 psia,
T3 = 140°F,
QC = 44 Btu/lbm.
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7E-30 :
Ammonia Carnot Vapor-Compression Heat Pump Cycle
6 pts
Consider the
Carnot ammonia heat pump cycle, shown below.
The
condenser operates at
4.0 MPa and converts
saturated vapor to
saturated liquid. The
evaporator operates at
200 kPa. Determine
QH,
QC,
Wturb,
Wcomp,
Wcycle and the
thermal efficiency of the
power cycle.
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