Warm air is conatined in a piston-and-cylinder device oriented horizontally, as shown below. The air cools slowly from an initial volume of 0.003 m3 to a final volume of 0.002 m3. During this process, the spring exerts a force that varies linearly from 900 N to a final value of zero N. The atmospheric pressure is 100 kPa and the area of the piston face is 0.018 m2. Friction between the piston and cylinder wall can be neglected because the process occurs so slowly. For the air, determine the initial and final pressures in kPa and the boundary work for the process in kJ.

## Tuesday, September 30, 2008

### TE 303 - HW #4, P2 - Work and Heat Transfer for a Closed, 3-Step Cycle - 15 pts

A closed system undergoes a thermodynamic cycle consisting of the following processes:

Process 1-2: Adiabatic compression from P1 = 50 psia, V1 = 3.0 ft3 to V2 = 1 ft3 along a path described by :

Process 2-3: Constant volume.

Process 3-1: Constant pressure with U1 - U3 = 46.7 Btu.

There are no significant changes in kinetic or potential energies in any of the processes.

a.) Sketch this cycle on a PV Diagram.

b.) Calculate the net work for the cycle in Btu.

c.) Calculate the heat transfer for process 2-3.

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Process 1-2: Adiabatic compression from P1 = 50 psia, V1 = 3.0 ft3 to V2 = 1 ft3 along a path described by :

Process 2-3: Constant volume.

Process 3-1: Constant pressure with U1 - U3 = 46.7 Btu.

There are no significant changes in kinetic or potential energies in any of the processes.

a.) Sketch this cycle on a PV Diagram.

b.) Calculate the net work for the cycle in Btu.

c.) Calculate the heat transfer for process 2-3.

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### TE 303 - HW #4, P3 - COMPUTER ANALYSIS: P-V Data - 20 pts

Measured data for pressure versus volume during the expansion of gases within the cylinder of an internal combustion engine are given in the table below:

Data Point V (cm^3) P (bar)

1 300 15

2 361 12

3 459 9

4 644 6

5 903 4

6 1608 2

Using data from the table and using EXCEL, complete the following:

(a) Determine the value of d such that the data are fit by an equation of the form PVd = constant. (HINT: take the log of both sides and rearrange into a linear equation.) You are expected to extract the value of d from either doing a curve fit with something like least squares, or from the slope or intercept function in Excel for the appropriate graph.

(b) Evaluate analytically the work done by the gases, in kJ, using the appropriate equation from class along with the result from (a).

(c) Using numerical integration of the data, evaluate the work done by the gases, in kJ (NOTE: Be careful about converting your units!). A common numerical integration method is the Trapezoidal Rule for Unevenly Spaced Data. Using this method, you can approximate the integral in the following way:

where Ai is the area of each rectangular interval, and n is the number of rectangular intervals.

For more information on the Trapezoidal Rule, please see the following website: http://oregonstate.edu/~haggertr/487/integrate.htm

For the "analysis" section of your Engineering Model, be sure to compare the different methods for estimating the work used in parts (b) and (c).

Data Point V (cm^3) P (bar)

1 300 15

2 361 12

3 459 9

4 644 6

5 903 4

6 1608 2

Using data from the table and using EXCEL, complete the following:

(a) Determine the value of d such that the data are fit by an equation of the form PVd = constant. (HINT: take the log of both sides and rearrange into a linear equation.) You are expected to extract the value of d from either doing a curve fit with something like least squares, or from the slope or intercept function in Excel for the appropriate graph.

(b) Evaluate analytically the work done by the gases, in kJ, using the appropriate equation from class along with the result from (a).

(c) Using numerical integration of the data, evaluate the work done by the gases, in kJ (NOTE: Be careful about converting your units!). A common numerical integration method is the Trapezoidal Rule for Unevenly Spaced Data. Using this method, you can approximate the integral in the following way:

where Ai is the area of each rectangular interval, and n is the number of rectangular intervals.

For more information on the Trapezoidal Rule, please see the following website: http://oregonstate.edu/~haggertr/487/integrate.htm

For the "analysis" section of your Engineering Model, be sure to compare the different methods for estimating the work used in parts (b) and (c).

### TE 303 - HW #4, P4 - Combined Convection and Radiation Heat Loss - 8 pts

A 3.0 m2 hot black surface at 80oC is losing heat to the surrounding air at 25oC by convection with a convection heat transfer coefficient of 12 W/m2-oC, and by radiation to the surrounding surfaces at 15oC. Determine the total rate of heat loss from the surface in W.

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### TE 303 - HW #4, P5 - Minimum Insulation Thickness for a Hot Surface - 10 pts

A flat surface is covered with insulation with a thermal conductivity of 0.08 W/m-K. The temperature at the interface between the surface and the insulation is 300oC. The outside of the insulation is exposed to air at 30oC and the convection heat transfer coefficient between the insulation and the air is 10 W/m2-K. Ignoring radiation heat transfer, determine the minimum thickness of the insulation, in m, such that the outside surface of the insulation is not hotter than 60oC at steady-state.

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### TE 303 - HW #4, P6 - Isobaric Expansion of R-134a - 15 pts

A piston-and-cylinder device with a set of stops contains 10 kg of R-134a. Initially, 8.0 kg of the refrigerant is in the liquid phase and the temperature is -8.0oC. Now, heat is transferred slowly into the refrigerant until the piston hits the stops. At this point, the volume is 400 L. Determine:

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a.) The temperature of the R-134a when the piston reaches the stops.

b.) The boundary work done during this expansion process.

c.) The heat transfer during this expansion process.

d.) Show this process on a PV Diagram.

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### TE 303 - HW #4, P7 - 1st Law Analysis of Steam in a Closed System - 8 pts

As shown in the figure below, 5.0 kg of steam contained within a piston-and-cylinder device undergoes an expansion from state 1 where the specific internal energy is 2709.9 kJ/kg to state 2 where the specific internal energy is 2659.6 kJ/kg. During the process, there is heat transefer to the steam with a magnitude of 80 kJ. Also, a paddle wheel transfers energy to the steam by work in the amount of 18.5 kJ. There is no significant change in the kinetic or gravitational potential energies of the steam. Determine the work done by the steam on the piston during the process in kJ.

### TE 303 - HW #4, P8 - Work for a "Non-Standard" P-V Relationship - 9 pts

Oxygen (O2) gas within a piston-cylinder assembly undergoes an expansion from a volume V1 = 0.01 m3 to a volume V2 = 0.03 m3. The relationship between pressure and volume during the process is P = AV-1 + B, where A = 0.06 bar m3, and B = 3.0 bar. For the O2 , determine the following:

a.) The initial and final pressures, each in bar.

b.) The work, in kJ.

a.) The initial and final pressures, each in bar.

b.) The work, in kJ.

## Wednesday, September 17, 2008

### TE 303 - HW #3, P1 - Steam NIST / TFT Fundamentals - 8 pts

Complete the following table for water (revisited from HW2) using either the NIST Webbook or the Thermal Fluids Excel Plug in. Be sure to cite which one that you used. Your grade will be based mostly on the use of technology, not on the answers. Your solution must be different than your solution from HW2.

T(oC) P(kPa) H(kJ/kg) x(kg vap/kg) Phase Description

a.) P = 200 kPa and x = 0.7 kg vap/kg

b.) T = 140 degC and H = 1800 kJ/kg

c.) P = 950 kPa and x = 0 kg vap/kg

d.) T = 80 degC and P = 500 kPa

e.) P = 800 kPa and H = 3161.7 kJ/kg

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T(oC) P(kPa) H(kJ/kg) x(kg vap/kg) Phase Description

a.) P = 200 kPa and x = 0.7 kg vap/kg

b.) T = 140 degC and H = 1800 kJ/kg

c.) P = 950 kPa and x = 0 kg vap/kg

d.) T = 80 degC and P = 500 kPa

e.) P = 800 kPa and H = 3161.7 kJ/kg

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### TE 303 - HW #3, P2 - R-134a NIST/TFT Fundamentals - 12 pts

Complete the following table for R-134a(revisited from HW2) using either the NIST Webbook or the Thermal Fluids Excel Plug in. Be sure to cite which one that you used. Your grade will be based mostly on the use of technology, not on the answers. Your solution must be different than your solution from HW2.

Include an analysis of a comparison of this solution (including Problem 1) to using traditional data tables in HW2. Are the values comparable? Is interpolation still necessary? Which method is more efficient? Explain. (4 pts)

T(oF) P(psia) U(Btu/lbm) x(lbm vap/lbm) Phase Description

a.) P = 80 psia and U = 126 Btu/lbm

b.) T = 15 degF and x = 0.6 lbm vap/lbm

c.) T = 10 degF and P = 70 psia

d.) P = 180 psia and U = 226 Btu/lbm

e.) T = 110 degF and x = 1.0 lbm vap/lbm

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Include an analysis of a comparison of this solution (including Problem 1) to using traditional data tables in HW2. Are the values comparable? Is interpolation still necessary? Which method is more efficient? Explain. (4 pts)

T(oF) P(psia) U(Btu/lbm) x(lbm vap/lbm) Phase Description

a.) P = 80 psia and U = 126 Btu/lbm

b.) T = 15 degF and x = 0.6 lbm vap/lbm

c.) T = 10 degF and P = 70 psia

d.) P = 180 psia and U = 226 Btu/lbm

e.) T = 110 degF and x = 1.0 lbm vap/lbm

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### TE 303 - HW #3, P3 - Determining DH Using Heat Capacity Polynomials - 16 pts

Determine the change in the specific enthalpy of nitrogen (N2), in kJ/kg, as it is heated from 600 to 1500 K, using:

a.) The empirical specific heat equation (Shomate Eqn) from the NIST Website.

b.) "The CoP value at the average temperature. (Use the heat capacity polynomial to determine this CoP value.)

c.) The CoP value at room temperature, 25oC. (Use the heat capacity polynomial to determine this CoP value.)

In your analysis, be sure to include a comparison of these three methods. (4 pts)

HINT: You can get the parameters for the Shomate Equation from the NIST Webbook by searching by "name", then click on "gas phase data", then "gas phase thermochemistry data". Part (a) Integral of CoP with respect to T...just like in class. Parts (b) and (c) are easier. Just evaluate CoP at ONE T and then assume CoP has this value and it is constant.

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a.) The empirical specific heat equation (Shomate Eqn) from the NIST Website.

b.) "The CoP value at the average temperature. (Use the heat capacity polynomial to determine this CoP value.)

c.) The CoP value at room temperature, 25oC. (Use the heat capacity polynomial to determine this CoP value.)

In your analysis, be sure to include a comparison of these three methods. (4 pts)

HINT: You can get the parameters for the Shomate Equation from the NIST Webbook by searching by "name", then click on "gas phase data", then "gas phase thermochemistry data". Part (a) Integral of CoP with respect to T...just like in class. Parts (b) and (c) are easier. Just evaluate CoP at ONE T and then assume CoP has this value and it is constant.

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### TE 303 - HW #3, P4 - Determining DU Using Heat Capacity Polynomials - 16 pts

Determine the change in the specific internal energy of hydrogen (H2), in kJ/kg, as it is heated from 400 to 1000 K, using:

a.) The empirical specific heat equation (Shomate Eqn) from the NIST Website.

b.) The CoV value at the average temperature. (Use the heat capacity polynomial to determine this CoV value.)

c.) The CoV value at room temperature, 25oC. (Use the heat capacity polynomial to determine this CoV value.)

In your analysis, be sure to include a comparison of these three methods. (4 pts)

HINT: To start this problem, copy your spreadsheet from #3 after you solved it, and then modify it for this problem. Some of the calculations are the same! Part (a) Integral of CoV with respect to T...just like in class. Parts (b) and (c) are easier. Just evaluate CoV at ONE T and then assume CoV has this value and it is constant. Remember that you are using the IDEAL GAS heat capacity.

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a.) The empirical specific heat equation (Shomate Eqn) from the NIST Website.

b.) The CoV value at the average temperature. (Use the heat capacity polynomial to determine this CoV value.)

c.) The CoV value at room temperature, 25oC. (Use the heat capacity polynomial to determine this CoV value.)

In your analysis, be sure to include a comparison of these three methods. (4 pts)

HINT: To start this problem, copy your spreadsheet from #3 after you solved it, and then modify it for this problem. Some of the calculations are the same! Part (a) Integral of CoV with respect to T...just like in class. Parts (b) and (c) are easier. Just evaluate CoV at ONE T and then assume CoV has this value and it is constant. Remember that you are using the IDEAL GAS heat capacity.

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### TE 303 - HW #3, P5 - Clapeyron & Clausius-Clapeyron Equations - 16 pts

Estimate the latent heat of vaporization, in Btu/lbm, of ammonia at -10oF using:

a.) The Clapeyron equation

b.) The Clausius-Clapeyron equation

c.) The ammonia tables

In your analysis, be sure to include a comparison of these three methods and propose a reason for any significant differences. (4 pts)

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a.) The Clapeyron equation

b.) The Clausius-Clapeyron equation

c.) The ammonia tables

In your analysis, be sure to include a comparison of these three methods and propose a reason for any significant differences. (4 pts)

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### TE 303 - HW #3, P6 - Hypothetical Process Paths and the Latent Heat of Vaporization - 24 pts

Determine the change in enthalpy in Joules for 20.0 g of heptane (C7H16) as it changes from a saturated liquid at 300 K [State 1] to a temperature of 370 K and a pressure of 58.7 kPa [State 4]; you can follow the hypothetical process path in the diagram to the right. Do not use tables of thermodynamic properties, except to check your answers. (In other words, you will not get credit for the problem if you use the tables.)

First, draw the states on a P-V or T-V diagram (4 pts). Then, calculate the DH for each step in the path using what you know about the enthalpy for each step. You might want to use the Antoine Equation to estimate the heat of vaporization of heptane at 300 K. Use the average heat capacity of heptane gas over the temperature range of interest (is this assumption valid?).

Assume heptane gas is an ideal gas at the relevant temperatures and pressures.

For the analysis section, be sure to discuss how this result differs than what you would have done using just the thermodynamics data tables, as well as the validity of your assumptions (5 pts).

HINTS: The key to the first step in this HPP is the Clausius-Clapeyron Equation. Use the Antoine equation to help you estimate the latent heat of vaporization at T1. In the second step, interpolate on the Cp data from the NIST WebBook to determine Cp(T1) and Cp(T2). Then, use the average of these two Cp's to evaluate the change in enthalpy. All you need to do is think a little bit and you will see how to evaluate Î”U34.

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## Wednesday, September 10, 2008

### TE 303 - HW #2, P1 - Steam Table Fundamentals - 8 pts

Complete the following table for water. Be sure to cite which source of thermodynamic data tables that you used.

T(oC) P(kPa) H(kJ/kg) x(kg vap/kg) Phase Description

a.) P = 200 kPa and x = 0.7 kg vap/kg

b.) T = 140 degC and H = 1800 kJ/kg

c.) P = 950 kPa and x = 0 kg vap/kg

d.) T = 80 degC and P = 500 kPa

e.) P = 800 kPa and H = 3161.7 kJ/kg

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T(oC) P(kPa) H(kJ/kg) x(kg vap/kg) Phase Description

a.) P = 200 kPa and x = 0.7 kg vap/kg

b.) T = 140 degC and H = 1800 kJ/kg

c.) P = 950 kPa and x = 0 kg vap/kg

d.) T = 80 degC and P = 500 kPa

e.) P = 800 kPa and H = 3161.7 kJ/kg

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### TE 303 - HW #2, P2 - R-134a Table Fundamentals - 8 pts

Complete the following table for R-134a. Be sure to cite which source of thermodynamic data tables that you used.

T(oF) P(psia) U(Btu/lbm) x(lbm vap/lbm) Phase Description

a.) P = 80 psia and U = 126 Btu/lbm

b.) T = 15 degF and x = 0.6 lbm vap/lbm

c.) T = 10 degF and P = 70 psia

d.) P = 180 psia and U = 226 Btu/lbm

e.) T = 110 degF and x = 1.0 lbm vap/lbm

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T(oF) P(psia) U(Btu/lbm) x(lbm vap/lbm) Phase Description

a.) P = 80 psia and U = 126 Btu/lbm

b.) T = 15 degF and x = 0.6 lbm vap/lbm

c.) T = 10 degF and P = 70 psia

d.) P = 180 psia and U = 226 Btu/lbm

e.) T = 110 degF and x = 1.0 lbm vap/lbm

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### TE 303 - HW #2, P3 - R-134a Table Fundamentals - 9 pts

A 0.5 m3 vessel contains 10 kg of R-134a at -20oC. Determine…

a.) The pressure in kPa

b.) The total internal energy in kJ

c.) The volume occupied by the liquid phase in m3

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a.) The pressure in kPa

b.) The total internal energy in kJ

c.) The volume occupied by the liquid phase in m3

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### TE 303 - HW #2, P4 - Isochoric Heating of Water - 8 pts

Five kilograms of H2O are contained in a closed, rigid tank at an initial pressure of 20 bar and a quality of 50%. Heat transfer occurs until the tank contains only saturated vapor. Determine the volume of the tank, in m3, and the final pressure in bar.

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### TE 303 - HW #2, P5 - Isobaric Expansion of Water - 12 pts

A piston-and-cylinder device initially contains 50 L of liquid water at 25oC and 300 kPa. Heat is added to the water at constant pressure until the entire liquid is vaporized.

a.) What is the mass of the water in the cylinder in kg ?

b.) What is the final temperature of the water in the cylinder in oC ?

c.) Determine the total enthalpy change of the water for this process, in kJ.

d.) Show the process on a completely labeled TV Diagram.

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a.) What is the mass of the water in the cylinder in kg ?

b.) What is the final temperature of the water in the cylinder in oC ?

c.) Determine the total enthalpy change of the water for this process, in kJ.

d.) Show the process on a completely labeled TV Diagram.

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### TE 303 - HW #2, P6 - Inflating an Automobile Tire - 12 pts

The air in an automobile tire with a volume of 0.53 ft3 is at 90oF and 20 psig. Determine the mass of air that must be added to raise the pressure to the recommended value of 30 psig. Assume atmospheric pressure is 14.7 psia and both the temperature and the volume of the air in the tire remain constant as it is inflated. Assume that the air in the tire behaves as an ideal gas, but then check the validity of this assumption.

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### TE 303 - HW #2, P7 - An Application of Equations of State - 25 pts

A 0.016773 m3 tank contains 1 kg of R-134a at 110oC. Determine the pressure of the refrigerant using:

a.) The Ideal Gas EOS

b.) The Compressibility Factor EOS

c.) The R-134a Tables

d.) The van der Waal EOS

e.) The Soave-Redlich-Kwong EOS

In your analysis, be sure to discuss a comparison of these equations of states (5 points).

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a.) The Ideal Gas EOS

b.) The Compressibility Factor EOS

c.) The R-134a Tables

d.) The van der Waal EOS

e.) The Soave-Redlich-Kwong EOS

In your analysis, be sure to discuss a comparison of these equations of states (5 points).

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### TE 303 - HW #2, P8 - Relative Humidity and Fogged Glasses - 8 pts

The Campus Police heard that you were a thermodynamics guru, so they have come to you to help figure out if a witness to a crime is credible. The eyewitness claims that upon entering her apartment complex, she saw the suspect leaving the downstairs apartment with some electronics equipment. Since the eyewitness must wear glasses and stated that she was wearing them at the time, the Campus Police want to know if her glasses would have fogged up when entering the building and thus obstructed her view. The temperature of the apartment complex was measured to be 20 °C, and the outdoor temperature to be 10oC. A humidity gauge indicated that the relative humidity in the apartment complex is 55%. Assuming that the eyewitness did not have anti-fog lenses, do you think that this eyewitness could have been obstructed by fogged lenses? Provide supporting calculations.

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