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AP Physics Chapter 10 Temperature

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Title: AP Physics Chapter 10 Temperature


1
AP Physics Chapter 10 Temperature
2
Chapter 10 Temperature
  • 10.1 Temperature and Heat
  • 10.2 The Celsius and Fahrenheit Temperature
    Scales
  • 10.3 Gas Laws and Absolute Temperature
  • 10.4 Thermal Expansion
  • 10.5 The Kinetic Theory of Gases
  • 10.6 (omit)

3
Learning Objectives
  • Kinetic Theory and Thermodynamics Ideal Gases
  • Students will understand the kinetic theory
    model of an ideal gas, so they can
  • a) State the assumptions of the model.
  • b) State the connection between temperature and
    mean translational kinetic energy, and apply it
    to determine the mean speed of gas molecules as
    a function of their mass and the temperature of
    the gas.

4
Learning Objectives
  • Kinetic Theory and Thermodynamics Ideal Gases
  • Students will understand the kinetic theory
    model of an ideal gas, so they can
  • c) State the relationship among Avogadris
    number, Boltzmanns constant, and the gas
    constant R, and express the energy of a mole of
    a monatomic ideal gas as a function of its
    temperature.
  • d) Explain qualitatively how the model explains
    the pressure of a gas in terms of collisions
    with the container walls, and explain how the
    model predicts that, for fixed volume, pressure
    must be proportional to temperature.

5
Learning Objectives
  • Heat Transfer and Thermal Expansion
  • Students will understand heat transfer and
    thermal expansion so they can
  • a) Calculate how the flow of heat through a slab
    of material is affected by changes in the
    thickness or area of the slab, or the temperature
    difference between the two faces of the slab.
  • b) Analyze what happens to the size and shape of
    an object when it is heated.

6
Homework for Chapter 10
  • Read Chapter 10
  • HW 10.A 7,8,17,22,24,27-32,34,36,38.
  • HW 10.B 45-49, 65-68, 71.


7
10.1 Temperature and Heat
8
Warmup Sky High Cooking Physics Warmup
89
The boiling temperature for water is dependent on
the atmospheric pressure. At standard atmospheric
pressure, the boiling temperature is 100C. At
altitudes below sea level, where the atmospheric
pressure is greater, the boiling temperature is
higher. Altitudes above sea level would result in
water boiling below 100C.

Pressure cookers allow
the cook to regulate the air pressure inside the
cooker at levels greater than standard
atmospheric pressure. When a recipe calls for
cooking something in boiling water, it is assumed
that the water is at a temperature of 100C.
Suppose you had a cooking thermometer and a
pressure cooker available. Explain how you could
stay true to the intent of a recipe, which called
for cooking in boiling water if you were in Death
Valley, California (significantly below sea
level) and Denver, Colorado (significantly above
sea level).
Answer Use the thermometer to regulate
temperature at 100C, even though it is not
boiling. Denver Use the pressure cooker to raise
the pressure to 1 atm.
9
10.1 Temperature and Heat
temperature a relative measure, or indication,
of hotness and coldness Temperature is
associated with molecular motion (translational,
linear vibration, rotation). heat the net
energy transferred from one object to another
because of a temperature difference internal
energy the total energy (kinetic plus
potential) of all molecules of a body or a
system When heat is transferred out of or
into a system while there is no other physical
process present, the internal energy of the
system will change. thermal contact when heat
is transferred between two objects, even if they
are not physically touching thermal equilibrium
when there is no longer a net heat transfer
between objects in thermal contact, and they are
at the same temperature
10
10.2 The Celcius and Fahrenheit Temperature
Scales
11
Warmup Up on the Roof Physics Warmup 90
The color of your roof can play a major role in
how hot or cold your house becomes when the sun
shines on it. Dark colors absorb much of the
suns heat energy, while lighter colors will
reflect a good portion of that energy. On hot
summer days it would be better to have a light
roof, while on cold winter days it would be
better to have a darker roof.

Obviously, you can only
have one color of roof on your house. For your
geographic location, explain which color roof
would be better in terms of energy efficiency
over the course of a year.
Answer In the Northern U.S., a darker roof would
be better due to longer winters, shorter summers,
and less direct sunlight. In the South, a lighter
roof would be better due to longer summers,
shorter winters, and more direct sunlight. In the
Central U.S. it would not make much of a
difference either way.
12
10.1 Temperature and Heat
The two most common temperature scales are the
Celsius temperature scale and the Fahrenheit
temperature scale. A measure of temperature is
obtained using a thermometer. Liquid-in-glass
thermometers are based on the thermal
expansion liquids expand when heated.
Between the ice and steam fixed points, there are
100 degrees on the Celsius scale and 180 degrees
on the Fahrenheit scale.
13
10.1 Temperature and Heat
14
10.1 Temperature and Heat
15
10.1 Temperature and Heat
Example 10.1 What is the temperature 50.0F on
the Celsius scale? Example 10.2 The
temperature changes from 35F during the night to
75F during the day. What is the temperature
change on the Celsius scale?
16
10.3 Gas Laws and Absolute Temperature
17
Warmup To What Degree? Physics Warmup 81
Temperature is often measured using different
temperature scales. The Farenheit Scale has long
been used in the United States to describe the
air temperature in weather reports and for
cooking temperatures in recipes. Other countries
use the Celsius scale for the same applications.
Science often has to use another scale, called
the Kelvin scale, when absolute values of
internal energy are to be analyzed. A reading on
any of these scales can easily be converted to
readings on the other two using the equations TF
(9/5 TC) 32 and TK TC 273.15.

Put each of the
temperatures below from hottest to coldest.
0 K 0C 0F 96C 100 K
212F (hottest) ___________ ___________ _
__________ ___________ ___________ (co
ldest) ___________
212F
96C
0C
0F
100 K
0 K
18
10.3 Gas Laws and Absolute Temperature
A low-density gas kept at a constant volume gives
a straight line on a p vs. T graph. When the line
is extended to the zero pressure value, a
temperature of absolute zero is obtained.
19
10.1 Temperature and Heat
The Kelvin scale also uses the triple point of
water as a fixed point of reference. The triple
point of water is a unique set of conditions
where water exists simultaneously in equilibrium
as a solid, liquid, and gas. This point is 610
Pa, at temperature of 273.16 K (or 0.01 C).
20
10.3 Gas Laws and Absolute Temperature
A unit interval on the Kelvin scale is called a
kelvin and is abbreviated K. A kelvin is
equivalent to a temperature change of 1 Celsius
degree. Absolute zero is usually rounded to
-273 C for convenience. A temperature of
0 C is equal to 273 kelvins.
21
10.3 Gas Laws and Absolute Temperature
Example 10.3 What is -40F on the Kelvin
scale?
22
10.3 Gas Laws and Absolute Temperature
Activity Go to Novas Website, Absolute
Zero. http//www.pbs.org/wgbh/nova/zero/ Clic
k on A Sense of Scale interactive. Find in F,
C, K a) the temperature of a lightning bolt
b) the coldest surface temperature on earth
ever recorded c) the hottest temperature
achieved in a lab Click on A Matter of
Degrees. Create and name your own temperature
scale.
23
10.3 Gas Laws and Absolute Temperature
Assignment Read the article, Absolute Hot and
write a Ten Percent Summary. Writers Purpose
You will write the main ideas in your own words.
Include the most important details if the word
limit permits. You will want clear and accurate
information with no opinion. Remember, this is a
summary not an evaluation. Writers Role You
will take the role of a researcher or analyst who
has been hired by MainIdeas.com to distill
information for interested adults. Audience
Your audience will be busy, smart adults who want
to get the main ideas of articles to see if they
should read the article completely. Form You
will write a summary of your assigned article in
approximately ten percent of the words not
exactly ten percent, but approximately ten
percent. This article is approximately 1500
words, so you will write 130-170 words.
24
10.3 Gas Laws and Absolute Temperature
  • ideal gas perfect gas all gases exhibit
    similar behavior at low density and low pressure
  • Collisions are elastic (kinetic energy is
    conserved).
  • The variables that describe the behavior or a
    given mass of gas are
  • pressure (p)
  • volume (V)
  • temperature (T)

25
10.3 Gas Laws and Absolute Temperature
26
10.3 Gas Laws and Absolute Temperature
27
10.3 Gas Laws and Absolute Temperature
Hint PV constant
28
10.3 Gas Laws and Absolute Temperature
29
10.3 Gas Laws and Absolute Temperature
constant
30
10.3 Gas Laws and Absolute Temperature
31
10.3 Gas Laws and Absolute Temperature
Hint Must convert to Kelvin.
32
10.3 Gas Laws and Absolute Temperature
33
10.3 Gas Laws and Absolute Temperature
Boyles Law and Charles Law can be combined to
form the ideal gas law. p V constant or p1
V1 p2 V2 T T1 T2 The ideal
gas law can be written in a microscopic and
macroscopic form. microscopic form small
scale, molecular level pV NkBT p
pressure V volume N the number of molecules
in the sample of gas kB Boltzmanns constant
1.38 x 10-23 J/K T temperature in kelvins
On Gold Sheet
34
10.3 Gas Laws and Absolute Temperature
macroscopic form large scale can be measured
with ordinary lab equipment pV nRT p
pressure V volume n the
number of moles of the gas R
universal or ideal gas constant
8.31J/molK T temperature in
kelvin
On Gold Sheet
35
10.3 Gas Laws and Absolute Temperature
mole a quantity of a substance that contains
Avogadros number of molecules. abbreviated
mol Avogadros number (NA) 6.02 x 1023
molecules / mol standard temperature and
pressure (STP) - 0C at 1 atm of pressure n
(number of moles) N (number of molecules)
NA (Avogadros number)
36
10.3 Gas Laws and Absolute Temperature
Formula mass is determined from the chemical
formula and atomic mass from the periodic table
(in grams). It is calculated in
grams/mol. Molecular mass is the formula mass
divided by Avagodros number. It is calculated in
grams/molecule. example H20 is two hydrogen and
1 oxygen atom. Hydrogen has a atomic mass of 1
and oxygen has an atomic mass of 16. Therefore,
water has a formula mass of 1.0 1.0 16.0
18.0 g. 1 mol of water has a mass of 18.0 g or
0.018 kg. The molecular mass of water is 18.0
g / 6.02 x 1023 molecules/mol 2.99 x 10-23
g/molecule or 2.99 x 10-26
kg/molecule Molecular mass Formula
mass Avogadros number
37
10.3 Gas Laws and Absolute Temperature
(macroscopic form)
On Gold Sheet
  • ideal gas constant is also known as the
    universal gas constant
  • 1 liter 1 x 10-3 m3.
  • STP is standard temperature (0 C) and pressure
    (1 atm or 1.01 x 105 Pa).

38
10.3 Gas Laws and Absolute Temperature
39
10.3 Gas Laws and Absolute Temperature
Example 10.4 A gas has a volume of 0.20 m3, a
temperature of 30C, and a pressure of 1.0 atm.
It is heated to 60C and is compressed to a
volume of 0.15 m3. Find the new pressure in
atmospheres.
40
10.3 Gas Laws and Absolute Temperature
Example 10.5 An ideal gas in a container of
volume 1000 cm3 (one liter) at 20.0C has a
pressure of 1.00 x 104 N/m2. Determine the number
of gas molecules and the number of moles of gas
in the container.
41
10.3 Gas Laws and Absolute Temperature Check
for Understanding
  • 1. The temperature used in the ideal gas law is
  • Celcius
  • Fahrenheit
  • Kelvin
  • any of the preceding

Answer c
42
10.3 Gas Laws and Absolute Temperature Check
for Understanding
  • 2. When the temperature of a quantity of gas is
    increased
  • the pressure must increase
  • the volume must increase
  • both the pressure and volume must increase
  • none of the preceding

Answer d pV/T constant
43
10.3 Gas Laws and Absolute Temperature Check
for Understanding
44
10.3 Gas Laws and Absolute Temperature Check
for Understanding
45
Homework 10.A
  • HW 10.A 7,8,17,22,24,27-32,34,36,38.

46
10.4 Thermal Expansion
47
Warmup Hotter Than You Think Physics
Warmup 83
The Kelvin temperature scale is sometimes called
the absolute temperature scale because a reading
of zero truly means the lowest temperature
possible. If the temperature of an object were
100K, then it would need to be raised to 200 K in
order for the object to be twice as
hot.

On the same scale as originally used, to what
temperature would each need to be raised to be
twice as hot? (Hint TK TC 273)
  • Original Temperature Twice as Hot
  • ice in freezer -20C ___________
  • melting ice 0C ___________
  • body temperature 37C ___________
  • boiling water 100C ___________

506K
546K
620K
746K
48
10.4 Thermal Expansion
49
10.4 Thermal Expansion

The coefficient for volume expansion is
approximately equal to 3a, and applies to
three-dimensional volume changes for solids. For
fluids with no definite shape, only volume
expansion is applicable, and a special thermal
coefficient of volume expansion ß is used. ?
V ß ? T (for fluids) V0
50
10.4 Thermal Expansion
Example 10.6 You are installing some outdoor
copper electric wire to a backyard fish pond on a
hot 40C summer day. The temperature could be as
low as -20C in your area during a cold winter
night. How much extra wire (minimum) do you have
to include to allow for thermal expansion if the
distance from the electric service to the pond is
100 m?
51
10.4 Thermal Expansion
Example 10.7 A 500-milliliter glass beaker of
water is filled to the rim at a temperature of
0C. How much water will overflow if the water is
heated to a temperature of 95C? (Ignore the
expansion of the beaker, why?)
52
10.5 The Kinetic Theory of Gases
53
Warmup Loosen Up! I Physics Warmup 82
When energy is added to most objects, they
expand. For equal changes in temperature, the
amount of expansion depends in part on the
dimensions of the object as well as the material
it is made of. Two rods of different metals but
of equal length would expand different amounts
due to the difference in material. Two rods made
of the same material but of different lengths
would expand different amounts due to the
difference in their lengths.

A common way to loosen a
metal lid that is screwed tightly to a glass jar
is to run hot water over the lid and jar top.
Explain why this loosens the lid.
Answer The rim of the lid is a circle. As the
metal expands, the circumference expands. Metal
expands more than glass.
54
10.5 The Kinetic Theory of Gases
KEave ½ mvrms2 3/2 kB T
On Gold Sheet
m mass of the molecule vrms root-mean-square
speed kB Boltzmanns constant T absolute
temperature in kelvin
55
10.5 The Kinetic Theory of Gases
56
10.5 The Kinetic Theory of Gases
Since KEave 3/2 kBT ½ mv2rms,
we can solve for vrms ______ vrms v 3kBT/m
, where m (? on gold sheet) is the mass of one
molecule of gas, in kg
or _______ vrms v 3RT/M , where M is the
molar mass in kg m kg (gold sheet uses
? instead of m) M kg molecule
mol n
number of mols N number of molecules So, Nm
nM kg
On Gold Sheet
On Gold Sheet
57
10.5 The Kinetic Theory of Gases
The ideal gas law can be expressed in terms of
the root-mean-square speed of the
molecules. _______ vrms v 3RT/M Solve
for RT RT ? M (vrms)2 Substitute into pV
nRT
pV ? nMv2rms or pV ? Nmv2rms where n is
the number of moles M is the number of kilograms
per mole N is the number of gas molecules and
m (? on gold sheet) is mass of a gas molecule
in kilograms
58
10.5 The Kinetic Theory of Gases
U N (KEave)
U n (KEave)
59
10.5 The Kinetic Theory of Gases
60
10.5 The Kinetic Theory of Gases
Example 10.8 Calculate the rms
(root-mean-square) speed of a hydrogen molecule
and an oxygen molecule at a temperature of 300 K.
(The masses of hydrogen and oxygen molecules are
3.3 x 10-27 kg and 5.3 x 10-26 kg, respectively)
61
10.5 The Kinetic Theory of Gases
Example 10.9 If the temperature of a gas
increases from 20C to 40C, by what factor does
the rms speed increase?
62
10.5 The Kinetic Theory of Gases Check for
Understanding
The thermal coefficient of volume expansion for a
solid is a) a b) 2 a c) 3 a d) a3
Answer c
63
10.5 The Kinetic Theory of Gases
If the kinetic energy of an average ideal gas
molecule in a sample at 20C doubles, its final
temperature must be a) 10C b) 40C c)
313C d) none of the preceding
Answer c) because 20C 293 K and 2 x 293 K
586 K 313C
64
10.5 The Kinetic Theory of Gases
If the temperature of a quantity of ideal gas is
raised from 20C to 40C, its internal energy is
a) doubled b) tripled c) unchanged d)
none of the preceding
Answer d) Internal energy is proportional to the
Kelvin temperature.
65
10.5 The Kinetic Theory of Gases Check for
Understanding
66
10.5 The Kinetic Theory of Gases Check for
Understanding
67
Homework 10.B
  • HW 10.B 45-49, 65-68, 71.

68
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