Physics 262/266 - exam#1
1.
(30 pts) Answer the following questions. (Use the space provided below
and the next page if needed.)
a). (9pts) Two boxes of ideal gas are kept at the same temperature but box A contains
twice the number of molecules as in box
Physics 262/266 - exam#1
1.
(25 pts) Answer the following questions. (Use the space provided below
and the next page if needed.)
a). (9pts) Systems A and B are in thermal equilibrium with each other. i) Do they
necessarily have the same internal energy? i
Another Example of Component Lens
Two converging lens with f1 20cm and f 2 10cm and the lens are 20 cm apart.
Object is located 30cm to the left of lens #1, find the location of final image.
f1
f2
f2
f1
f2
f2
Another Example of Component Lens
1 1
1
s1 s1
Refraction at a Spherical Surface
2
1
Ray 1 from P going through V (normal to the interface) will not
suffer any deflection.
Ray 2 from P going toward B will be refracted into nb according to
Snells law.
Image will form at P where these two rays converge.
Physics 262/266
George Mason University
Prof. Paul So
Chapter 20: The 2nd Law of
Thermodynamics
Preferential Direction in
Thermodynamic Processes
Heat Engine and Efficiency
The 2nd Law of
Thermodynamics
The Carnot Cycle (the most
efficient heat engine)
En
PHYS 262
George Mason University
Prof. Paul So
Chapter 36: Diffraction
Diffraction and Huygens
Principle
Diffraction from a Single
Slit
Intensity in the Single-Slit
Pattern
Double-Slit Diffraction
Diffraction Grating
x-Ray Diffraction
Resolving Power
Diff
Physics 262 - exam#2
1. (25pts) Answer the following questions. Justify your answers. (Use the
space provided below and the next page)
a). (9pts) A student made a thin glass lens with two different radii of curvature, R1 and
R2 . The student reported the
Physics 262
George Mason University
Prof. Paul So
Chapter 35: Interference
Interference and
Coherent Sources
Two-Source
Interference of Light
Intensity of
Interference Patterns
Interference in Thin
Films
The Michelson
Interferometer
Wave Nature of Light
P
Lorentz Transformation
Reduction back to Galilean Transformation in the regime: u < c.
For
u
1
1
1
2
2
c
1 u c
x ' 1 x ut x ut
u
t ' 1 t 2 x t
c
(Galilean Transformation)
Einstein Relativity is more general and it reduces to previous results
(Galilea
2nd Law (S > 0 & Clausius Statement)
Clausius Statement: Heat cant spontaneously transfer from TC to TH.
We will prove this by contradiction using Stot > 0.
Assume the contrary,
cold
S H
SC
Q
TH
Q
(heat absorbed into TH)
Q
(heat released by TC)
TC
(with
Thermal Equilibrium
heat:
the transfer of energy btw. objects
when the objects have different temperatures
thermal contact:
two objects are in thermal contact if heat can transfer btw. them
doesnt have to be physical contact
thermal equilibrium:
2 object
Reversible vs. Non-Reversible Processes
reversible:
quasi-static
non-reversible:
non-quasi-static
small changes in forcing:
may increase or decrease the volume reversibly
example:
no small changes can stop the gas from filling the container after the
Adiabatic Processes
Quasi-static adiabatic expansion:
expanding gas
work is done by gas
W>0
U<0
energy flows out of gas
ideal gas:
U is a function of T only
U < 0 also implies T < 0
temperature drops
Adiabatic free expansion (non-quasi-static):
gas exp
Thermal Properties of Matter
equations of state:
ideal gas equation
PV Diagrams
kinetic-molecular model of an ideal gas
heat capacities
distribution of molecular speeds
phases of matter
state variables
physical variables
describe the macroscopic state o
Kinetic-Molecular Model of an Ideal Gas
micro and macro
descriptions for an ideal gas
expressions of P & T
microscopic quantities
macroscopic:
description of gases
P, V, T
ideal gas law
microscopic:
description of gas molecules
v, p, F, KE
kinetic theory
Disorder and Thermodynamic Processes
2nd law of thermodynamics:
physical principle
delineates the preferred direction of natural processes
degree of disorder of the resulting state
natural processes in isolation
move toward a state w/ larger degree of di
Internal Energy
internal energy
U
total amount of energy
KE and PE
intrinsic to the system
microscopic components
at rest with the object
mechanical KE and PE do not equal parts of the system
using U
KE:
translational
rotational
vibrational
PE:
with
Types of Averages
average speed:
mean value
Root Mean Square
RMS
vav does not equal vrms
most probable speed:
max value of the distribution function
mean free path for gas molecules:
molecule with finite radius
r
point-like particles do not collide
num
Heat Engines
devices that convert a given amount of heat
turns the heat into mechanical energy
engines carry working substances through a process
cyclic
releases residual heat to cold reservoir
TC
mechanical work is done by an engine
it absorbs heat f
Temperature & Heat
thermometers/temperature scales:
absolute zero
Kelvin scale
thermal = equilibrium
physical systems:
microscopic properties of atoms/molecules
they make up the system
macroscopic bulk properties of the system
not directly associated wi
Intensity in Two-Slit Interference
Putting this expression for the phase difference into our previous
intensity equation for a two-slit interference pattern, we have,
1 2 d
I I 0 cos 2 I 0 cos 2
sin
2
2
d
I I 0 cos 2
sin
Intensity in Two-Slit In
PHYS 262
George Mason University
Prof. Paul So
Chapter 33: The Nature and
Propagation of Light
The nature of light
Reflection and
Refraction
Total internal reflection
Dispersion
Polarization
Huygens principle
The Nature of Light
Light is a propagating ele
PHYS 262
George Mason University
Prof. Paul So
Chapter 37: Relativity
Events and Inertial
Reference Frames
Principles of Einsteins
Special Relativity
Relativity of Simultaneity,
Time Intervals, Length
Lorentz Transformation
Relativistic Momentum &
Energy
Single-Slit Diffraction
Central Maximum (= 0, straight ahead)
All waves from each wavelets travel
the same distance to the screen (far
away) and they arrive in phase
constructive interference.
There will be a bright fringe in the
middle at .
Side note: P
PHYS 262
George Mason University
Prof. Paul So
Chapter 34: Geometric Optics
Reflection &
Refraction at a Plane
Surface
Reflection &
Refraction at a
Spherical Surface
Thin Lenses
Optical Instruments
Images Formed by Flat Mirrors
Rays tracing to find image:
Mechanisms of Heat Transfer
Conduction
H
T T
dQ
kA H C
dt
L
(+H is in the dir.
of decreasing T)
H heat current [J/s]
(heat flow rate)
k thermal conductivity W / m K
(characteristic of the material)
R = L/k thermal resistance
(larger is better)
Thermal R
Physics 262/266
George Mason University
Prof. Paul So
PHYS 262/266: Course Info
Website:
http:/complex.gmu.edu/www-phys/phys262
http:/complex.gmu.edu/www-phys/phys266
Mastering Physics (automated web-based
assignment system):
http:/www.masteringphysics.co
Cp and Cv for an Ideal Gas
Two different ways to change dT=T2 - T1 :
Process a: Constant V
a
a
b
b
a
dQa nCv dT
Cp and Cv for an Ideal Gas
For the same dT :
Process b: Constant P
a
a
b
b
b
dQb nCP dT
Which is bigger, dQa or dQb?
Cp and Cv for an Ideal Gas
Physics 262 - exam#2
1. (30pts) Answer the following questions. Justify your answers. (Use the
space provided below and the next page)
a). (9pts) An object (an arrow) is placed as shown in front of each of the following
optical instruments. Describe the i
Phase of water changes: During these periods, temperature stays
constant as heat is added: Q mL
Ice melts to
liquid water
at 0 C
Ice warms
Liquid water vaporizes
to steam at 100 C
Liquid water warms
Steam warms
Temperature of water changes: During these p