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Chapter 10
Temperature and Kinetic
Theory
Units of Chapter 10
Temperature and Heat
The Celsius and Fahrenheit Temperature Scales
Gas Laws, Absolute Temperature, and the
Kelvin Temperature Scale
Thermal Expansion
The Kinetic Theory of Gases
Kinetic Theory, Diatomic Gases, and the
Equipartition Theorem
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10.1 Temperature and Heat
Temperature is a measure of relative hotness
or coldness.
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10.1
Temperature
and Heat
Heat is the net energy transferred from one
object to another due to a temperature
difference.
This energy may contribute to the total internal
energy of the object, or it may do work, or both.
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10.1 Temperature and Heat
A higher temperature does not necessarily
mean that one object has more internal energy
than another; the size of the object matters as
well.
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10.2 The Celsius and Fahrenheit
Temperature Scales
A thermometer is used to measure
temperature; it must take advantage of some
property that depends on temperature. A
common one is thermal expansion.
When heat is transferred from one object to
another, they are said to be in thermal contact.
Two objects in thermal contact without heat
transfer are in thermal equilibrium.
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10.2 The Celsius and Fahrenheit
Temperature Scales
In everyday use, temperature is
measured in the Fahrenheit or
Celsius scale.
Question 10.1
Which is the largest unit:
one Celsius degree, one
Kelvin degree, or one
Fahrenheit degree?
Degrees
a) one Celsius degree
b) one Kelvin degree
c) one Fahrenheit degree
d) both one Celsius degree and
one Kelvin degree
e) both one Fahrenheit degree
and one Celsius degree
To convert from one to the
other:
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Question 10.2
Freezing Cold
It turns out that –40°C is the same
temperature as –40°F. Is there a
temperature at which the Kelvin and
Celsius scales agree?
a) yes, at 0°C
b) yes, at −273°C
c) yes, at 0 K
d) no
10.3 Gas Laws, Absolute Temperature,
and the Kelvin Temperature Scale
When the temperature of an ideal gas is held
constant,
When the pressure is held constant,
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10.3 Gas Laws, Absolute Temperature,
and the Kelvin Temperature Scale
10.3 Gas Laws, Absolute Temperature,
and the Kelvin Temperature Scale
The ideal gas law can also be written
Combining gives the ideal gas law:
or
where n is the number of moles of gas and R
is the universal gas constant:
with Boltzmann s constant:
A mole of a substance contains Avogadro s
number of molecules:
N is the total number of molecules in the gas.
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10.3 Gas Laws, Absolute Temperature,
and the Kelvin Temperature Scale
A constant-volume gas thermometer is useful
because the temperature is directly proportional
to the pressure. If P-T curves are plotted for
different gases, they converge at zero pressure.
© 2010 Pearson Education, Inc.
10.3 Gas Laws, Absolute Temperature,
and the Kelvin Temperature Scale
The temperature at which this occurs is called
absolute zero—no lower temperature is
possible.
The Kelvin temperature scale has the same
increments as the Celsius scale, but has its
zero at absolute zero.
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10.3 Gas Laws, Absolute Temperature,
and the Kelvin Temperature Scale
The three temperature
scales are shown here. In
physics calculations, the
Kelvin temperature scale is
used.
10.4 Thermal Expansion
Most materials expand when heated. For small
changes in temperature, the change in length is
proportional to the change in temperature.
The Kelvin scale is also
called the absolute scale, as
the Kelvin temperature is
proportional to the internal
energy.
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10.4 Thermal Expansion
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10.4 Thermal Expansion
The changes in area and in volume can be
derived from the change in length.
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Question 10.4
Glasses
a) run hot water over them both
Two drinking glasses are
stuck, one inside the other.
How would you get them
b) put hot water in the inner one
c) run hot water over the outer one
d) run cold water over them both
unstuck?
Question 10.5b Steel Expansion II
Metals such as brass expand when
heated. The thin brass plate in the
movie has a circular hole in its
center. When the plate is heated,
what will happen to the hole?
a) gets larger
b) gets smaller
c) stays the same
d) vanishes
e) break the glasses
10.4 Thermal Expansion
Water behaves nonlinearly near its freezing
point—it actually expands as it cools. This is
why ice floats, and why frozen containers may
burst.
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10.5 Kinetic Theory of Gases
10.5 Kinetic Theory of Gases
According to the kinetic
theory of gases, pressure
is due to elastic collisions
of molecules with
container walls.
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10.5 Kinetic Theory of Gases
Using the kinetic theory, it can be shown that
The mass and speed are those of an individual
molecule.
The internal energy of a monatomic gas is due
to the kinetic energy of its atoms, and is
therefore related to its temperature.
The molecular kinetic energy can be related
to the temperature:
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Question 10.8a Nitrogen and Oxygen I
Which has more molecules—a
mole of nitrogen (N2) gas or a
mole of oxygen (O2) gas?
a) oxygen
b) nitrogen
c) both the same
10.5 Kinetic Theory of Gases
The kinetic theory of gases also helps us
understand diffusion as a result of the motion
of molecules.
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10.6 Kinetic Theory, Diatomic Gases,
and the Equipartition Theorem
The equipartition theorem tells us what the
contribution of the rotational states is to the
internal energy.
Question 10.8b Nitrogen and Oxygen II
Which weighs more—a mole
a) oxygen
of nitrogen (N2) gas or a mole
b) nitrogen
of oxygen (O2) gas?
c) both the same
10.6 Kinetic Theory, Diatomic Gases,
and the Equipartition Theorem
The atoms in a monatomic
gas have only translational
equilibrium to contribute to
the internal energy. A
diatomic molecule can also
rotate around two distinct
axes (x and y).
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10.6 Kinetic Theory, Diatomic Gases,
and the Equipartition Theorem
The predicted internal energy of a diatomic
gas is then:
A diatomic molecule has 5 degrees of freedom
—translation in x, y, or z, rotation around x,
and rotation around y.
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PV Constant in Boyle s Law
Boyle s Law
Boyle s Law states that
In Boyle s Law
•  The product P x V is constant as long as T and n do
not change.
•  The pressure of a gas
is inversely related to
its volume when T and
n are constant.
P1V1 = 8.0 atm x 2.0 L = 16 atm L
P2V2 = 4.0 atm x 4.0 L = 16 atm L
•  If the pressure
increases, volume
decreases.
P3V3 = 2.0 atm x 8.0 L = 16 atm L
•  Boyle s Law can be stated as
P1V1
=
P2V2 (T, n constant)
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Solving for a Gas Law
Factor
Calculation with Boyle s Law
The equation for Boyle s Law can be rearranged to
solve for any factor.
P1V1 = P2V2
Boyle s Law
Freon-12, CCl2F2, is used in refrigeration systems.
What is the new volume (L) of a 8.0 L sample of Freon
gas initially at 550 mm Hg after its pressure is changed
to 2200 mm Hg at constant T?
To solve for V2 , divide both sides by P2.
P1V1
= P2V2
P2
P2
V1 x
P1
P2
=
32
STEP 1 Set up a data table
Conditions 1
Conditions 2
P1 = 550 mm Hg
P2 = 2200 mm Hg
V1 = 8.0 L
V2 =
V2
?
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Calculation with Boyle s Law
(Continued)
STEP 2 Solve Boyle s Law for V2. When pressure
increases, volume decreases.
P1V1 = P2V2
V2
V2
= V1 x P1
P2
= 8.0 L x 550 mm Hg = 2.0 L
2200 mm Hg
pressure ratio
decreases volume
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Learning Check
For a cylinder containing helium gas
indicate if cylinder A or cylinder B
represents the new volume for the
following changes (n and T are
constant):
1) Pressure decreases
2) Pressure increases
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Solution
Charles Law
For a cylinder containing helium gas
indicate if cylinder A or cylinder B
represents the new volume for the
following changes (n and T are
constant):
In Charles Law
•  The Kelvin temperature
of a gas is directly
related to the volume.
•  P and n are constant.
1) Pressure decreases B
•  When the temperature
of a gas increases, its
volume increases.
2) Pressure increases A
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Charles Law: V and T
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Learning Check
•  For two conditions, Charles Law is written
V1 = V2 (P and n constant)
T1
T2
Solve Charles Law expression for T2.
V1 = V2
T1
T2
•  Rearranging Charles Law to solve for V2
V2 = V1 x T2
T1
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Ideal Gas Law
Solution
V1
T1
= V2
T2
•  The relationship between the four
properties (P, V, n, and T) of gases can
be written equal to a constant R.
PV = R
nT
•  Rearranging this expression gives the
expression called the ideal gas law.
PV = nRT
Cross multiply to give
V1T2 =
V2T1
Isolate T2 by dividing through by V1
V1T2 =
V2T1
V1
V1
T2
=
T1 x V2
V1
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Universal Gas Constant, R
Learning Check
The universal gas constant, R
•  Can be calculated using the molar volume of a gas at STP.
•  Calculated at STP uses 273 K,1.00 atm, 1 mole of a gas, and a
molar volume of 22.4 L.
P
V
R =
PV =
(1.00 atm)(22.4 L)
nT
(1 mole) (273K)
n
T
=
0.0821 L atm
mole K
Another value for the universal gas
constant is obtained
using mm Hg for the STP pressure.
What is the value
of R when a pressure of 760 mm Hg is
placed in the R
value expression?
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Question 10.9a Ideal Gas Law I
Solution
What is the value of R when a pressure of 760
mm Hg is placed in the R value expression?
R
=
PV
nT
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Two identical cylinders at the same
a) cylinder A
temperature contain the same gas. If
b) cylinder B
A contains three times as much gas
c) both the same
as B, which cylinder has the higher
pressure?
d) it depends on
temperature T
= (760 mm Hg) (22.4 L)
(1 mole) (273 K)
= 62.4 L mm Hg
mole K
Question 10.9b Ideal Gas Law II
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Question 10.9c Ideal Gas Law III
Two cylinders at the same
a) PB = ½ PA
Two identical cylinders at the same
a) cylinder A
pressure contain the same gas. If A
b) cylinder B
contains three times as much gas as
c) both the same
the number of moles as A, how does
c) PB = ¼ PA
d) it depends on the
the pressure in B compare with the
d) PB = 4 PA
pressure in A?
e) PB = PA
B, which cylinder has the higher
temperature?
pressure P
temperature contain the same gas.
If B has twice the volume and half
b) PB = 2 PA
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