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 Equation
b.) 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) R
b.) 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 Function
b.) Relative pressure
c.) 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 Function
b.) Relative pressure
c.) 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 increases
b.) 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-K
b.) Variable CP for air and the Ideal Gas Property Tables
c.) 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-°R
b.) Variable CP for nitrogen and the Ideal Gas Property Tables
c.) 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/lbm
b.) 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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