There might be some confusion in this problem about whether or not it is an open system. Even though the problem states that it is a "steady flow" process, none of the values or conditions given involve rates, and in fact, the amount of substance given is a constant (not a rate). Therefore, you might consider whether or not you really think this is an open system.
MSS
Friday, February 29, 2008
Two quick notes from class today
(1) I found a small typo in the heat capacity calculations handout. In the last equation on the first page, there is a T1^2 that should be a T1^3. A corrected version is posted on the website. Also, if you find any more typos, please let me know so that I can correct the document.
(2) In discussing the microscopic derivation of the entropy, I neglected to mention the following: since S = k ln Omega, and since Omega counts the number of configurations of molecules, the second law really says that molecules like to maximize their number of configurations. This underlies the statement that the entropy always increases; molecules never spontaneously decide to choose a smaller subset of configurations than the total number that are available to them.
Earlier we had said that the second law is not about increasing disorder. Instead, it is about increasing numbers of configurations. The two are not the same. For example, if one very quickly cools a liquid below its freezing temperature and then suddenly places it in an isolated container, as the liquid starts to freeze, the entropy increases. This actually happens because there are more configurations when some of the liquid becomes frozen. This seems counterintuitive, since one intuitively wants to think of a liquid as having more configurations than a crystal. But for very low temperature liquids, there are simply less configurations for the molecules than there would be if some of those molecules could vibrate around lattice sites in a crystal. One can even calculate this and show it to be true. Therefore, our intuitive notion of "order" and "disorder" is not really quantitative, and not always related to the number of configurations, which is what is really important.
(2) In discussing the microscopic derivation of the entropy, I neglected to mention the following: since S = k ln Omega, and since Omega counts the number of configurations of molecules, the second law really says that molecules like to maximize their number of configurations. This underlies the statement that the entropy always increases; molecules never spontaneously decide to choose a smaller subset of configurations than the total number that are available to them.
Earlier we had said that the second law is not about increasing disorder. Instead, it is about increasing numbers of configurations. The two are not the same. For example, if one very quickly cools a liquid below its freezing temperature and then suddenly places it in an isolated container, as the liquid starts to freeze, the entropy increases. This actually happens because there are more configurations when some of the liquid becomes frozen. This seems counterintuitive, since one intuitively wants to think of a liquid as having more configurations than a crystal. But for very low temperature liquids, there are simply less configurations for the molecules than there would be if some of those molecules could vibrate around lattice sites in a crystal. One can even calculate this and show it to be true. Therefore, our intuitive notion of "order" and "disorder" is not really quantitative, and not always related to the number of configurations, which is what is really important.
Tuesday, February 26, 2008
Question box: more interactive problem sessions?
We received a question box comment asking if we could have more group-worked problems similar to those done during the interactive problem session, presumably during recitation hours.
This is a very useful comment to us, and we're particularly glad to hear that the interactive problem session was well appreciated. In terms of incorporating more such activities during class time, it is a bit challenging for us to do that at this point because it would require a restructuring of the remaining classes (both lectures and recitation), which are tightly balanced to cover the remaining material. This is, however, a helpful note for us in planning out course material for future years.
On the other hand, the problem sets are an excellent source of examples that you can utilize in a manner similar to the interactive problem session. You should of course attempt these problems on your own at first, but working with other students in small groups after this first attempt can help you resolve difficulty and enhance your understanding through discussions. Furthermore, Prof. Chmelka, Matt, and I hold weekly open office hours which you can use by yourself or with a group to work interactively through problem spots in the homework sets. These times have been dedicated explicitly to helping you, and we also enjoy chatting with and getting to know you better.
Cheers,
MSS
This is a very useful comment to us, and we're particularly glad to hear that the interactive problem session was well appreciated. In terms of incorporating more such activities during class time, it is a bit challenging for us to do that at this point because it would require a restructuring of the remaining classes (both lectures and recitation), which are tightly balanced to cover the remaining material. This is, however, a helpful note for us in planning out course material for future years.
On the other hand, the problem sets are an excellent source of examples that you can utilize in a manner similar to the interactive problem session. You should of course attempt these problems on your own at first, but working with other students in small groups after this first attempt can help you resolve difficulty and enhance your understanding through discussions. Furthermore, Prof. Chmelka, Matt, and I hold weekly open office hours which you can use by yourself or with a group to work interactively through problem spots in the homework sets. These times have been dedicated explicitly to helping you, and we also enjoy chatting with and getting to know you better.
Cheers,
MSS
Wednesday, February 13, 2008
Statistics for the midterm
Here is a summary of the midterm results:
Average: 56
Standard deviation: 13.5
High: 78
If you are trying to get a sense of how you did, here are some breakdowns of different point ranges:
First, try not to get too attached to the absolute value of the numbers. We take into account the performance of the entire class on the exam, and the statements above should let you know how you're doing. What's most important is that you focus on the mistakes you made, and not on the specific numbers, so that you can get a sense of what you need to improve.
Second, if you didn't do as well as you had hoped on the exam, don't let that unmotivate you. There is plenty of room to make progress on the final exam, and in the homework sets from this point on. Just make sure you identify ways to help you improve your work and studying, and you utilize all of the resources available to you (including the office hours).
MSS
Average: 56
Standard deviation: 13.5
High: 78
If you are trying to get a sense of how you did, here are some breakdowns of different point ranges:
- Greater than 70 (9 count): excellent job on the exam; you're showing that you are familiar with and can apply the material in class.
- 60-70 (11 count): good job on the exam; you have most concepts down, but there are just a few stumbling blocks where you need improvement.
- 50-60 (23 count): your performance was average; you are grasping some concepts, but you should spend some time making sure you have a firmer understanding of the material.
- Less than 50 (17 count): your performance was below average; you need to identify areas that are problematic for you and work on them by either reading the book, working through examples, or seeing the professors or TAs.
First, try not to get too attached to the absolute value of the numbers. We take into account the performance of the entire class on the exam, and the statements above should let you know how you're doing. What's most important is that you focus on the mistakes you made, and not on the specific numbers, so that you can get a sense of what you need to improve.
Second, if you didn't do as well as you had hoped on the exam, don't let that unmotivate you. There is plenty of room to make progress on the final exam, and in the homework sets from this point on. Just make sure you identify ways to help you improve your work and studying, and you utilize all of the resources available to you (including the office hours).
MSS
HW 5
Here are some of the common mistakes on homework 5:
On number 20, many people did not account for the units - you need to change Cp into m^2/(s^2*C). (Cp for water = 4.184X10^3 m^2/(s^2*C)). Or you could have changed the kinetic energy into kJ/kg. Make sure you pay attention to the signs (temperature increased in this problem).
On 21, the problem was a liquid. Therefore you cannot use the ideal gas equations for work. Also, although there was a small change in volume, there was a very large pressure change so you cannot say that there was no work done. Also, be careful you copy the equations done correctly. The second term in kappa was multiplied by P, so kappa depended on P. Therefore when you take the integral, you cannot pull kappa outside of the integral.
On 22, many people struggled with taking the derivatives. The first step was to solve the equation for V in part a and P in part b. Then differentiate. The chain rule and multiplication (or quotient) rules were necessary on part b. Many people first solved for beta and used other properties to get dP/dT. While this was correct, I believe it was a little more difficult than solving for (dP/dT)v directly. Also, the problem specified that V should not be in the answer, so you should have substituted in what V equaled in the end.
On 23, make sure you say specifically how you solved for the answer. It was OK to use your calculator or computer, but make sure you say how you got the answer. Also, make sure your answers make sense - all three methods should have given similar results. If you got something way different, make sure to check it.
On 24 and 25, you can not assume ideal behavior or constant density for the liquid. The point of these problems was to use the more detailed equations in the text. There were mutliple ways of solving these problems (RK, Lee-Kesler, generalized correlations if appropriate), but ideal gas was not a valid assumption.
On number 20, many people did not account for the units - you need to change Cp into m^2/(s^2*C). (Cp for water = 4.184X10^3 m^2/(s^2*C)). Or you could have changed the kinetic energy into kJ/kg. Make sure you pay attention to the signs (temperature increased in this problem).
On 21, the problem was a liquid. Therefore you cannot use the ideal gas equations for work. Also, although there was a small change in volume, there was a very large pressure change so you cannot say that there was no work done. Also, be careful you copy the equations done correctly. The second term in kappa was multiplied by P, so kappa depended on P. Therefore when you take the integral, you cannot pull kappa outside of the integral.
On 22, many people struggled with taking the derivatives. The first step was to solve the equation for V in part a and P in part b. Then differentiate. The chain rule and multiplication (or quotient) rules were necessary on part b. Many people first solved for beta and used other properties to get dP/dT. While this was correct, I believe it was a little more difficult than solving for (dP/dT)v directly. Also, the problem specified that V should not be in the answer, so you should have substituted in what V equaled in the end.
On 23, make sure you say specifically how you solved for the answer. It was OK to use your calculator or computer, but make sure you say how you got the answer. Also, make sure your answers make sense - all three methods should have given similar results. If you got something way different, make sure to check it.
On 24 and 25, you can not assume ideal behavior or constant density for the liquid. The point of these problems was to use the more detailed equations in the text. There were mutliple ways of solving these problems (RK, Lee-Kesler, generalized correlations if appropriate), but ideal gas was not a valid assumption.
Resources for class
Dear class-
Since we are now in the middle of the quarter, it is a good idea for you to step back and take a broad assessment of your understanding of the course material. If you feel like you are missing key concepts or are having trouble solving problems in the homework sets and exam, you should take action to get up to speed. Here are some things you can do:
MSS
Since we are now in the middle of the quarter, it is a good idea for you to step back and take a broad assessment of your understanding of the course material. If you feel like you are missing key concepts or are having trouble solving problems in the homework sets and exam, you should take action to get up to speed. Here are some things you can do:
- If you are not already reading the book, this needs to become a priority. In some courses, you may have been able to get by without reading the book. This is not one of those courses.
- Prepare a summary sheet of the key equations of the course. Make sure to distinguish between which are fundamental and which are specific to a particular substance (e.g., ideal gas).
- Take advantage of either the TA's, Professor Chmelka's, or my office hours to help you resolve lingering confusion about the material. If you are unable to make these, schedule an appointment instead.
- Tau Beta Pi also offers tutoring specifically for this course, if you are looking for a student perspective. Tutoring takes place on a regular basis in the Undergraduate Conference Room in Bldg 698. I can give you more details if you are interested, or consult the webpage http://www.engineering.ucsb.edu/~tbp/.
MSS
Thursday, February 7, 2008
Correction: sign convention for work done
Hi all,
There is another correction. There is an error in the earlier post about the sign convention used for calculating work done.
The sign convention for work done, as adopted in class and in the book (pg. 9) is expressed as:
dW = - P dV
For example, for an ideal gas, going from V1 to V2 in a mechanically reversible isothermal process,
W = -RT ln(V2/V1) = RT ln(V1/V2)
W = -RT ln(P1/P2) = RT ln(P2/P1)
Hence a compression process results in positive work, and expansion process results in negative work.
Sorry for the error in the earlier post. The solutions to HW 4 as posted use the correct sign convention, so you can refer to those and you should be OK.
thanks
badri
There is another correction. There is an error in the earlier post about the sign convention used for calculating work done.
The sign convention for work done, as adopted in class and in the book (pg. 9) is expressed as:
dW = - P dV
For example, for an ideal gas, going from V1 to V2 in a mechanically reversible isothermal process,
W = -RT ln(V2/V1) = RT ln(V1/V2)
W = -RT ln(P1/P2) = RT ln(P2/P1)
Hence a compression process results in positive work, and expansion process results in negative work.
Sorry for the error in the earlier post. The solutions to HW 4 as posted use the correct sign convention, so you can refer to those and you should be OK.
thanks
badri
Wednesday, February 6, 2008
Graded HW4 set
Hi class-
Your graded homework 4 sets will be outside of my office until 6:30pm today. I don't want to leave them there overnight, but you will be able to pick them up tomorrow morning 8:30am and on as well.
MSS
Your graded homework 4 sets will be outside of my office until 6:30pm today. I don't want to leave them there overnight, but you will be able to pick them up tomorrow morning 8:30am and on as well.
MSS
HW 4 solution error
There is an error in the solution set posted for HW 4. The solution to Problem 17 is NOT 119. 15 F, it is 109.24 F. Sorry!
Badri
Badri
HW 3 and HW 4 common mistakes, notes
Hi everyone,
A few common problems people faced in HW 3:
1. Integrating dW = PdV correctly to find the work done:
For constant volume processes, W = 0. (If the process is also adiabatic, Q = 0 and therefore delta(U) = 0 by First Law).
When there is work done, we use an equation of state (EOS) or similar relation to find P as a function of V so that we can integrate the equation, e.g. for an ideal gas we use P = RT/V and obtain the equation W = R.T. ln(V2/V1). If you have a different EOS as in Problem 12, you have to use the appropriate relation for P as a function of V.
2. Sign convention for work/heat:
Be very careful about the sign! I noticed a lot of errors (especially when you add up work done or heat associated with multi-step processes) due to incorrect sign. Remember, work done by a system (i.e. expansion work) is positive and work done on a system (i.e. compression work) is negative.
now, on to HW 4:
Open vs. closed systems: with regard to Problem 17:
You cannot apply the relations derived for adiabatic closed systems to relate T2 to T1 in this case! There is continuous mass flow in and out of the system, and that is an immediate indication that you have to perform mass and energy balances for the open system. This will allow you to calculate the change in enthalpy as a function of change in flows, work done, heat inputs, etc. The enthalpy, of course, depends on the state variables (P and T) and this will let you find their values.
Energy balance units:
You have to convert all the terms in the equation to the same system of units. Note that the delta(u^2) terms has units of m^2/s^2, which is equivalent to J/kg. If your enthalpy units are kJ/kg, you must convert before plugging into the energy balance equation or your answers will be way off.
Finally, I was a bit disappointed to see answers on Problem 18 with exit diameters greater than 6 cm. The problem statement itself specifies that the system has a converging nozzle, i.e. D2 MUST be less than D1! If your calculations say otherwise, they are obviously wrong and you should try to find the error. Common sense is your biggest ally while performing engineering calculations.
Good luck on the midterm.
Badri
A few common problems people faced in HW 3:
1. Integrating dW = PdV correctly to find the work done:
For constant volume processes, W = 0. (If the process is also adiabatic, Q = 0 and therefore delta(U) = 0 by First Law).
When there is work done, we use an equation of state (EOS) or similar relation to find P as a function of V so that we can integrate the equation, e.g. for an ideal gas we use P = RT/V and obtain the equation W = R.T. ln(V2/V1). If you have a different EOS as in Problem 12, you have to use the appropriate relation for P as a function of V.
2. Sign convention for work/heat:
Be very careful about the sign! I noticed a lot of errors (especially when you add up work done or heat associated with multi-step processes) due to incorrect sign. Remember, work done by a system (i.e. expansion work) is positive and work done on a system (i.e. compression work) is negative.
now, on to HW 4:
Open vs. closed systems: with regard to Problem 17:
You cannot apply the relations derived for adiabatic closed systems to relate T2 to T1 in this case! There is continuous mass flow in and out of the system, and that is an immediate indication that you have to perform mass and energy balances for the open system. This will allow you to calculate the change in enthalpy as a function of change in flows, work done, heat inputs, etc. The enthalpy, of course, depends on the state variables (P and T) and this will let you find their values.
Energy balance units:
You have to convert all the terms in the equation to the same system of units. Note that the delta(u^2) terms has units of m^2/s^2, which is equivalent to J/kg. If your enthalpy units are kJ/kg, you must convert before plugging into the energy balance equation or your answers will be way off.
Finally, I was a bit disappointed to see answers on Problem 18 with exit diameters greater than 6 cm. The problem statement itself specifies that the system has a converging nozzle, i.e. D2 MUST be less than D1! If your calculations say otherwise, they are obviously wrong and you should try to find the error. Common sense is your biggest ally while performing engineering calculations.
Good luck on the midterm.
Badri
Review session
The review session for the midterm will be at 7pm on Thursday Feb 7. The room is tentatively set to 3361.
HW3 common mistakes
Here were some of the common issues on HW 3:
1. Some had trouble integrating dW = PdV to find the work done under various conditions. Be sure to know when pressure is constant and when it varies (and how). On Problem 11, many people failed to realize that the system is adiabatic and hence there is no change in temperature/internal energy since it is an ideal gas. On Problem 12, many people tried to find W as a function of P1 and P2, i.e. they didn't know which variable to substitute between P and V (several people also tried to substitute V as f(P) after integration).
2. There were many 'intuitive' answers for Problem 9 based on Raoult's law etc. Credit was given if the reasoning was accurate, but the phase rule is a more general and powerful explanation since it can be applied to ternary and higher systems etc.
3. On Problem 13, there was some confusion about the sign for W.
1. Some had trouble integrating dW = PdV to find the work done under various conditions. Be sure to know when pressure is constant and when it varies (and how). On Problem 11, many people failed to realize that the system is adiabatic and hence there is no change in temperature/internal energy since it is an ideal gas. On Problem 12, many people tried to find W as a function of P1 and P2, i.e. they didn't know which variable to substitute between P and V (several people also tried to substitute V as f(P) after integration).
2. There were many 'intuitive' answers for Problem 9 based on Raoult's law etc. Credit was given if the reasoning was accurate, but the phase rule is a more general and powerful explanation since it can be applied to ternary and higher systems etc.
3. On Problem 13, there was some confusion about the sign for W.
Friday, February 1, 2008
Web resource for thermophysical properties
In addition to the book, there are a number of websites that maintain property databases. The National Institute of Stantards and Technology (NIST) maintains an extensive listing of properties for many substances that are easily user-customized in terms of ranges of temperature or pressure, choice of units, etc. That website can be located here:
http://webbook.nist.gov/chemistry/
MSS
http://webbook.nist.gov/chemistry/
MSS
HW5, problem 21
There may be a little bit of confusion about how to proceed on this problem. You will have to make an approximation at some point in order to evaluate the solution. You should first try to carry your equations as far as possible towards the end goal, and then make your approximation at the end. (Hint: think about what aspects of the process will change by a large and small amounts).
-MSS
-MSS
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