Final exams

Class,

If you did not get back your final exams, you may stop by my office this week to get them.

In addition, if you have subscribed to this blog by email, you may want to remove yourself at this point, as it will be used for future courses that I teach.

Good luck in your future studies,

MSS

Final exam and course grades

Dear class,

Summaries of grade distributions for the final exam and the course grades can be found at the course website.

Also, I will be handing out the graded exams the first day of the 110B course next week. We will also discuss the solutions then.

MSS

Leftover HW9 sets

If you didn't get your graded HW9 back, you can pick it up at my office tomorrow morning.

MSS

HW9

HW9 solutions have been posted and the graded problem sets will be distributed at the review session.

MSS

Review Session

Badri and I will be holding a Review Session on Thursday Evening at 7 pm in Engr. II 3361. We will mainly be answering questions so bring any questions that you have.

I am not planning on holding any official office hours today or tomorrow, so if you have questions you want answered before the review session (or if you can't make the review session), feel free to email me (mblack@engr.ucsb.edu) with questions or to set up a meeting.

-Matt

How to study for the final

I've had a couple of folks inquire as to the best way to study for the final. Here are my thoughts on that.

It is very easy to feel like there are a tremendous number of equations, processes, and special cases to deal with, particularly in the last few chapters on engines that we covered this week and last. You should not try to memorize each and every case. Instead, you should try to understand what are the systematic approaches you take to solve these problems so that you can tackle any problem!

So what should you know? How should you approach a problem?

(1) Sketch out complete diagrams. Make flow diagrams, labeling streams in complete detail, if it is an open system. Make PV diagrams, labeling all points and processes, including work and heat flows and their signs. Making complete diagrams should tell you immediately what is known and what is unknown. Moreover, this process helps you translate the textual description of the problem into a clearer more organized format that will be easier to work from.

(2) Apply the fundamental equations. We wrote these out for you on a handout so you could see what these are. Each and every problem you have tackled can essentially be worked out starting from these equations. The book spends a lot of time deriving special case formulas based on these, but it is much more productive for you to understand how to get from the fundamental equations to the final answer without having to flip through the book looking for the specific case formula (which can often cause you to make errors during exams if you are time crunched and don't read the text surrounding the equations). On the exam, our main intent for having open book is so that you have access to reference data like heat capacities, equation of state parameters, etc. You should not have to flip through the book to find equations for each problem.

(3) Use variables as much as possible, and plug in numbers at the very end. This helps prevent numerical and units mistakes.

(4) Do consistency checks. Do the units work out? Are the numbers physically reasonable?

In studying for the final, I would recommend you go back to all of the homework problem statements. Look at the problems, without looking at the solutions, and ask yourself: "Can I solve this right now from the fundamental equations, without looking up a bunch of formulas in the book or reading the text?" If you can do that, you are good to go. If you can't, I would try to sketch an outline for the solution to that problem again starting from fundamentals.

A good way to test yourself would be to pick one of the application-oriented problems from the book in the later chapters we've been studying, and see how far you can get through it without having to rely on text in the book.

Prof. Chmelka and I will both be around next week if you would like to see us. You can come in if our office doors are open; otherwise, feel free to shoot us an email to find a good time to meet.

MSS

Some information on summer jobs

Dear class-

I happen to come across a couple of links regarding summer internship and research opportunities, and I'm passing these on to you in case you are interested. Now actually is the time to get going on these, as many deadlines for internships and research occur in March.

The NSF runs a program called Research Experience for Undergraduates (REU). Many departments in different scientific and engineering disciplines around the country run this program. I believe Professor Chmelka mentioned one such program at U. Delaware earlier in the course. The following is a student-centric website provided by NSF that has a search function for all of the participating departments, as well as links to the individual programs:

http://www.nsf.gov/crssprgm/reu/

If you are interested in an internship, the AIChE website has a list of links to companies that commonly offer such opportunities to chemical engineering students. For many of these, you can click through to get to the company website, and then follow the link to "careers" to get to an internship-specific information section. The list is at:

http://www.aiche.org/Students/Careers/internships.aspx

MSS

TA Office Hours Switch

TA Office hours will be held next week on Wednesday at 4 and Thursday at 9 in the TA office (there will be no office hours on Monday or Tuesday). I will also be available immediately after class on Wed. If you have other questions, you can email me (mblack@engr.ucsb.edu).

Thanks,

Matt

Calculating residual properties using equations of state

Yesterday in class I worked an example for how to calculate residual properties using the van der Waals equation of state. The first step of performing such calculations was to convert the integrals for the residual properties to a form that allowed easy substitution of an equation of state in the form P(T,rho). This meant we had to convert the integrals in P to integrals in rho.

I know we went through this very quickly, due to time constraints, but just keep in mind that this is just a mathematical manipulation of the equations to swap rho for P. It is just like any other variable substitution you have done in integral calculus. The book has a detailed derivation on pages 216 and 217 that shows exactly how to do this manipulation.

The final equations for the residual properties are given in 6.58, 6.59, and 6.60. These equations are fundamentally no different than those we discussed earlier (shown in the book in 6.46, 6.48, and 6.49); they simply involve integrals using rho rather than P.

This should be helpful in your working with problem 44 on the homework.

MSS

A question about ideal gas heat capacities

I was asked why the heat capacity in problem 38 is Cp = 5/2R, rather than 7/2R. Here is a short explanation of heat capacities for ideal gases:

Generally, an ideal gas is something that obeys PV=RT and that has U(T) only (i.e., U is not a function of pressure or volume). Saying that something is an ideal gas does not immediately specify the heat capacities, although it does say that they are independent of P or V since U(T) and H(T) only.

In some specific instances, however, we can use some approximations to the heat capacities for the ideal gas if we know about the molecular structure:

Cp=5/2R for a monoatomic system
Cp=7/2R for a diatomic system

Thus it depends on the kind of ideal gas that you have (monoatomic or diatomic). So in problem 38, it is likely that the problem refers to an ideal gas with a monoatomic molecular structure.

Why should diatomic gases have a higher heat capacity? Recall that the heat capacity measures how much the internal energy or enthalpy changes with temperature. In a diatomic ideal gas, energy can be stored in the bond that connects the two atoms, in addition to the kinetic energy of the molecule. By stretching and compressing like a spring, the bond can contain potential energy. Therefore, the heat capacity is higher than for a monatomic gas because there is this additional place to store energy as the temperature increases.

In other more complicated systems, the heat capacity for an ideal gas can be a function of temperature, which is usually well-fitted by the form that we've been using in class. Note, however, that still for an ideal gas, these forms do not have a P or V dependence. This is why they are still called "ideal gas heat capacities". The way in which we figure out what the properties of real gases are, for example the enthalpy, is to first figure out what the ideal gas enthalpy would be at the given temperature and pressure using these heat capacity expressions, and then to add back in the part that might need to account for deviations from ideal gas behavior:

Delta H = Delta Hig + Delta Hresidual

where the Delta Hig comes from the ideal gas heat capacity integral and Delta Hresidual comes form the expressions developed recently in class that use PVT data.

MSS

Common Mistakes on HW7

On problem 32, some people didn't look up the correct Tn to plug into the equations 4.12 and 4.13.
Overall, make sure that you are computing the integrals for Cp correctly. It seemed there a lot of people that had the right set up, but did not get the correct answer.
On 33, some people ignored the fact that there were 3 different deltaH's that needed to be calculated (heating the liquid to 368, delta H of vaporization, and heating the gas from 368 to 500).

On 35, make sure all your signs are correct - the heat is being removed from the system (so Q is negative).

On 36, you only needed to concern yourself with the amount that was reacted. While it was technically correct to cool the steam and non-reacting species to 298 and then heat them up again, you should realize that if they do not react, these actions will cancel each other out (since it was isothermal). So you only need to compute all the deltaH's for the .33 moles of butene that reacts (for a 1 mole basis feed).

-Matt

HW8, problem 43

The efficiency is defined differently in this problem than in the case for a heat engine. The reason for this difference is that what we are putting in is a work (the work required to refrigerate) rather than a heat (the boiler in the Carnot cycle, for example). Here, the efficiency is closer to the "isentropic efficiency" we discussed in class for the turbine. For cases in which we expect the nonideal work to be less than the ideal work (as in a turbine), we have:

eta = (actual work required) / (work required in the ideal reversible case)

On the other hand, for cases in which we expect the nonideal work to be greater (as in refrigeration), we have:

eta = (work required in the ideal reversible case) / (actual work required)

Regardless, eta is always defined so that it is less than one.

In general, efficiencies tend to measure works relative to an ideal case. In the special case of a heat engine (like a Carnot engine), the efficiency we discussed is relative to a sort-of "super ideal" case in which all of the boiler heat is converted to work.

So the general way in which one treats problems like this is almost always the same:
(1) Solve the system as if it were ideal (reversible processes) -- in this case, it is a straightforward application of the open energy balance and the entropy generation equation.
(2) Use the efficiency to relate the actual work to the ideal work.

MSS