Questions regarding HW6

Some questions and answers-

The table C.1 has values of B divided by 10^3, but the examples in the book have 10^-3. Could that be a typo?

What the book is reporting is the value of B times 10^3, so that the actual value of B is a factor of 10^3 smaller. Think of the number listed in the table as a value x. Then, we have B*10^3 = x so that B = x * 10^-3. Similar for C and D.

I am trying to work on problem 4.2 part a, using the example 4.3 as a guide. So for the iteration of the mean heat capacity over R, how can I compute it without having a value for tau? Should I assume first it equals to 1, starting with T = Tzero, then getting a value for heat capacity, plug it into T = deltaH/Cp + Tzero. Then using the new T, with new tau , get another value for Cp, then another value for T and so on?

Yes, exactly. Remember, the mean heat capacity depends on both the initial and final temperatures. Consider constant pressure heating where the heat duty is specified. In this case, the first law is:

Delta H = Q/n

We can rewrite Delta H using the mean heat capacity and the temperature change:

(Tf - T0) Cpavg = Q/n

We can solve this for Tf, but it is highly nonlinear in Tf. Why? This is because Tf not only appears in the temperature difference, but it is part of the expression for (by way of tau). Setting up an iteration helps us solve this nonlinear equation:

Tf = (Q/n) /Cpavg + T0

You start with a guess for Tf and plug it in. The easiest guess is just to use T0. Then, you use this equation to continue to get new guesses for Tf until you converge on one value. At that point, you have found the value of Tf that solves the original equation.

Cheers,
MSS

Office hours on Monday 2/15/10

Dear Class,
I will have regular office hours on Monday (2/15/10) from 10-11am in Engr. II 3301.
-Nathan

Problem Set 5

Dear Class,

If you turned in Problem Set 5 on Monday and would like to work on it during your extension, you can pick up your Problem Set from me in my office (Engr. 3218) until 5:00 pm today or during office hours from 5-6 pm in Engr. II 3301.

Cheers,
Nathan

Classroom change reminder

Dear class,

This is a reminder that today's class will be our first in the new classroom, EII 1519. It is located in the new construction of the EII quad, on ground level immediately to the right of the large stairway as you walk up to Chemical Engineering.

MSS

Extension on HW5

Dear class,

Since there are a number of midterms this week and last, I will extend the deadline for turning in HW5 until Wednesday at the beginning of class. However, I will still hand out HW6 today.

Cheers,
MSS

Questions and answers

Here are a few questions that I received through email and responses that may be useful to you.

I was just wondering how much of the virial expansion we will need to know. I am assuming everything we learned, to be safe. But I was wondering if there was a certain emphasis you wanted us to have, such as where the equation comes from or solving a problem like the example we had in class.

What we covered in lecture should be sufficient for understanding the virial equation. Generally, anything presented in lecture is what you should know very well, especially since we are covering a lot of material in just 10 weeks.

When do you know where to use the virial expansion? In the book example and the one in lecture the values for B and C were given, indicating that the virial equation would be used. Is there a table in the book for the values?I couldn't find one. Or would we be given the values if they were needed?

Second (and sometimes third) virial coefficients are tabulated for a wide range of systems because they are often easy to measure experimentally, but I don't think the book has a table. Generally if we work a problem these values will be given. In your later courses, you may see a lot more of the virial equation because it is frequently used to model dilute suspensions and colloidal solutions. But for the purposes of modeling fluids, the cubic equations of state and, even more so, the generalized correlations are usually more accurate.

Are the isothermal compressibility and the thermal volume expansivity generally constant for a specific material, or do they vary with temperature and pressure? For an ideal gas can we assume they are constant?

In general, these parameters are state-dependent, and thus depend on the specific pressure and temperature of the system. They do depend on state for an ideal gas. I believed we derived the ideal gas expressions for these parameters in lecture, but it should also be in the book if you want a second perspective.

MSS

Review session for midterm

Dear class-

We will have a question and answer review session on Wednesday 7-8pm in room 3301, Engineering II.

Cheers,
MSS