# Homework Problems

## Entropy Change for a Heat Transfer Process

### 3 pts

Calculate the entropy change of each reservoir when 1000 kJ of heat is transferred directly from a hot reservoir at 1000 K to a cold reservoir at 400 K. Calculate the entropy change of the universe for this process. Does this process violate the principle of increasing entropy?
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## Rate of Entropy Increase for a Heat Transfer Process

### 3 pts

A hot reservoir at 944 K transfers heat to a cold reservoir at 298 K. If the rate of heat transfer is 25 kW, determine the rate at which the entropy of the two reservoirs combined changes (in kW/K) and determine if the second law is satisfied.
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## Entropy Changes Associated with an Evaporator

### 4 pts

A refrigerator using R-134a as the refrigerant removes 200 kJ of heat from its refrigerated space. This heat is absorbed by a mixture of saturated liquid and saturated vapor that enters the evaporator at a pressure of 175 kPa. The R-134a leaves the evaporator as a saturated vapor. Determine
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## Power Output of an Isentropic Turbine

### 4 pts

An isentropic turbine produces shaft work as R-134a at 275 psia and 225oF expands through the turbine and exits at 35oF. Assuming the turbine is adiabatic, determine the power output of the turbine per lbm of R-134a flowing through it.
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## Entropy Change for an Isobaric Heating Process

### 4 pts

A piston-and-cylinder device holds 9.7 lbm of water at 250 psia in a volume of 3.6 ft3. Heat is added to the water until the temperature reaches 425oF. During this process, the pressure in the cylinder remains constant because the piston moves freely. Determine the change in the entropy of the water in Btu/oR.
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## Isentropic Compression of Water Vapor

### 3 pts

An isentropic compressor takes in H2O at 105 kPa and delivers it at 450 kPa. If the temperature of the feed is 180oC, determine the temperature and specific enthalpy of the H2O at the compressor outlet.
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## Isentropic Expansion of R-134a

### 4 pts

R-134a expands reversibly and adiabatically in a piston-and-cylinder device from 80 psia and 120oF to 5 psia. If the cylinder contains 17.4 lbm of R-134a, what are the total work done by the system during this process and the final temperature of the R-134a?
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## Vaporization of Water in a Rigid Tank

### 5 pts

An electric resistance heater is used to heat the contents of an insulated rigid tank that holds 23.1 kg of H2O. Initially, the pressure in the tank is 150 kPa and 44% of the mass inside the tank is saturated liquid and the remaining 56% is saturated vapor?. Power is applied to the heater until all of the H2O in the tank is saturated vapor. Determine the entropy change of the H2O and the total heat transfer during this process.
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## Expansion of Water into a Vacuum

### 5 pts

A rigid tank is divided into two equal parts by a wall. One part of the tank contains 0.74 kg of water at 100 kPa and 25oC. The other part is a perfect vacuum. The wall is now removed and the water expands to fill the entire tank. A thermocouple indicates that the final equilibrium temperature of the H2O in the tank is 50oC. Determine the entropy change of water and the total heat transfer to the system during this process.
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## Isobaric Condensation of R-134a

### 5 pts

The refrigerant R-134a is cooled in a piston-and-cylinder device from 190oF to 75oF. The piston moves freely and the initial pressure is 200 psia. Determine the specific entropy change of the refrigerant, the work per lbm and heat transfer per lbm during this process.
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## ΔS and Boundary Work for the Isobaric Expansion of Water

### 6 pts

Electrical work is done by an electrical resistance heater on H2O contained in an insulated piston-and-cylinder device. The cylinder initially contains 2.4 L of saturated liquid water at a pressure of 500 kPa. Assuming the piston moves freely, determine the total entropy change of the H2O during a process in which 1875 kJ of heat is transferred into the water. What is the boundary work for this process?
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## Reversible Expansion of R-134a in a Piston-and-Cylinder Device

### 4 pts

The refrigerant R-134a expands reversibly from 2 Mpa to 500 kPa in an insulated piston-and-cylinder device. The cylinder initially contains 15 L of R-134a with a quality of 1.0. Determine the final temperature of the R-134a in the cylinder and the work done during this process.
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## Minimum Power Required for Adiabatic Compression of R-134a

### 4 pts

An adiabatic compressor is used to increase the pressure from 105 kPa to 1.25 Mpa in a stream of R-134a with a volumetric flow rate of 1800 L/min. Determine the minimum power that must be supplied to the compressor.
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## Reversible Compression of Steam in a Closed System

### 4 pts

Superheated steam is reversibly compressed from 200 kPa to 1.4 Mpa in a well-insulated piston-and-cylinder device. The cylinder initially contains 0.175 m3 of steam at 250oC. Determine the final temperature of the steam and the work done on the steam during this process.
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## Heat and Work in an Isothermal Expansion of Steam

### 5 pts

Saturated water vapor is contained in a piston-and-cylinder device that is positioned in a constant-temperature bath at 250oC. The 5.7 kg of steam inside the cylinder expands reversibly and isothermally to a final pressure of 1.2 MPa. Determine the heat transferred between the constant-temperature bath and the water inside the cylinder as well as the work done by the H2O inside the cylinder during this process.
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## Isentropic Compression of High Quality Steam

### 5 pts

Steam is compressed isentropically to a final pressure of 5 MPa. The steam is initially at 25oC and has a quality of 91%. How much work does this process require, in kJ/kg, if the process takes place in... (a) A closed system? (b) An open system? (c) Explain why the answers to parts (a) and (b) are not the same.
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## Isothermal Process In a Closed System

### 4 pts

The refrigerant R-134a is contained in a piston and cylinder device. The device is submerged in a circulating water bath that maintains the temperature of the R-134a at 25oC. The initial pressure inside the cylinder is 300 kPa. In the final state, the R-134a has a quality of 0.35 kg vap/kg.Assuming the process is internally reversible, determine the total work per kg and the heat transfer per kg that occurred during this process.
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## Interpreting Heat Transfer on a TS Diagram

### 3 pts

A working fluid undergoes the reversible, two-step process shown in the TS Diagram, below. Determine the total heat transfer for the process, Q13, in kJ/kg.

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## Heat Transfer in the Two-Phase Envelope of a TS Diagram

### 3 pts

A working fluid undergoes the reversible, two-step process shown in the TS Diagram, below. During the process, the fluid evaporates and partially condenses. Determine the total heat transfer for the process, Q13, in kJ/kg.

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## Interpreting Heat Transfer on a TS Diagram

### 3 pts

A working fluid undergoes the reversible, two-step process shown in the TS Diagram, below. Determine the total heat transfer for the process, Q13, in kJ/kg.

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## Heat Transfer in the Two-Phase Envelope of a TS Diagram (AE)

### 4 pts

A working fluid undergoes the reversible, two-step process shown in the TS Diagram, below. Determine the total heat transfer for the process, Q13, in Btu/lbm.

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## Entropy Change for Boiling Water

### 4 pts

Heat is transferred into 1 kg of H2O contained in a piston and cylinder device with a free-floating piston that maintains the pressure at 500 kPa. a.) Use enthalpy values found in thermodynamic data to calculate the heat transfer required for a process in which the H2O changes from a saturated liquid to a saturated vapor.b.) Use the definition of entropy to determine the change in the specific entropy of the H2O in this process. c.) Use specific entropy values found in thermodynamic data to calculate the change in the specific entropy for the process. d.) Compare your answers for parts (b) and (c) and comment on the results.
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## Problem Title

### 4 pts

Calculate the shaft work per kg produced as steam expands from 4 MPa to 100 kPa in an isentropic turbine. The inlet temperature is 500oC.
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## Problem Title

### 4 pts

The refrigerant R-134a in a home refrigerator enters the compressor as a saturated vapor at -5oF. At the compressor outlet, the pressure is 250 psia. Determine the minimum work required by this compressor in Btu/lbm.
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## Entropy Change for a Pressure Cooker

### 6 pts

A pressure cooker is a rigid vessel with an adjustable pressure relief valve. The pressure relief valve allows the user to set the maximum or setpoint pressure inside the vessel. When the pressure exceeds the setpoint pressure, the valve opens and some of the contents of the vessel, usually vapors, are allowed to flow out into the surroundings until the pressure in the vessel is reduced to the setpoint pressure. A 10 L pressure cooker with a setpoint pressure of 250 kPa contains water at 250 kPa with a quality of 7 percent. During the cooking process, heat is added from a high-temperature thermal reservoir until the quality of the water inside the pressure cooker is 35 percent. Determine the minimum entropy change (largest negative number) of the high-temperature thermal reservoir during this process.
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## Stirred Pressure Cooker

### 6 pts

A modified pressure cooker, similar to the one described in the previous problem, allows shaft work to be added to the contents of the pressure cooker by a stirring impeller. Solve the previous problem for a stirred pressure cooker in which 65 kJ of shaft work are added during the heating process. Determine the minimum entropy change of the thermal reservoir during this process.
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## Compression and Cooling of R-134a in a Closed System

### 4 pts

Five kilograms of R-134a in a piston and cylinder device at -5oC and a quality of 95% undergo a two-step process. In step 1-2, the R-134a is compressed reversibly and adiabatically to 1200 kPa. In step 2-3, the R-134a is cooled reversibly until all of the R-134a is a saturated liquid. a.) Sketch the two-step process on a TS diagram. Be sure to include the two-phase envelope and any relevant isobars. Determine... b.) the work done on the R-134a in kJ in step 1-2, c.) the heat transferred from the R-134a in kJ in step 2-3.
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