ECH 6709: Electrochemical Engineering: Fundamentals and Design
Fall 2013
Homework Set #5
Date: October 7, 2013
Due: Thursday, October 10, 2013
1.
During a thesis defense, a professor noted that the standard cell potentials listed by the student for
the re
Question 1:
Chlorine occurs naturally in two stable isotopes: Cl35 with an atomic weight of 35 and an
abundance of 76% and Cl37 with an atomic weight of 37 and an abundance of 24%. Chlorine gas
is a diatomic molecule, which can be synthesized from natural
Project 3: Simulations of a two-dimensional Lennard-Jones Model
This is the final project, and is due by 5pm Wednesday December 11th.
Write a python function to create an initial configuration (x and y coordinates) for a 5X5 array of
particles. It is best
Project 1: Simulations of Ideal Polymers in 2D due Monday October 7th
In class I described a way of generating conformations of an ideal chain by using a random walk. For
this project, your first task is to write a simulation of a two-dimensional ideal ch
Project 2: Simulations of a two-dimensional Ising Model due Tuesday November 12th
In the IPython shell create an initial state vector S0 for a 20x20 array of spins, with half of them up and
half of them down, as shown in Fig. 6.3 (left panels) on page 167
Solutions 13.
The derivation of the heat capacity follows the same lines as in the 3D case start with the partition
function and differentiate twice with respect to .
N
N
N
ln Q = U ( X0 ) + n=1 h n + i=n ln ( 1 exp [ h n ] ) .
N
( h n )2 exp ( h n )
2 (
Solutions to HW 2
1) In thermodynamics problems it will frequently be useful to identify an appropriate set of
independent variables. This helps clarify our thinking. Clearly N is a good independent variable
because its fixed. Our other choices are E, S,
3a) Three segments with 4 choices of direction for each segment so 43 = 64.
b) The easiest way to make the calculation is to figure out how many distinct configurations there are.
There are many different ways to construct the sum, including considering e
3) For the end-to-end distance we have x=3 and y=2 (in units of the lattice spacing). So RE = 131/2 ~3.6.
For RG we first need to choose an origin say bottom left. Then the mass points are at:
(0,0), (0,1), (1,1), (2,1), (2,2), (3,2).
The center of mass i
5.24) This problem requires some work to figure out what the possible states are. Once you have done
that its not all that hard. This is a simple model of a ferroelectric phase transition, which is where a
material spontaneously polarizes or takes up an e
3.18: The problem specifies the independent variables as , H , N. However when we look at the
Hamiltonian (or energy) for the spin system we see that energy for a given state is related to the
magnetization:
N
N
E =i =1 ni , H = M H , where the magnetizat
1.15 Rewrite 1st law: dS = dE p dV dN. Legendre transformations give the two potentials:
1= S E , and 2=S E N.
The differential relations are:
d 1= E d p dV dN , and d 2= E d p dV N d .
Note that the thermodynamic forces (or conjugate variables) in this c
Homework 2 due Monday September 2
1) Study Sections 1.3 (pp 11-13) in Chandler. I covered some of this in class, but it is not so easy
to follow; make sure you understand the arguments.
2) Solve problems 1.13 (at least find the chemical potential) and 1.1
An Introduction to Python 8: Debugging in Python
By this point you have probably discovered that your programs do not always work first time.
This is not necessarily cause for despair because there are a number of tools to help you. The first
hurdle to ov
An Introduction to Python 7: Customizing Figures
Plotting Multiple Graphs in the Same Figure
So far, you used the following command to plot a graph of a single function:
plot(x,y)
This command plots y as a function of x. You may have already noticed that
An Introduction to Python 6: File handling and plotting
You will frequently want to save the results of your calculations for example plots of data or
perhaps the data itself. We can save data using the pickle module, which can be loaded in the usual
way,
An Introduction to Python 5: Conditional Statements
You often need to perform different operations depending on whether a particular condition is
satisfied or not. For example, it can be a good idea to prevent users from entering nonsensical data. In
this
An Introduction to Python: 4. Loops
You will often need to perform repetitive tasks. For example, to simulate the time evolution of a
molecular system you will have to repeat very similar calculations at each time-step. These tasks can be
automated by usi
An Introduction to Python: 3. Modules, Editors, Reusing Functions
This tutorial will show you how to write and save a simple program so that it can re reused
whenever you want. To do this you need to learn how to use the editor (fortunately this is easy)
An Introduction to Python: 2. Lists and Arrays, Functions, and Modules
This tutorial introduces some basic programming concepts within Python. It is by no means a
complete discussion just some notes to help you get started.
1) Lists and Arrays
Python list
An Introduction to Python: 1. Getting Started
1) What is Python?
Python is an open-source (meaning you can download the entire source code) programming
language which runs under Windows, Mac OS, and Linux or in other words anything (possibly
including you
Computer Memory Limits
The fast memory on your computer (called Dynamic Random Access Memory or DRAM) is limited
typically to between 1 and 4 gigabytes depending on the age of the computer. In the Windows Task
Manager (Performance tab) you can find infor