Assignment 3 Solutions
(1) The macrostate probability is Binomial[N,n]/2^N. Here are a few loops that define these probabilities for different
values of N. I also calculate the maximum of the distribution, and the value of n where the distribution falls t
Chapter 4
Engines and Refrigerators
Were surrounded by machines, devices that consume energy. How is this energy produced? How
do engines actually work? How can we reduce our environmental impact without sacricing our
technological progress? These are the
1
PHYS 449 - Statistical Mechanics I
Midterm Solutions
Part 2: Each question is worth 30 points (30 points total)
1. (a) Initially we have an ideal gas satisfying the equation of state P V = nkB T and mean energy U = (f /2)N kB T ,
where f counts the numb
PHYS 449 - Statistical Mechanics I
Assignment 6 Solutions
1. Lets start the cycle at volume V1 and pressure P1 . First we have an isobaric expansion, bringing the system
to a new volume V2 but at the same pressure P1 (thats what an isobar is!). The temper
PHYS 449 - Statistical Mechanics I
Assignment 5 (50 points total)
Due Thursday, Oct. 31, 2013 at 3:30pm
1. (10 points) The quantized energy levels for a one-dimensional particle in a box of length are n = h2 2 n2 /2mL2 ,
as derived in class using Bohr-Som
PHYS 449 - Statistical Mechanics I
Assignment 1 (35 points total)
Due Thursday, Sep. 19, 2013 at 3:30pm
1. (5 points) Obtain an account on the Physics Junior Labs computers (see Peter Gimby, ST042,
220-5403, e-mail: [email protected]). Be sure to as
PHYS 449 - Statistical Mechanics I
Assignment 3 (60 points total)
Due Thursday, Oct. 10, 2013 at 3:30pm
1. (30 points)
(a) (10 points) Use Mathematica or Maple to plot the probabilities of obtaining n heads for a fair (i.e. equally
weighted) two-sided coi
PHYS 449 - Statistical Mechanics I
Assignment 4 Solutions
1. The Shannon entropy is
d
pi log2 pi .
S=
i=1
The Boltzmann entropy is the same, other than a prefactor of kB and the base of the log is e. Neither of those
things are important for this proof, s
PHYS 449 - Statistical Mechanics I
Assignment 1 Solutions
1. That was an easy 5 points, eh?
2. (a) First of all lets assume that the gas is made up of mostly nitrogen (diatomic) molecules,
which is correct for air. A bit of searching on the web (actually
2
Human Coding
Human coding is a popular method for compressing data with variable-length codes.
Given a set of data symbols (an alphabet) and their frequencies of occurrence (or, equivalently, their probabilities), the method constructs a set of variable
PHYS 449 - Statistical Mechanics I
Assignment 5 Solutions
1. (a) To estimate the number of occupied levels at room temperature (though any suitable temperature of your
choosing is ok with me), we would use
h
2 2 n2
max
= kB T.
2mL2
This gives
2mL2 kB T
n
PHYS 449 - Statistical Mechanics I
Assignment 7 Solutions
1. (a) Return now to problem #2 in Assignment 5, where only three energy levels of a particle in a one-dimensional
box are accessible to a particle: = cfw_0, 1, 4 1 , where 1 = h2 2 /2mL2 . The par
PHYS 449 - Statistical Mechanics I
Assignment 2 Solutions
1. (a) If the system is thermally isolated, and the process is suciently slow, there is no heat associated with the
process. So the change in energy is entirely due to work. For the left side, the
PHYS 449 - Course Notes 2012
25
2.5
(This section skipped)
2.6
Entropy
Entropy is the fundamental postulate of statistical mechanics (at least, after the ergodic
principle!). Boltzmann suggested that the entropy of a system S is somehow related to the pro