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 st
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 d
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
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
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 th
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 +
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 v
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 diffe
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),
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 wh
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
magneti
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
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 probl
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