Physics 209
Fall 2013
Thermal Physics Class #14
Thermal Averages and the Equipartition Theorem
Friday, October 4, 2013
I. Thermal Averages
A. Expectation Value: The expectation value of a quantity A is given by
X
hAi =
(Probability of A) A.
poss. values o

Example Problem 1. The emissivity of tungsten is 0.35. A tungsten sphere with radius 1.50 cm is
suspended Within a large evacuated enclosure Whose walls are at 290 K. Find the electrical power input that
is required to maintain the sphere at temperature o

Example Problem 1. Example Heat Engine.
When thinking about heat engines, it is often useful to have a specic example in mind. Below is a silly,
but simple example of a heat engine which operates in a cycle that is used to lift sand to a platform. The
ass

Example Problem 1. A 1.0 kg ice block at 0C slowly melts in a room that is very slightly warmer than
the ice cube. Find the change in entropy of the ice cube.
A. Model. Is the process reversible? If not, what reversible process will you use to calculate t

Example Problem 1. You are asked to design the most efcient possible heat engine that can lift a 15 kg
mass 2.0 In each cycle While using 500 J of heat input from a high temperature reservoir that is at 500C. (a)
What type of cycle will you use? Sketch th

Entropy Changes in Macroscopic
Processes
Thermal Physics Class 16, Monday, October 1, 2012
NO Journal Club Monday
Chris Ramsey
Washington University Dual Degree Program
Tuesday, October 8th
12:10 p.m., Goodrich 104
Entropy of Ideal Monatomic Gas
By calcul

Phys 209 Homework #17
Due: Fri, Oct. 11
Name:
Problem 1. (20 points) A heat engine takes 0.350 moles of air around a cycle as follows:
1 2: The air initially at 300 K and 1.00 atm is heated isochorically until the temperature
doubles to 600 K.
2 3: Then t

Example Problem 1. Estimate the rms speed of an air molecule in a room at normal room temperature.
A. Model.
B. Visualize/Parameterize.
C. Math. [Formula First]
ID. Assess.
Solution.
A A$UVK +l 'lk/ \ptatl gas Racy/l 3x5 val)l
ma M, New ,2; Maj In, 6:490t

Physics 209
Spring 2013
Thermal Physics Class #3
Heat Conduction
Friday, September 6, 2013
I. Heat Conduction: Heat flow via direct thermal contact between bodies at different temperatures.
The rate of heat flow through a material of cross-sectional area

#WD!
goloJmom W
Name:
Problem 1. (10 points) Some 3.0 X 1022 molecules of nitrogen gas at 280 K are in a chamber with a piston
that expands isothermally to 3 times its original volume. (a) Sketch a PVdiagram of this process. (b)
Explain Why heat must en

HW 12 -
Name:
Problem 1. Consider two Einstein solids A (contains 1 atom) and B (contains 2 atoms) which have a
combined energy U A + U13 = 65. These systems, which are isolated from their surroundings, are placed
into thermal contact. (a) Without using

golUlYOY) 3 _HL
Problem 1. (10 points) Imagine that a quantum system has exactly three energy states, with energies 0.020
eV, 0.040 eV, and 0.060 eV, respectively. At room temperature, out of every 1000 of these systems, about
how many are in each state?

Name:
Phys 209 TP-HW#05
Due: Wed., Sep. 11
Problem 1. (10 points) The rate at which radiant energy from the sun reaches the earths upper atmosphere
is about 1370 W/m2 . The distance from the earth to the sun is 1.50 1011 m, and the radius of the sun is
6.

Physics 209
Spring 2013
Thermal Physics Class #0
Thermal Energy
Friday, August 30, 2013
I. Definitions
A. Heat (Q): The energy that flows across the boundary between two objects as a result of a
difference in temperature between them.
B. Work (W ): The en

TPHW16
g 0 ii) l )O M S =
Problem 1. (10 points) (a) Imagine that the temperature of a 220g block of aluminum sitting in the sun
increases from 18C to 26C. By how much has its entropy increased? (b) A puddle containing 0.80 kg of
water at 0C freezes on a

Physics 209
Fall 2013
Thermal Physics Class #8
Thermodynamic Processes
Wednesday, September 18, 2013
I. Thermodynamic Processes
A. Quasistatic Process: A process that occurs at rate much slower than the typical relaxation
times of the system so that it al

E ale 7* low c; W
Name:
Problem 1. (10 points) Your lab partner claims that physicists have it all backward: cold things actually
have more thermal energy than hot things, and energy actually ows from cold to hot. What evidence could 1
you point out that

HW08
90 mm -
Problem 1. (10 points) Argon gas is conned to a cylinder With a piston. The gas has an initial pressure
of 120 kPa and a volume of 100 cm3. The piston is slowly Withdrawn until the gass volume has increased by
0.5%. (a) Estimate the work done

TPHWl 5 I
Name:
Problem 1. (10 points) Consider a molecule that has 4 energy levels, 1 level with energy E1, 1 level with
energy 2E1, and 2 levels which have energy 3E1. (a) If each level is equally likely, nd the average energy
(E) of this molecule. (

Physics 209
Fall 2013
Thermal Physics Class #10
Macrostates and Microstates
Monday, September 23, 2013
I. Questions:
A.
B.
C.
D.
Why do systems naturally reach equilibrium when left alone?
What determines a systems equilibrium state?
Why does heat flow fr

Example Problem 1. The supersonic Concorde was 62.1 m long when sitting on the ground on a typical
day (T = 15C). When in ight at Mach 2.0, air friction warmed the skin so that the aircraft lengthened by
about 25 cm. (The passenger cabin was on rollers, a

Physics 209
Fall 2013
Class #15
Entropy Changes in Macroscopic Processes
Monday, October 7, 2013
I. Volume Dependence of Entropy: For a gas of N particles confined to a container of volume V ,
the multiplicity V N . For a monatomic ideal gas,
3
U
3
S(U,

Example Problem 1. How does one write ex as a power of 10? Use this to write 61332 as a power of 10.
Solution.
WC +ymr+ wfll" K
n
x
cfw_f
Ul
)
ylo 1CD
EL) 20610.14 4) 1038: 0.439261 Se
Ckrchlkb 6.11144 MaWwzq-Hgq ,
mm: on32 / N
om: 3. 021689915166

Physics 209
Fall 2013
Class #16
Heat Engines and Refrigerators
Wednesday, October 9, 2013
I. Heat Engines
A. Heat Engine: A device that takes in heat and converts some of it to work. Examples: steam,
gasoline, and Diesel engines.
B. Cyclic Process: A sequ

Example Problem 1. An Einstein solid of N A = 2 atoms with energy UA = 35 is placed in thermal contact
with another Einstein solid of N B = 3 atoms with energy U B 2 56. (a) What is the macropartition of the
system at the instant they are placed in therma

Name:
Phys 209 TP-HW #09
Due: Fri., Sep. 20
Problem 1. (10 points) Some 3.0 1022 molecules of nitrogen gas at 280 K are in a chamber with a piston
that expands isothermally to 3 times its original volume. (a) Sketch a P V -diagram of this process. (b)
Exp

Example Problem 1. Suppose you were to use an electric mixer with fan blades attached to the heaters
to heat a glass of water. (Assume the mixer draws 100 W of electrical power from the outlet.)
A. Model.
B. Visualize/Parameterize.
C. Math. [Formula First

Physics 209
Fall 2013
Thermal Physics Class #12
Entropy and the Second Law of Thermodynamics
Monday, September 30, 2013
I. Observation: Macroscopic systems (which have very large numbers of particles N and energy units
q = U/) tend to rearrange themselves

Example Problem 1. A 500 g ice cube is taken out of freezer with a temperature of 10 C and placed
inside a thermos bottle which has a 100 W heating element. The heating element is turned on and the
temperature of the interior of the thermos is measured by

Example Problem 1. 4.0 moles of hydrogen gas are in a container with a volume of 5.0 m3 at T = 30 C
when 100 J of heat is added isochorically. (3.) Draw a PVdiagram of the process. (b) Find the work done
during the process. (c) Find the temperature of the

Name:
Phys 209 TP-HW #16
Due: Wed., Oct. 09
Problem 1. (10 points) (a) Imagine that the temperature of a 220-g block of aluminum sitting in the sun
increases from 18 C to 26 C. By how much has its entropy increased? (b) A puddle containing 0.80 kg of
wate

TP-HW01
Name: g 69 0-) cfw_0 M S -
Problem 1. A 22kg block of iron drops out of the back of a pickup truck traveling at 55 mi /h. The block
slides on the road for 150 In before coming to rest.
A. Model.
B. Visualize/Parameterize.
C. Math. [Formula First]

Name:
Phys 209 TP-HW #4
Due: Mon., Sep. 9
Problem 1. (10 points) One end of an unsulating metal rod is placed in a container of boiling water at
100 C, and the other end is in an ice-water mixture at 0 C. The rod is 60.0 cm long and has a cross-sectional

Name:
Phys 209 TP-HW #8
Due: Wed., Sep. 18
Problem 1. (10 points) Argon gas is confined to a cylinder with a piston. The gas has an initial pressure
of 120 kPa and a volume of 100 cm3 . The piston is slowly withdrawn until the gass volume has increased by