Homework 5 Solutions
Problem 5.1 (practice): Power from the ocean It has been proposed to use the thermal gradient of
the ocean to drive a heat engine. Supoose that at a certain location the water temperature is 22o C at the
ocean surface and 4o C at the
Physics 112, Spring 2013, Holzapfel
Problem Set 5 (6 problems). Due Wednesday, March 6th , 5 PM
Problem 1: Seeing in the Dark
Consider a light bulb with a tungsten lament at a temperature of T f = 3500 K.
(a) If the power input is 100 W and the emssivity
Physics 112, Spring 2013: Holzapfel
Problem Set 4 (6 problems). Due Wednesday, February 27, 5 PM
Problem 1: Temperature of the Earth & Greenhouse Effect
As seen from the earth, the sun subtends an angle of 1/2 degree. The spectral intensity I of the obser
Physics 112, Spring 2013: Holzapfel
Problem Set 3 (6 problems). Due Wednesday, February 20, 5 PM
Problem 1: Energy uctuations
(a) Kittel, Problem 3.4
(b) Consider the case of the ideal gas and calculate
become of order 10 percent of the total energy?
<(U
Physics 112, Spring 2013: Holzapfel
Problem Set 2 (6 problems). Due Wednesday, February 13, 5 PM
Problem 1: Paramagnetism
(a) Kittel, Problem 2.2
(b) Roughly plot the entropy and the temperature as a function of energy. Notice that the temperature is
nega
Physics 112, Spring 2013: Holzapfel
Problem Set 1 (7 problems). Due Wednesday, February 6, 5 PM
Problem 1: Combinations.
Welcome to Oskis Seven Flavors Ice Cream Shop. Your bowl holds four scoops and we want to know how
many ways we can ll it from the sev
Physics 112, Spring 2013: Holzapfel
Problem Set 6 (6 problems). Due Monday, March 18, 5PM
Problem 1: Centrifuge
Kittel 5.1
Problem 2: Active Transport
Kittel 5.4
Problem 3: Carbon monoxide poisoning
Kittel 5.8
Problem 4: Concentration Fluctuations
Kittel
Physics 112, Spring 13: Holzapfel
Problem Set 7 (6 Problems). Due Monday, April 1, 2013, 5 PM
Problem 1: Distribution Function for Double Occupancy Statistics
Kittel 6.3
Problem 2: Energy of Gas of Extreme Relativistic Particles
Kittel 6.4
Problem 3: The
Physics 112, Spring 2013: Holzapfel
Problem Set 8 (6 Problems). Due Monday April 8, 5 PM
Problem 1: Density of orbitals in one and two dimensions
Kittel 7.1
Problem 2: Energy of a Relativistic Fermi Gas
Kittel 7.2
Problem 3: Liquid 3 He as a Fermi gas
Kit
Statistical Physics: October 9, 2012
Solutions for the Homework 5
Problem 7.8: Suppose you have a box in which each particle may occupy any of 10 single-particle
states. For simplicity, assume that each of these states has energy zero.
(a) What is the par
RwVio
WWW
mu L W
MW
A [rm \
'ﬂgf'fgalwi/M‘NE g Q EM ma}? Aw}
Q" 61
M: ' ” r , *M’m mum m)
+ a “£3433; Problem 7.6. It’s easiest to start from the right—hand side of the desired relation and
work backwards:
kT 6E kT _3_ _[E(a)—pN(s)}/kT
_—-— _ —Z_ 28: d
Physics 112 Spring 2013
Professor William Holzapfel
Homework 9 Solutions
Problem 1, Kittel 7.13: Chemical Potential versus Concentration
(a) We know for a classical ideal gas / = ln nn , so for nn
1 we expect a logarithmic
Q
Q
1) the
behavior of the chemi
Physics 112 Spring 2013
Professor William Holzapfel
Homework 8 Solutions
Problem 1, Kittel 7.1: Density of Orbitals in one and two dimensions
In one dimension the orbitals are of the form n (x) = A sin(nx/L) where n is a positive integer.
The energy is
2
Physics 112 Spring 2013
Professor William Holzapfel
Homework 7 Solutions
Problem 1, Kittel 6.3: Double Occupancy Statistics
(a) In this problem were considering a new particle which can at most doubly occupy an orbital
(as opposed to single occupancy for
Physics 112 Spring 2013
Professor William Holzapfel
Homework 6 Solutions
Problem 1, Kittel 5.1: Centrifuge
When the gas is in equilibrium, we know that the total chemical potential will be constant throughout. The total chemical potential is = int + ext ,
Physics 112 Spring 2013
Professor William Holzapfel
Homework 5 Solutions
Problem 1: Seeing in the dark
(a) Treating the lament as a blackbody, we know that total power is given by Pb = B T 4 A, so the
area is:
=
100
100 W
=
m2
B T 4
.30 5.67 108 (3500)4
=
Physics 112 Spring 2013
Professor William Holzapfel
Homework 4 Solutions
Problem 1: Temperature of the Earth and the Greenhouse Eect
(a) We know that at equilibrium, the earth must absorb as much power as it emits: if it absorbed
more, its temperature wou
Physics 112 Spring 2013
Professor William Holzapfel
Homework 3 Solutions
Problem 1: Energy Fluctuations
a) Kittel 3.4
From the denition of mean square uctuation we have
)2 = < ( < >)2 > = <
(
=<
2
2
2 < > + < >2 >
> < >2 .
We also have
U=
1
Z
s /
se
s
a
Physics 112 Spring 2013
Professor William Holzapfel
Homework 2 Solutions
Problem 1: Magnetization
a) For the paramagnet, we can use the Gaussian approximation to the multiplicity
in terms of the total number of spins N and the spin excess s:
g (N, s) = g