ChE 151: Process Simulation and Mathematical Techniques for Chemical Engineers Prof. Davis Spring 2016 Homework 1: 30 points total Due Monday, February 1st (at the beginning of class) Be sure to write your name and the names of your other group members on your submission. Please E-mail me or come to office hours if you have questions. 1. (5 points) Give an example of a system of linear equations that might arise in a chemical

engineering problem from mass and energy balances. (Hint: your Felder and Rousseau textbook will help you). Explain the process in 2-3 sentences (What is the feed? What are the products? What are you making/doing?) AND draw a picture of it (block flow diagram or BFD). Make sure you mention why you know the system is linear. If you take your example from a source, make sure you cite the source.

2. (6 points total)

A. (3 points) Show that the Peng-Robinson equation of state:

2 2 2RT aP

V b V bV ba

= +

Can be expressed as a polynomial of the dimensionless compressibility factor (Z) when T and P are known. Use the same parameters A and B that we used in class for the SRK equation of state. YOU MUST SHOW ALL WORK TO GET FULL CREDIT!

B. (3 points) Explain why this rearranged equation of state is a more numerically convenient way to determine the density of a gas at a given temperature and pressure by comparing it to the original equation. (2-3 sentences)

3. (8 points) Problem 2 from exercise set 1.2 in Faires and Burden (p. 14) be sure to show all work for full credit. Label your answers a. through d. on your paper. Dont forget to PROVE the function properties necessary to apply the proof.

4. (6 points) Problem 10 from exercise set 1.2 in Faires and Burden (p. 15) be sure to show all

work for full credit. You may need to read a little bit about error and accuracy in section 1.2; please come to office hours or E-mail me if you cant determine what the problem is asking for.

5. (5 points) Open up Matlab (its available in the 8th floor computer lab). Click on the New icon in the top left corner to create a new *.m file (a script). Save it as FirstnameLastname.m, but use your first name instead of Firstname and your last name instead of Lastname. Type in the following, one line at a time:

% You make a comment in Matlab using the percent sign (it turns green) % I promise I typed this all out with my own fingers and didnt just copy and paste it clear all % This clears the workspace (memory) of all variables this is

% useful so that you dont use an old value when you run the script again format long % This makes the output show more digits (double precision format) clc % This clears the command window (where the outputs are displayed) close all % This closes all open figures (useful when you make lots of them) w = Hello, world!; % This is how you make a string variable in Matlab; the variable v

% now represents a string of text, but you cant do math with strings. . . y = 8; % The semicolon means the command isnt displayed y is now 8 z = 4 % No semicolon = command is displayed in the command window disp(w) % This will display the string v in the command window x = linspace(0,1,1000); % This will make a vector/array of 1000 points from 0 to 1 fx = 3*x.^2 + 0.5*x.^0.5 log(x/3); % This will make f(x) you need to have .^ for vectors plot(x,fx,k-); % This will plot f(x) v. x as a black line Pressing F5 will run your script. Typing help, then a space, then the name of the function you want to use (e.g. linspace or disp) will tell you about that function. Add to your *.m file as many other Matlab subroutines (functions) as you like / want to learn / already know and then upload the file to Moodle. Make sure your scripts runs correctly with all the things you added. Print out a hard copy and hand it in with your submission; please do this for every script I ask you to write in this class unless I specify otherwise. 6. (0 points) List the number of hours you spent on work for this class for this week, not

counting time spent in class. Put it on the very top of your homework, under your name and the names of your other group members like this:

Name 1

Name 2 Hours spent on 151 this week: 5.5 hours

Objectives addressed on this assignment:

Give bounds on the error in the solution to a problem using a numerical method Explain where a linear system of equations might come from and when they are solvable