Transcript Chapter 1 Units and Problem Solving

AP Physics
Chapter 10
Temperature
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)
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.
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 Avogadri’s number,
Boltzmann’s 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.
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.
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.
10.1 Temperature and Heat
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 100°C. 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
100°C.
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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 100°C. 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 100°C, even though it
is not boiling. Denver: Use the pressure cooker to raise the pressure to 1 atm.
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
10.2 The Celcius and Fahrenheit
Temperature Scales
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 sun’s 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.
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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.
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.
10.1 Temperature and Heat
10.1 Temperature and Heat
10.1 Temperature and Heat
Example 10.1: What is the temperature 50.0°F on the Celsius scale?
Example 10.2: The temperature changes from 35°F during the night to 75°F
during the day. What is the temperature change on the Celsius scale?
10.3 Gas Laws and Absolute
Temperature
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.
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Put each of the temperatures below from hottest to coldest.
0K
0°C
0°F
96°C
212°F
(hottest) ___________
96°C
___________
0°C
___________
0°F
___________
100 K
___________
0K
(coldest) ___________
100 K
212°F
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.
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).
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.
10.3 Gas Laws and Absolute Temperature
Example 10.3: What is -40°F on the Kelvin scale?
10.3 Gas Laws and Absolute Temperature
Activity: Go to Nova’s Website, “Absolute Zero”.
http://www.pbs.org/wgbh/nova/zero/
Click 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.
10.3 Gas Laws and Absolute Temperature
Assignment: Read the article, “Absolute Hot” and write a Ten Percent
Summary.
Writer’s 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.
Writer’s 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 130170 words.
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)
10.3 Gas Laws and Absolute Temperature
10.3 Gas Laws and Absolute Temperature
10.3 Gas Laws and Absolute Temperature
Hint: PV = constant
10.3 Gas Laws and Absolute Temperature
10.3 Gas Laws and Absolute Temperature
= constant
10.3 Gas Laws and Absolute Temperature
10.3 Gas Laws and Absolute Temperature
Hint: Must convert to Kelvin.
10.3 Gas Laws and Absolute Temperature
10.3 Gas Laws and Absolute Temperature
Boyle’s Law and Charles’ Law can be combined to form the ideal gas law.
p V = constant
T
or
p1 V1 = p2 V2
T1
T2
The ideal gas law can be written in a microscopic and macroscopic
form.
microscopic form – small scale, molecular level
pV = NkBT
On Gold Sheet
p = pressure
V = volume
N = the number of molecules in the sample of gas
kB = Boltzmann’s constant = 1.38 x 10-23 J/K
T = temperature in kelvins
10.3 Gas Laws and Absolute Temperature
macroscopic form: large scale; can be measured with ordinary lab
equipment
pV = nRT
On Gold Sheet
p = pressure
V = volume
n = the number of moles
of the gas
R = universal or ideal gas
constant = 8.31J/mol·K
T = temperature in
kelvin
10.3 Gas Laws and Absolute Temperature
mole – a quantity of a substance that contains Avogadro’s number of molecules.
abbreviated: mol
Avogadro’s number (NA) = 6.02 x 1023 molecules / mol
standard temperature and pressure (STP) - 0°C at 1 atm of pressure
n (number of moles) = N (number of molecules)
NA (Avogadro’s number)
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 Avagodro’s 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
Avogadro’s number
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).
10.3 Gas Laws and Absolute Temperature
10.3 Gas Laws and Absolute Temperature
Example 10.4: A gas has a volume of 0.20 m3, a temperature of 30°C, and a
pressure of 1.0 atm. It is heated to 60°C and is compressed to a volume of 0.15
m3. Find the new pressure in atmospheres.
10.3 Gas Laws and Absolute Temperature
Example 10.5: An ideal gas in a container of volume 1000 cm3 (one liter) at
20.0°C 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.
10.3 Gas Laws and Absolute Temperature: Check for Understanding
1. The temperature used in the ideal gas law is:
a) Celcius
b) Fahrenheit
c) Kelvin
d) any of the preceding
Answer: c
10.3 Gas Laws and Absolute Temperature: Check for Understanding
2. When the temperature of a quantity of gas is increased:
a) the pressure must increase
b) the volume must increase
c) both the pressure and volume must increase
d) none of the preceding
Answer: d ; pV/T = constant
10.3 Gas Laws and Absolute Temperature: Check for Understanding
10.3 Gas Laws and Absolute Temperature: Check for Understanding
Homework 10.A
• HW 10.A: 7,8,17,22,24,27-32,34,36,38.
10.4 Thermal Expansion
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.
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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
1. ice in freezer
-20°C
506°K
___________
2. melting ice
0°C
546°K
___________
3. body temperature
37°C
620°K
___________
4. boiling water
100°C
746°K
___________
10.4 Thermal Expansion
10.4 Thermal Expansion
•
•
The coefficient for volume expansion is approximately equal to 3α, 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 β is used.
∆ V = β ∆ T (for fluids)
V0
10.4 Thermal Expansion
Example 10.6: You are installing some outdoor copper electric wire to a
backyard fish pond on a hot 40°C summer day. The temperature could be as
low as -20°C 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?
10.4 Thermal Expansion
Example 10.7: A 500-milliliter glass beaker of water is filled to the rim at a
temperature of 0°C. How much water will overflow if the water is heated to a
temperature of 95°C? (Ignore the expansion of the beaker, why?)
10.5 The Kinetic Theory of Gases
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.
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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.
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 = Boltzmann’s constant
T = absolute temperature in kelvin
10.5 The Kinetic Theory of Gases
10.5 The Kinetic Theory of Gases
Since KEave = 3/2 kBT
= ½ mv2rms, we can solve for vrms:
______
vrms = √ 3kBT/m , where m ( on gold sheet) is the mass of one
molecule of gas, in kg
On Gold Sheet
or
_______
vrms = √ 3RT/M , where M is the molar mass in kg
On Gold Sheet
m=
kg
(gold sheet uses  instead of m)
molecule
n= number of mols
So, Nm = nM = kg
M = kg
mol
N = number of molecules
10.5 The Kinetic Theory of Gases
The ideal gas law can be expressed in terms of the root-meansquare speed of the molecules.
_______
vrms = √ 3RT/M
Solve for RT:
RT = ⅓ M (vrms)2
Substitute into pV = nRT
pV = ⅓ nMv2rms
or
pV = ⅓ 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
10.5 The Kinetic Theory of Gases
U = N (KEave)
U = n (KEave)
10.5 The Kinetic Theory of Gases
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)
10.5 The Kinetic Theory of Gases
Example 10.9: If the temperature of a gas increases from 20°C to 40°C, by what
factor does the rms speed increase?
10.5 The Kinetic Theory of Gases: Check for Understanding
The thermal coefficient of volume expansion for a solid is:
a) α
b) 2 α
c) 3 α
d) α3
Answer: c
10.5 The Kinetic Theory of Gases
If the kinetic energy of an average ideal gas molecule in a sample at
20°C doubles, its final temperature must be
a) 10°C
b) 40°C
c) 313°C
d) none of the preceding
Answer: c) because 20°C = 293 K
and 2 x 293 K = 586 K
= 313°C
10.5 The Kinetic Theory of Gases
If the temperature of a quantity of ideal gas is raised from 20°C to
40°C, 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.
10.5 The Kinetic Theory of Gases: Check for Understanding
10.5 The Kinetic Theory of Gases: Check for Understanding
Homework 10.B
• HW 10.B: 45-49, 65-68, 71.