PHYS 333
Winter 2009
Assignment 1
Due: 5:00 pm Friday January 9 This assignment is a review maybe? of some math ideas that we will need fairly frequently in the course. If the ideas are new to you, then you should probably come and see me!
1. In Chapter 1
PHYS 333
Winter 2008
Assignment 10
1. Schroeder 7.16 A system of N (spinless) identical fermions has equally spaced energy levels which are all non-degenerate. (That is, each level holds only one fermion.) At low temperatures, it is useful to represent ea
PHYS 333
Winter 2009
Assignment 3
Due: 5:00 pm Friday January 23 Most of these problems are from Schroeders book.
1. Schroeder, problems 2.18/22/30 (a) Use Stirlings approximation to show that the multiplicity of an Einstein solid, for any large values of
PHYS 333
Winter 2009
Assignment 3
Most of these problems are from Schroeders book.
1. (a) Use Stirlings approximation to show that the multiplicity of an Einstein solid, for any large values of N and q , is approximately
q +N q q q +N N N
(N, q )
2q (q +
PHYS 333
Winter 2009
Assignment 9
1. Schroeder, 6.32, modied. Consider a classical particle moving in a one-dimensional potential well u(x), as shown in the gure. The particle is in thermal equilibrium with a reservoir at temperature T , so the probabilit
PHYS 333
Winter 2009
Assignment 2
Due: 5:00 pm Friday January 16 All of these problems are from Schroeders book.
1. Schroeder, problem 1.22 If you poke a hole in a container full of gas, the gas will start leaking out. In this problem you will make a roug
Signals
a) Speech
Produced by the vocal cord and perceived by the ears
Units measured in Hz
Domain is time ranging from 0 to infinity
Range is frequency measured in Hz
Voices of unusual frequency could be an indication of diseases such as vocal cord
We have identical particles each having a magnetic moment
having spin up and having spin down , so that
. There are two types of particles,
.
Internal chemical potentials for particles of type 1 and 2 are
External chemical potentials (due to magnetic mome
SJ
Chapter 2: Entropy and Tcmpemrure \
(c) How large is the fractio
nal error in the entropy when you ignore this
factor?
approxtmately the probability that the fractionat deviation fro
MNl is 10 or larger. Take N, = N2
use an asymptotic expansion for the
PHYS 333
Winter 2009
Assignment 8
1. A question on Osmosis. For this problem you need two additions to the theory of osmosis found in the textbook (page 203) and discussed in class. They are that: the chemical potential of a solvent containing two dilute
PHYS 333
Winter 2008
Assignment 7
1. The Helmholtz function The Helmholtz function is dened as F = U TS Starting from this denition, prove the following identities F T F V = S
V ,N
(1)
= P
T ,N
(2)
These require F to be written as a function of T , V and
PHYS 333
Winter 2009
Assignment 6
Due: 5:00 pm Monday March 3rd Most of these problems are from Schroeders book. Problems 2 and 3 use Tables 4.1, 4.2, 4.3 and 4.4 from the book: they are provided as a separate PDF le for those who need them.
1. Schroeder
PHYS 333
Winter 2009
Assignment 5
Due: 5:00 pm Friday February 20 Most of these problems are from Schroeders book.
1. A question concerning the mathematics of the T dS equation. In class, and in the textbook, we have seen the T dS equation: T dS = dU + P
PHYS 333
Winter 2009
Assignment 6
Due: 5:00 pm Friday March 6 Most of these problems are from Schroeders book. Problems 2 and 3 use Tables 4.1, 4.2, 4.3 and 4.4 from the book: they are provided as a separate PDF le for those who need them.
1. Schroeder 4.
PHYS 333
Winter 2009
Assignment 7
Due: 5:00 pm Friday March 20 1. The Helmholtz function The Helmholtz function is dened as F = U TS Starting from this denition, prove the following identities F T F V F N T2 = S
V ,N
(1) (2) (3) (4) (5)
= P
T ,N
=
T ,V
(
PHYS 333
Winter 2009
Assignment 8
Due: 5:00 pm Friday March 27
1. A question on Osmosis. For this problem you need two additions to the theory of osmosis found in the textbook (page 203) and discussed in class. They are that: the chemical potential of a s
PHYS 333
Winter 2009
Assignment 9
Due: 5:00 pm Friday April 3
1. Schroeder, 6.32, modied. Consider a classical particle moving in a one-dimensional potential well u(x), as shown in the gure. The particle is in thermal equilibrium with a reservoir at tempe
PHYS 333
Winter 2009
Assignment 10
Due: 5:00 pm Friday April 17
1. Schroeder 7.16 A system of N (spinless) identical fermions has equally spaced energy levels which are all non-degenerate. (That is, each level holds only one fermion.) At low temperatures,
PHYS 333
Winter 2009
Assignment 1
1. In Chapter 1 of Schroeders book, he talks about raindrops falling on a roof. He uses this example to introduce the thermodynamic limit when uctuations are extremely small. Divide up the roof into N B equal parts (N B =
PHYS 333
Winter 2009
Assignment 2
All of these problems are from Schroeders book.
1. Schroeder, problem 1.22 If you poke a hole in a container full of gas, the gas will start leaking out. In this problem you will make a rough estimate of the rate at which
PHYS 333
Winter 2009
Assignment 4
1. Entropy of Mixing. Calculate the increase in entropy when two dierent ideal gases diuse into each other. The two gases are originally in separate containers, but with the same pressure and temperature. There are NA mol
PHYS 333
Winter 2009
Assignment 5
1. A question concerning the mathematics of the T dS equation. In class, and in the textbook, we have seen the T dS equation: T dS = dU + P dV In many traditional textbooks, this equation is derived from thermodynamics, a
6
Chapter 4: Thermal Radiation and Float-k Dinriizurion
greenhouse cect. Because the thermal ux varies as T the new temperature
ofthc surface ofthe Earth' :3
TEA; = were a- cfw_m 280 K m 333 K, (60)
so that the greenhouse warming ofthc Eatth is 333 K w- 2