Chapter 6
Many Particle Systems
c
2009
by Harvey Gould and Jan Tobochnik
1 August 2009
We apply the general formalism of statistical mechanics to systems of many particles and discuss the
semiclassical limit of the partition function, the equipartition th
Indian Institute of Technology Guwahati
Department of Physics
Mid Semester Examination
Statistical Mechanics: PH404
Date: 2nd March 2016
Full Marks: 30
Time: 2 hours
Answer the following four questions:
1. Surfactant molecules such as those in soap or sha
INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI
Department of Physics
Statistical Mechanics: PH704
Problem set-II
1. Consider a monatomic ideal gas of N molecules confined in a volume V having total
energy E in thermodynamic equilibrium. Calculate the number of m
INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI
Department of Physics
MID SEMESTER EXAMINATION
Statistical Mechanics: PH704 Solution
1. There are two possible point defects in the crystal structure, Schottky and Frenkel
defects. In Schottky defect, the atoms are
Master TPA-M1
Statistical Mechanics
Problem set 5: Fermi-Dirac statistics
Ex.1 The 3d ideal fermion gas
Consider a 3d gas of N fermions in the thermodynamic limit.
a) Obtain the relationship between the grand potential J and the energy E of the gas. Deriv
1
INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI
DEPARTMENT OF PHYSICS
Mid Semester Examination
PH443:MC Methods and Applications
26th February 2014
Full Marks: 30
Time: 2 hours
Answer the following five questions:
1. (a) Starting from dE = T dS P dV , show that
Master TPA-M1
2013-2014
Statistical Mechanics
Problem set 4: The Grand Canonical Ensemble
Ex.1. Fluctuation of the number of particles
Prove the following relationship:
N
N
2
kT
N
T ,V
Ex.2. The monatomic ideal gas.
Let us consider a monatomic ideal gas i
INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI
Department of Physics
Statistical Mechanics: PH404
Tutorial-III
1. Calculate the number of accessible microscopic states of a system of two localized and
independent quantum oscillators, with fundamental frequencies
INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI
Department of Physics
Statistical Mechanics: PH704
Problem set-III
1. Consider a quantum particle with total angular momentum J = 1. Consider a basis
corresponding to the three eigenvectors of the z-component of ang
INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI
Department of Physics
Statistical Mechanics: PH704
Problem set-IV
1. A condensible vapor has a molar entropy
h
s = s0 + R ln C(v b)(u + a/v)5/2
i
where c and s0 are constants and u is the internal energy per mole. (
SCIENVP
Review
Week 5
ENVP.Rempillo@gmail.com
WORK and ENERGY
Capacity to do work
Energy
Formula for work
W = F * d * cos
Unit of work and energy
Joule
FORMS OF ENERGY
Energy stored in nucleus of an atom
NUCLEAR
Electromagnetic energy that travels in wav
Negative
Externalities of
Consumption
Where the consumption of
goods has spill over costs,
the consumers does not
fully take account of the
total costs to society.
ECO 13/4/3
Negative Externalities of Consumption
An example could be the consumption of
alc
Lecture 4: Heat and
Temperature
SCIENVP 3rd Term 2016
envp.rempillo@gmail.com
Thermal Energy and Temperature
Thermal Energy - The internal energy of
substances caused by vibration and
movement of atoms and molecules within the
substance.
Temperature degre
y
g
r
e
n
E
d
n
a
k
r
Wo
2
k
e
e
W
16
20
m
r
e
T
P3
Y
N
E
I
C
S
rd
?
y
g
r
e
n
E
s
i
t
a
Wh
k
r
o
w
o
d
o
t
y
t
i
c
a
Cap
What is Work?
NO
A teacher applies a force to the wall and
becomes exhausted
YES
A book falls of the table and falls to the
ground
N
Forms of Energy
SCIENVP 3rd Term 2016
Lecture 2
Kinetic and
Potential
Kinetic Energy - associated
with the MOTION of an object
Potential Energy associated
with the POSITION of an
object
Translational Kinetic
Energy2
K = mv
2
m = mass (kg)
velocity (m/s)
v
Climate Science
Lecture 7
envp.rempillo@gmail.com
Weather versus Climate
Weather is a condition of the atmosphere at a
particular time (short term, less predictable)
Climate is the long term average weather
(long term, more predictable)
Video:
http:/ch
Lecture 6:
Atmospheric Physics
Basics
envp.rempillo@gmail.com
Composition of the Atmosphere
http:/climate.ncsu.edu/edu/k12/.AtmComposition
Composition of the Atmosphere
Oxygen (O2)
we need for breathing
Carbon Dioxide (CO2)
photosynthesis, also a
greenh
Conservation of Mechanical
Energy
Lecture 3 SCIENVP 3rd Term 2016
ENVP.Rempillo@gmail.com
Review
Kinetic Energy
Movement
Potential Energy
Position
Mechanical Energy
movement and position
Conservation of Mechanical Energy
Formula Review
K = mv 2
Tra
Lecture 5
Thermodynamics application
Part I: Heat engine
ENVP.REMPILLO@gmail.com
Ideal Gas Law
PV = nRT
P = pressure (Pascal)
n = number of
moles
V = volume (m3)
T = temperature (K)
R = universal gas constant = 8.3145 J/ mol K
Note:
K is Kelvin = Celsius
MAPUA INSTITUTE OF TECHNOLOGY
Department of Physics
E302: HEAT AND CALORIMETRY
CERNA, Virgielyn
2012105962 BSECE-2 Group 3
PHY12L-A5
SCORE:
Analysis
Conclusion
Presentation
TOTAL
Engr. Ericson D. Dimaunahan
Instructor
Date of Submission: May 22, 2015
Anal
MAPUA INSTITUTE OF TECHNOLOGY
Department of Physics
E303: KUNDTS TUBE:
VELOCITY OF SOUND IN SOLID
CERNA, Virgielyn
2012105962 BSECE-2 Group 3
PHY12L-A5
SCORE:
Analysis
Conclusion
Presentation
TOTAL
Engr. Ericson D. Dimaunahan
Instructor
Date of Submission
MAPUA INSTITUTE OF TECHNOLOGY
Department of Physics
E301: LINEAR EXPANSION
CERNA, Virgielyn
2012105962 BSECE-2 Group 3
PHY12L-A5
SCORE:
Analysis
Conclusion
Presentation
TOTAL
Engr. Ericson D. Dimaunahan
Instructor
Date of Submission: May 15, 2015
Analysis
DISCUSSION
Of
RESULTS
And
CONCLUSIO
N
Name: Villanueva, Geryl Mikka M.
UNIFORMLY
ACCELERATED MOTION
2
Section: Q3A2
Group: 6
Date Performed: Aug. 23, 2016
Instructor:Ms. Grace Sanchez Date Submitted: Aug. 26,
2016
Discussion of Results
Guide Questions for
asa 2
1. uniform accelerated motion
FULL ANSWER
Uniformly accelerated motion is motion with a constant, uniform change in velocity. This often,
but does not always, include a change in speed. For instance, an object falling in a vacuum under
the influence
sociology
why study sociology?
to obtain factual information about our
society and different aspect of our social
life.
sociological information enables us to
understand our society more objectively
and to see our place in it.
through sociology, we develo
1. systems of measurement and their origin
english and metric
http:/physics.about.com/od/toolsofthetrade/a/SIunits.htm
In 1875, a uniform meter convention was introduced. There was a general trend during this time
to make sure that units were practical fo
RA1425
Also known as the Rizal Law
was signed on June 12, 1956
Authored by Claro M. Recto and
sponsored by Jose P. Laurel
Was implemented 30 days after
the signing
GOVERNMENT
Legislation ( Recto and Laurel)
Ministry of Education
Veteranos de la Revolu
LINEAR KINEMATICS
BASIC PRINCIPLES of UNIFORMLY ACCELERATED MOTION
Motion can be:
Uniform, in a straight line, with constant velocity, having constant acceleration = 0
Uniformly accelerated (having constant acceleration 0)
Uniform, circular, with const
LABORATORY 3
Uniformly Accelerated Motion
Purpose
In this laboratory we will investigate uniformly accelerated motion. In Experiment 1 we
will determine the acceleration of a freely falling object. In Experiment 2 we will
determine the acceleration of a c
Principles
Uniformly Accelerated Motion
Uniformly accelerated motion is motion under constant acceleration. Since the
acceleration is constant, the velocity of an object moving under uniform acceleration
changes by the same amount each second. This is evi