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PHY831 - Midterm 2, Monday October 22nd 2012
Answer all questions. Time for midterm - 50 minutes
Name:
Formulae that might be helpful
2
eax
+bx
b2
dx = ( )1/2 e 4a
a
(1)
Relations between partial derivatives,
x
y
x
y
z
x
w
=
z
x
y
= 1/
z
w
y
z
y
z
x
y
x
1
Solutions to problems for Part 2
Sample Quiz Problems
Quiz Problem 1. Write down the equation for the thermal de Broglie wavelength. Explain its importance in the
study of classical and quantum gases.
Solution
=
h
2mkB T
(1)
This is of the form h/pT ,
1
Solutions to sample quiz problems and assigned problems
Sample Quiz Problems
Quiz Problem 1. Prove the expression for the Carnot eciency for a perfectly reversible Carnot cycle using an
ideal gas.
Solution: The ideal Carnot cycle consists of four segmen
1
Solutions to sample quiz problems and assigned problems
Sample Quiz Problems
Quiz Problem 1. Prove the expression for the Carnot eciency for a perfectly reversible Carnot cycle using an
ideal gas.
Solution: The ideal Carnot cycle consists of four segmen
1
PHY831 - Midterm I, Monday September 24th 2012
Answer all questions. Time for midterm - 50 minutes
Name:
Formulae that might be helpful
2
eax
+bx
b2
dx = ( )1/2 e 4a
a
(1)
Relations between partial derivatives,
x
y
x
y
z
z
z
x
w
=
x
y
= 1/
y
z
w
y
z
x
y
1
Statistical Physics (PHY831): Part 4: Superconductors at nite
temperature. Introduction to dynamics of many component systems.
Phillip M. Duxbury, Fall 2012
Finite temperature
To extend the ground state calculations to nite temperature, we only need to
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Statistical Physics (PHY831): Part 1 - The foundations
Phillip M. Duxbury, Fall 2011
Course Outline
Part 1: (LL, PB) Foundations: (11 lectures)
History of thermodynamics, kinetic theory and equilibrium statistical mechanics. Axioms of equilibrium statis
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Statistical Physics (PHY831): Part 1 - The foundations
Phillip M. Duxbury, Fall 2012
I.
ORIGINS OF THERMODYNAMICS, KINETIC THEORY AND STATISTICAL MECHANICS
A.
Engines
Thermodynamics originated with the study of heat engines. A precursor to heat engines,
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PHY831 - Subject Exam Dec. 14th 2011, 10am - 1pm
Answer all questions (total points available is 100). Time for exam - 3 hours
Name:
dx eax
2
+bx
b2
= ( )1/2 e 4a ;
a
0
dx
= Sinh1 (x);
(1 + x2 )1/2
0
2
6,
where (s) = (s 1)! for s a positive integer, and
1
Solutions to problems for Part 2
Solutions to Quiz 3 are at the end of problems.
Sample Quiz Problems
Quiz Problem 1. Write down the equation for the thermal de Broglie wavelength. Explain its importance in the
study of classical and quantum gases.
Solu
1
Solutions to problems for Part 3
Assigned problems and sample quiz problems
Sample Quiz Problems
Quiz Problem 1. Draw the phase diagram of the Ising Ferromagnet in an applied magnetic eld. Indicate the
critical point. Plot the magnetization as a functio
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PHY831 - Midterm I, Monday September 24th 2012
Answer all questions. Time for midterm - 50 minutes
Name:
Formulae that might be helpful
2
eax
+bx
b2
dx = ( )1/2 e 4a
a
(1)
Relations between partial derivatives,
x
y
x
y
z
z
z
x
w
=
x
y
= 1/
y
z
w
y
z
x
y
1
PHY831 - Midterm I, Monday September 26th 2011
Answer all questions. Time for midterm - 50 minutes
Name:
Formulae that might be helpful
dx eax
2
+bx
b2
= ( )1/2 e 4a ;
a
0
2
dx xn eax =
0
n+1
1
(
)
2
2a(n+1)/2
xs1 dx
= (s) (s),
ex 1
where (s) = (s 1)! f
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PHY831 - Midterm I with Solutions, Monday September 26th 2011
Answer all questions. Time for midterm - 50 minutes
Name:
Formulae that might be helpful
2
eax
+bx
b2
dx = ( )1/2 e 4a
a
(1)
Relations between partial derivatives,
x
y
x
y
z
z
z
x
w
=
x
y
= 1
1
PHY831 - Midterm IV, Wednesday December 7th 2011
Answer all questions. Time for midterm - 30 minutes
Name:
dx eax
2
+bx
b2
= ( )1/2 e 4a ;
a
0
dx
= Sinh1 (x);
(1 + x2 )1/2
x
y
x
y
y
z
z
z
z
x
x
Q
T
CV =
S =
1
V
U
cd
=d
Ld
h
1
2
x
w
z
z
H
T
V
P
y
gGL =
1
Solutions to assigned problems and sample quiz problems for Part 4
Sample Quiz Problems
Quiz Problem 1. Write down the BCS gap equation at nite temperature and compare it to the zero temperature
expression. Explain the origin of the dierences between th
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Solutions to problems for Part 4
Sample Quiz Problems
Quiz Problem 1. Describe the physical meaning of the coherence length ( ) in superconductors. By considering
the linearized Ginzburg-Landau equation in zero eld nd a solution describing the attenuati
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Solutions to problems for Part 3
Sample Quiz Problems
Quiz Problem 1. Draw the phase diagram of the Ising Ferromagnet in an applied magnetic eld. Indicate the
critical point. Plot the magnetization as a function of the applied eld for three temperatures