ECH 6709: Electrochemical Engineering: Fundamentals and Design
Homework Set #5
Date: October 7, 2013
Due: Thursday, October 10, 2013
During a thesis defense, a professor noted that the standard cell potentials listed by the student for
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
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 .
ln Q = U ( X0 ) + n=1 h n + i=n ln ( 1 exp [ h n ] ) .
( h n )2 exp ( h n )
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
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
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