This HW covers CB chapters 9-11 or LT chapters 9 & 10.

The homework consists of 7 problems for a total of 48 pts.

Please begin your question with the problem number you are asking about.

9.116 - Brayton Cycle with Regeneration - 8 pts

11.76 - Helium Gas Refrigeration Cycle - 6 pts

WB-1 : Brayton Cycle with Variable Heat Capacities - 6 pts

WB-2 : Effect of Turbine Feed T on Rankine Cycle Efficiency - 6 pts

Wb-3 : Special Rankine Cycle with Reheat and Regeneration - 8 pts

Wb-4 : Ammonia Cascade Refrigeration Cycle - 8 pts

WB-5 : Vapor-Compression Heat Pump - 6 pts

## Tuesday, May 24, 2011

## Friday, May 20, 2011

### ENGR 224 - Test #2 , May 24, 2011

Please post any questions relating to the second test as comments on this blog post.

Test 2 will focus on CB chapters 6 & 7 or LT chapters 6 - 8. Material from earlier chapters will also be part of this test, although it will not be the focus.

The test will be available for you to take between 8AM and 7PM in the Testing Center on Tuesday, 5/24/11. It is a 2-hour, closed book test. You will be allowed to use TWO 8.5"x11" cheat sheets. You can write or print on both sides of your cheat sheets. You will be penalized ONE point for every TWO minutes over 2 hours that you have the test in your possession. Do NOT forget the time stamps !

We will have an optional test-prep class on Mon, 5/23, and NO CLASS MEETING on Tue, 5/24. There is a QUIZ on 5/25. It is not my fault. The testing center situation messed up our schedule.

Best of luck to you !

Test 2 will focus on CB chapters 6 & 7 or LT chapters 6 - 8. Material from earlier chapters will also be part of this test, although it will not be the focus.

The test will be available for you to take between 8AM and 7PM in the Testing Center on Tuesday, 5/24/11. It is a 2-hour, closed book test. You will be allowed to use TWO 8.5"x11" cheat sheets. You can write or print on both sides of your cheat sheets. You will be penalized ONE point for every TWO minutes over 2 hours that you have the test in your possession. Do NOT forget the time stamps !

We will have an optional test-prep class on Mon, 5/23, and NO CLASS MEETING on Tue, 5/24. There is a QUIZ on 5/25. It is not my fault. The testing center situation messed up our schedule.

Best of luck to you !

## Monday, May 16, 2011

### ENGR 224 - HW #6

This HW covers CB chapter 7 or LT chapter 8.

The homework consists of 15 problems for a total of 71 pts.

Please begin your question with the problem number you are asking about.

Cengel & Boles: Ch 7:

7.127 - Power Requirement for an Air Compressor - 5 pts

7.131 - Analysis of an R-134a Compressor - 6 pts

7.146+ - Lost Work in a Heat Exchanger - 6 pts

Additional part c.) Determine the rate at which work is lost due to the irreversible nature of heat transfer in this process in kW. Assume the surroundings are at 20oC.

WB-1 - Back-Work Ratio of a Steam Power Cycle - 7 pts

Problem Statement :

Consider a steam power plant that operates between the pressure limits of 8 MPa and 20 kPa. Steam enters the pump as a saturated liquid and leaves the turbine as a saturated vapor. Determine the back work ratio (BWR is the ratio of the work delivered by the turbine to the work consumed by the pump). Assume the entire cycle to be reversible and the heat losses from the pump and the turbine to be negligible.

Hints :

Assume the cycle operates at steady-state and that the ump and turbine are reversible.

I suggest you make a table with 6 columns. The 1st column lists all the important properties you may need to evaluate for each steam in the cycle. Make a column for each of the 4 streams in the cycle. The last column should list the units for each variable. This table should help you keep track of what you know and what you still need to determine.

Make a nice process flow diagram. Make a nice TS Diagram. Include the 2-phase envelope and the two key isobars. Apply the 1st and 2nd Laws to the pump and turbine and you should be able to determine the BWR.

Two double-interpolations are required unless you use NIST or a plug-in for Excel or your calculator.

Ans.: BWR ~ 240

WB-2 - Polytropic Compression of N2 with Varying δ - 6 pts

Problem Statement : Nitrogen gas is compressed from 80 kPa and 27oC to 480 kPa by a 10 kW compressor. Determine the mass flow rate of nitrogen through the compressor assuming the compression process is …

a.) Isentropic, γ = 1.4

b.) Polytropic with δ = 1.3

c.) Isothermal

d.) Ideal, two-stage polytropic with δ = 1.3

Hints :

The compressor operates at steady-state.

Changes in kinetic and potential energies are negligible.

Flow work and shaft work are the only forms of work that cross the system boundary.

Nitrogen (N2) behaves as an ideal gas in all parts of this problem.

The heat capacities of N2 are constant and, therefore, γ is also constant.

The intercooler in part (d) cools the effluent from the first compressor back down to T1 before it enters the second compressor.

Parts (b), (c) and (d) should be plug-and-chug.

Ans.: a.) Mdot ~ 0.048 kg/s , c.) Mdot ~ 0.063 kg/s

WB-3 - Entropy Change, Heat Transfer and Irreversibilities - 7 pts

Problem Statement :

A closed system undergoes a process in which work is done on the system and heat transfer Q occurs only at temperature Tb. For each case listed below, determine whether the entropy change of the system is positive, negative, zero or indeterminate (you cannot tell for sure from the given information).

a.) Internally reversible process with Q > 0.

b.) Internally reversible process with Q = 0.

c.) Internally reversible process with Q < 0. d.) Internal irreversibilities present with Q > 0.

e.) Internal irreversibilities present with Q = 0.

f.) Internal irreversibilities present with Q < 0. Hints : Consider the sign of each term in the defining equation for entropy generation.

WB-4 - Entropy Generation and Lost Work in a Nozzle - 6 pts

Problem Statement :

Oxygen, O2, enters a nozzle operating at steady-state at 3.8 MPa, 387oC and 10 m/s. At the nozzle exit, the conditions are 150 kPa, 37oC and 790 m/s.

a.) For a system that encloses the nozzle only, determine the heat transfer (kJ/kg) and the change in specific entropy (kJ/kg-K), both per kg of oxygen flowing through the nozzle. What additional information would be required to evaluate the rate of entropy production in this process ?

b.) Using an enlarged system boundary that includes the nozzle and a portion of its immediate surroundings, evaluate the rate of entropy generation (kJ/kg-K) and the rate of lost work (kJ/kg), both per kg of oxygen flowing through the nozzle. Assume that heat exchange at the enlarged system boundary takes place at the ambient temperature, 20oC.

Treat O2 as an ideal gas with variable heat capacities. Verify that the ideal gas assumption is valid.

Hints :

In part (a), use the 1st Law and the ideal gas property tables to determine Q.

In part (b), evaluate the entropy generation from its definition, using the Ideal Gas Property Tables and Gibbs 2nd Equation.

Lost work is just the product of Tsurr and Sgen.

Ans.: a.) Q ~ -30 kJ/kg , b.) Sgen ~ 0.2 kJ/kg-K and Wlost ~ 61 kJ/kg

WB-5 - Lost Work in an Air Compressor and HEX - 7 pts

Problem Statement :

Air flows through the compressor and heat exchanger in the system shown in the diagram. A separate liquid water stream (CP,W = 4.18 kJ/kg-K) also flows through the heat exchanger. The data given on the diagram are based on steady-state operation. Consider the air to be an ideal gas and neglect heat exchange with the surroundings as well as changes in kinetic and potential energies. Determine...

a.) The compressor power requirement in kW and the mass flow rate of the cooling water in kg/s.

b.) The rate of entropy generation in kW/K and the rate at which work is lost in kW for the compressor. Assume the temperature of the surroundings is 300 K.

c.) The rate of entropy generation in kW/K and the rate at which work is lost in kW for the heat exchanger. Assume the temperature of the surroundings is 300 K.

Hints :

Use the ideal gas EOS and the volumetric flow rate to determine the mass flow rate.

Use an energy balance to determine the work for the compressor in kW.

To determine the water flow rate, draw the control volume enclosing the heat exchanger. This control volume has 4 mass flows entering or leaving but no Q or W. An energy balance on this control volume yields the water flow rate.

Very important point- the air and the water DO NOT MIX in the heat exchanger !

Determine the change in enthalpy of the water using: ΔH = Cp ΔT and determine the entropy change of the water using ΔS = CP Ln[T2/T1].

Part (b) Don't forget about the cooling water when you calaculate the entropy generated.

Ans.: a.) WS ~ -50 kW, b.) Sgen,comp ~ 0.020 kW/K , Wlost,comp ~ 6 kW , b.) Sgen,HEX ~ 0.015 kW/K

The homework consists of 15 problems for a total of 71 pts.

Please begin your question with the problem number you are asking about.

Cengel & Boles: Ch 7:

7.127 - Power Requirement for an Air Compressor - 5 pts

7.131 - Analysis of an R-134a Compressor - 6 pts

7.146+ - Lost Work in a Heat Exchanger - 6 pts

Additional part c.) Determine the rate at which work is lost due to the irreversible nature of heat transfer in this process in kW. Assume the surroundings are at 20oC.

WB-1 - Back-Work Ratio of a Steam Power Cycle - 7 pts

Problem Statement :

Consider a steam power plant that operates between the pressure limits of 8 MPa and 20 kPa. Steam enters the pump as a saturated liquid and leaves the turbine as a saturated vapor. Determine the back work ratio (BWR is the ratio of the work delivered by the turbine to the work consumed by the pump). Assume the entire cycle to be reversible and the heat losses from the pump and the turbine to be negligible.

Hints :

Assume the cycle operates at steady-state and that the ump and turbine are reversible.

I suggest you make a table with 6 columns. The 1st column lists all the important properties you may need to evaluate for each steam in the cycle. Make a column for each of the 4 streams in the cycle. The last column should list the units for each variable. This table should help you keep track of what you know and what you still need to determine.

Make a nice process flow diagram. Make a nice TS Diagram. Include the 2-phase envelope and the two key isobars. Apply the 1st and 2nd Laws to the pump and turbine and you should be able to determine the BWR.

Two double-interpolations are required unless you use NIST or a plug-in for Excel or your calculator.

Ans.: BWR ~ 240

WB-2 - Polytropic Compression of N2 with Varying δ - 6 pts

Problem Statement : Nitrogen gas is compressed from 80 kPa and 27oC to 480 kPa by a 10 kW compressor. Determine the mass flow rate of nitrogen through the compressor assuming the compression process is …

a.) Isentropic, γ = 1.4

b.) Polytropic with δ = 1.3

c.) Isothermal

d.) Ideal, two-stage polytropic with δ = 1.3

Hints :

The compressor operates at steady-state.

Changes in kinetic and potential energies are negligible.

Flow work and shaft work are the only forms of work that cross the system boundary.

Nitrogen (N2) behaves as an ideal gas in all parts of this problem.

The heat capacities of N2 are constant and, therefore, γ is also constant.

The intercooler in part (d) cools the effluent from the first compressor back down to T1 before it enters the second compressor.

Parts (b), (c) and (d) should be plug-and-chug.

Ans.: a.) Mdot ~ 0.048 kg/s , c.) Mdot ~ 0.063 kg/s

WB-3 - Entropy Change, Heat Transfer and Irreversibilities - 7 pts

Problem Statement :

A closed system undergoes a process in which work is done on the system and heat transfer Q occurs only at temperature Tb. For each case listed below, determine whether the entropy change of the system is positive, negative, zero or indeterminate (you cannot tell for sure from the given information).

a.) Internally reversible process with Q > 0.

b.) Internally reversible process with Q = 0.

c.) Internally reversible process with Q < 0. d.) Internal irreversibilities present with Q > 0.

e.) Internal irreversibilities present with Q = 0.

f.) Internal irreversibilities present with Q < 0. Hints : Consider the sign of each term in the defining equation for entropy generation.

WB-4 - Entropy Generation and Lost Work in a Nozzle - 6 pts

Problem Statement :

Oxygen, O2, enters a nozzle operating at steady-state at 3.8 MPa, 387oC and 10 m/s. At the nozzle exit, the conditions are 150 kPa, 37oC and 790 m/s.

a.) For a system that encloses the nozzle only, determine the heat transfer (kJ/kg) and the change in specific entropy (kJ/kg-K), both per kg of oxygen flowing through the nozzle. What additional information would be required to evaluate the rate of entropy production in this process ?

b.) Using an enlarged system boundary that includes the nozzle and a portion of its immediate surroundings, evaluate the rate of entropy generation (kJ/kg-K) and the rate of lost work (kJ/kg), both per kg of oxygen flowing through the nozzle. Assume that heat exchange at the enlarged system boundary takes place at the ambient temperature, 20oC.

Treat O2 as an ideal gas with variable heat capacities. Verify that the ideal gas assumption is valid.

Hints :

In part (a), use the 1st Law and the ideal gas property tables to determine Q.

In part (b), evaluate the entropy generation from its definition, using the Ideal Gas Property Tables and Gibbs 2nd Equation.

Lost work is just the product of Tsurr and Sgen.

Ans.: a.) Q ~ -30 kJ/kg , b.) Sgen ~ 0.2 kJ/kg-K and Wlost ~ 61 kJ/kg

WB-5 - Lost Work in an Air Compressor and HEX - 7 pts

Problem Statement :

Air flows through the compressor and heat exchanger in the system shown in the diagram. A separate liquid water stream (CP,W = 4.18 kJ/kg-K) also flows through the heat exchanger. The data given on the diagram are based on steady-state operation. Consider the air to be an ideal gas and neglect heat exchange with the surroundings as well as changes in kinetic and potential energies. Determine...

a.) The compressor power requirement in kW and the mass flow rate of the cooling water in kg/s.

b.) The rate of entropy generation in kW/K and the rate at which work is lost in kW for the compressor. Assume the temperature of the surroundings is 300 K.

c.) The rate of entropy generation in kW/K and the rate at which work is lost in kW for the heat exchanger. Assume the temperature of the surroundings is 300 K.

Hints :

Use the ideal gas EOS and the volumetric flow rate to determine the mass flow rate.

Use an energy balance to determine the work for the compressor in kW.

To determine the water flow rate, draw the control volume enclosing the heat exchanger. This control volume has 4 mass flows entering or leaving but no Q or W. An energy balance on this control volume yields the water flow rate.

Very important point- the air and the water DO NOT MIX in the heat exchanger !

Determine the change in enthalpy of the water using: ΔH = Cp ΔT and determine the entropy change of the water using ΔS = CP Ln[T2/T1].

Part (b) Don't forget about the cooling water when you calaculate the entropy generated.

Ans.: a.) WS ~ -50 kW, b.) Sgen,comp ~ 0.020 kW/K , Wlost,comp ~ 6 kW , b.) Sgen,HEX ~ 0.015 kW/K

## Wednesday, May 04, 2011

### ENGR 224 - HW #5

This HW covers CB chapter 7 or LT chapter 7.

The homework consists of 13 problems for a total of 59 pts.

Please begin your question with the problem number you are asking about.

Cengel & Boles: Ch 7: 14(2pts), 15(2pts), 18(2pts), 28E(4pts), 29(6pts), 66(6pts)

WB-1(4pts) , WB-2(6pts), WB-3(4pts) , WB-4(4pts), WB-5(8pts) , WB-6(5pts), WB-1(6pts)

The homework consists of 13 problems for a total of 59 pts.

Please begin your question with the problem number you are asking about.

Cengel & Boles: Ch 7: 14(2pts), 15(2pts), 18(2pts), 28E(4pts), 29(6pts), 66(6pts)

WB-1(4pts) , WB-2(6pts), WB-3(4pts) , WB-4(4pts), WB-5(8pts) , WB-6(5pts), WB-1(6pts)

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