Lecture Outlines
Chapter 17
Physics, 3rd Edition
James S. Walker
© 2007 Pearson Prentice Hall
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Chapter 17
Phases and Phase Changes
Units of Chapter 17
• Ideal Gases
• Kinetic Theory
• Solids and Elastic Deformation
• Phase Equilibrium and Evaporation
• Latent Heats
• Phase Changes and Energy
Conservation
17-1 Ideal Gases
Gases are the easiest state of matter to
describe, as all ideal gases exhibit similar
behavior.
An ideal gas is one that is thin enough, and far
away enough from condensing, that the
interactions between molecules can be ignored.
17-1 Ideal Gases
If the volume of an ideal
gas is held constant, we
find that the pressure
increases with
temperature:
17-1 Ideal Gases
If the volume and
temperature are kept
constant, but more gas is
added (such as in
inflating a tire or
basketball), the pressure
will increase:
17-1 Ideal Gases
Finally, if the
temperature is constant
and the volume
decreases, the pressure
increases:
17-1 Ideal Gases
Combining all three observations, we write
where k is called the Boltzmann constant:
17-1 Ideal Gases
Rearranging gives us the equation of state for
an ideal gas:
Instead of counting molecules, we can count
moles. A mole is the amount of a substance
that contains as many elementary entities as
there are atoms in 12 g of carbon-12.
17-1 Ideal Gases
Experimentally, the number of entities (atoms
or molecules) in a mole is given by
Avogadro’s number:
Therefore, n moles of gas will
contain
molecules.
17-1 Ideal Gases
Avogadro’s number and the Boltzmann constant
can be combined to form the universal gas
constant and an alternative equation of state:
17-1 Ideal Gases
The atomic or molecular mass of a substance
is the mass, in grams, of one mole of that
substance. For example,
Helium:
Copper:
Furthermore, the mass of an individual atom
is given by the atomic mass divided by
Avogadro’s number:
17-1 Ideal Gases
Boyle’s law, which is
consistent with the ideal
gas law, says that the
pressure varies inversely
with volume. These curves
of constant temperature are
called isotherms.
17-1 Ideal Gases
Charles’s law, also
consistent with the
ideal gas law, says
that the volume of a
gas increases with
temperature if the
pressure is constant.
17-1 Ideal Gases
In this photograph,
the balloon was
inflated at room
temperature and
cooled with liquid
nitrogen. The
decrease in volume
of the air in the
balloon is obvious.
17-2 Kinetic Theory
The kinetic theory relates microscopic
quantities (position, velocity) to macroscopic
ones (pressure, temperature). Assumptions:
• N identical molecules of mass m are inside a
container of volume V; each acts as a point
particle.
• Molecules move randomly and always obey
Newton’s laws.
• Collisions with other molecules and with the
walls are elastic.
17-2 Kinetic Theory
Pressure is the result
of collisions between
the gas molecules
and the walls of the
container.
It depends on the mass and speed of the
molecules, and on the container size:
17-2 Kinetic Theory
Not all molecules in a gas will have the same
speed; their speeds are represented by the
Maxwell distribution, and depend on the
temperature and mass of the molecules.
17-2 Kinetic Theory
We replace the speed in the previous
expression for pressure with the average
speed:
Including the other two directions,
Therefore, the pressure in a gas is
proportional to the average kinetic energy of
its molecules.
17-2 Kinetic Theory
Comparing this expression with the ideal gas
law allows us to relate average kinetic energy
and temperature:
The square root of
mean square (rms) speed.
is called the root
17-2 Kinetic Theory
Solving for the rms speed gives:
17-2 Kinetic Theory
The rms speed is slightly greater than the
most probable speed and the average speed.
17-2 Kinetic Theory
The internal energy of an ideal gas is the sum
of the kinetic energies of all its molecules. In
the case where each molecule consists of a
single atom, this may be written:
17-3 Solids and Elastic Deformation
Solids have definite shapes (unlike fluids), but
they can be deformed. Pulling on opposite
ends of a rod can cause it to stretch:
17-3 Solids and Elastic Deformation
The amount of
stretching will depend
on the force; Y is
Young’s modulus and is
a property of the
material:
17-3 Solids and Elastic Deformation
Another type of deformation is called a shear
deformation, where opposite sides of the
object are pulled laterally in opposite
directions.
17-3 Solids and Elastic Deformation
As expected, the deformation is proportional
to the force. S is the shear modulus.
17-3 Solids and Elastic Deformation
Finally, if a solid is uniformly compressed, it
will shrink.
17-3 Solids and Elastic Deformation
Here, the proportionality constant, B, is called
the bulk modulus.
17-3 Solids and Elastic Deformation
The applied force per
unit area is called the
stress, and the resulting
deformation is the
strain. They are
proportional to each
other until the stress
becomes too large;
permanent deformation
will then occur.
17-4 Phase Equilibrium and Evaporation
If a liquid is put into a sealed container so that
there is a vacuum above it, some of the
molecules in the liquid will vaporize. Once a
sufficient number have done so, some will
begin to condense back into the liquid.
Equilibrium is reached when the numbers
remain constant.
17-4 Phase Equilibrium and Evaporation
The pressure of the gas when it is in
equilibrium with the liquid is called the
equilibrium vapor pressure, and will depend
on the temperature.
17-4 Phase Equilibrium and Evaporation
The vaporization curve determines the boiling
point of a liquid:
A liquid boils at the temperature at which its
vapor pressure equals the external pressure.
This explains why water boils at a lower
temperature at lower pressure – and why you
should never insist on a “3-minute egg” in
Denver!
17-4 Phase Equilibrium and Evaporation
This curve can be expanded. When the liquid
reaches the critical point, there is no longer a
distinction between liquid and gas; there is
only a “fluid” phase.
17-4 Phase Equilibrium and Evaporation
The fusion curve is the
boundary between the solid
and liquid phases; along that
curve they exist in
equilibrium with each other.
Almost all materials have a
fusion curve that resembles
(a); water, due to its unusual
properties near the freezing
point, follows (b).
17-4 Phase Equilibrium and Evaporation
Finally, the sublimation curve marks the
boundary between the solid and gas phases.
The triple point is where all three phases are in
equilibrium. This is shown on the phase
diagram below.
17-4 Phase Equilibrium and Evaporation
A liquid in a closed container will come to
equilibrium with its vapor. However, an open
liquid will not, as its vapor keeps escaping – it
will continue to vaporize without reaching
equilibrium. As the molecules that escape
from the liquid are the higher-energy ones, this
has the effect of cooling the liquid. This is why
sweating cools us off.
17-4 Phase Equilibrium and Evaporation
If we look at the Maxwell speed distributions for
water at different temperatures, we see that there
is not much difference between the 30° C curve
and the 100° C curve. This means that, if 100° C
water molecules can escape, many 30° C
molecules will also.
17-4 Phase Equilibrium and Evaporation
This same evaporation process can cause a
planet to lose its atmosphere – some molecules
will have speeds exceeding the escape velocity.
The evaporation process will be faster for
lighter molecules and for less massive planets.
17-5 Latent Heats
When two phases coexist, the temperature
remains the same even if a small amount of
heat is added. Instead of raising the
temperature, the heat goes into changing the
phase of the material – melting ice, for
example.
17-5 Latent Heats
The heat required to convert from one phase to
another is called the latent heat.
The latent heat, L, is the heat that must be
added to or removed from one kilogram of a
substance to convert it from one phase to
another. During the conversion process, the
temperature of the system remains constant.
17-5 Latent Heats
The latent heat of fusion is the heat needed to
go from solid to liquid; the latent heat of
vaporization from liquid to gas.
17-6 Phase Changes and Energy
Conservation
Solving problems involving phase changes is
similar to solving problems involving heat
transfer, except that the latent heat must be
included as well.
Summary of Chapter 17
• An ideal gas is one in which interactions
between molecules are ignored.
• Equation of state for an ideal gas:
• Boltzmann’s constant:
• Universal gas constant:
• Equation of state again:
• Number of molecules in a mole is Avogadro’s
number:
Summary of Chapter 17
• Molecular mass:
• Boyle’s law:
• Charles’s law:
• Kinetic theory: gas consists of large
number of pointlike molecules
• Pressure is a result of molecular collisions
with container walls
Summary of Chapter 17
• Molecules have a range of speeds, given by
the Maxwell distribution
• Relation of kinetic energy to temperature:
• Relation of rms speed to temperature:
Summary of Chapter 17
• Internal energy of monatomic gas:
• Force required to change the length of a
solid:
• Force required to deform a solid:
Summary of Chapter 17
• Pressure required to change the volume of a
solid:
• Applied force per area: stress
• Resulting deformation: strain
• Deformation is elastic if object returns to its
original size and shape when stress is
removed
Summary of Chapter 17
• Most common phases of matter: solid, liquid,
gas
• When phases are in equilibrium, the number
of molecules in each is constant
• Evaporation occurs when molecules in liquid
move fast enough to escape into gas phase
• Latent heat: amount of heat required to
transform from one phase to another
• Latent heat of fusion: melting or freezing
Summary of Chapter 17
• Latent heat of vaporization: vaporizing or
condensing
• Latent heat of sublimation: sublimation or
condensation directly between gas and solid
phases
• When heat is exchanged within a system
isolated from its surroundings, the energy of
the system is conserved