Download Chapter 12 Notes - Madison County Schools

Chapter 12 Lecture
Pearson Physics
Gases, Liquids,
and Solids
Prepared by
Chris Chiaverina
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Chapter Contents
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Gases
Fluids at Rest
Fluids in Motion
Solids
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Gases
• A substance that can flow from one location to
another and has no set shape of its own is
referred to as a fluid.
• Gases and liquids are both fluids. They differ in
that gases expand to fill their container, whereas
liquids have a definite volume and may only
partially fill their container.
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Gases
• As the figure below
shows, the pressure in a
gas (or any fluid) acts
equally in all directions.
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Gases
• In addition, the pressure is always at right angles
to any surface it acts on.
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Gases
• If a car runs over a nail and a tire goes flat, it
may be reasonable to think that the pressure
inside the tire is zero. This is not so.
• Since the hole in the tire allows air to pass freely
from the inside of the tire to the atmosphere, the
pressure in the tire is equal to atmospheric
pressure.
• When the tire is patched and inflated to a typical
value of 241 kPa (about 35 lb/in2), the pressure
inside the tire is greater than atmospheric
pressure by 241 kPa.
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Gases
• In fact, the pressure in the inflated tire is
P = 241 kPa + Patmospheric
= 241 kPa + 101 kPa
= 342 kPa
• However, the pressure you read on the gauge
is—appropriately enough—described as gauge
pressure. Gauge pressure is defined as
follows:
Pgauge= P − Patmospheric
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Gases
• In this equation, the pressure P is the pressure
inside the tire. The pressure that you read on a
tire gauge is the gauge pressure, which is less
than the pressure in the tire.
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Gases
• In physics, idealized cases are often well
approximated by many real-world situations.
This is the case with the air surrounding us, in
which the particles have little effect on one
another. Behavior such as this can be
considered ideal.
• Thus an ideal gas is one in which the particles
have no effect on one another. Like the air
around us, most real gases are good
approximations to an ideal gas.
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Gases
• Pressure is the key to understanding the
behavior of an ideal gas. The following are three
common ways of changing the pressure exerted
by a gas.
– Increasing the number of gas particles in an
enclosed space increases the pressure.
– Decreasing the volume of an enclosed gas
increases the pressure.
– Heating an enclosed gas increases the
average kinetic energy of its particles, causing
an increase in pressure.
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Gases
• These three observations can be combined into
one simple equation for the pressure of an ideal
gas:
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Gases
• In this equation, N is the number of gas
particles, T is the Kelvin temperature, and V is
the volume of gas. The k is known as the
Boltzmann constant. It is named for the Austrian
physicist Ludwig Boltzmann (1844–1906). Its
numerical value is
1.38 x 10-23 J/K
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Gases
• The ideal gas equation is also sometimes written
in an equivalent form:
PV = NkT
• The ideal gas equation shows that the gas
pressure increases if the number of gas
molecules increases, the temperature of the gas
increases, or the volume of the gas decreases.
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Gases
• In many cases it's more convenient to talk about
the amount of gas in terms of weight rather than
in terms of the number of particles.
• This way of measuring the amount of gas uses
moles.
• A mole (mol) is the amount of a substance that
contains as many particles as there are atoms in
12 grams of carbon-12.
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Gases
• Experiments show that the
number of particles in 12
grams of carbon-12 is
6.022 x 1023. This number
is known as Avogadro's
number, NA, named for the
Italian physicist Amedeo
Avogadro (1776−1856).
• The photograph below
offers examples of a mole
of various substances.
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Gases
• If n is used to represent the number of moles in
an amount of gas, then the number of particles,
N, is the number of moles times Avogadro's
number:
N = nNA
• Using this expression for N in the ideal gas
equation (PV = NkT) yields
PV = nNAkT
• This equation may be simplified by replacing
NAk with the universal gas constant, R.
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Gases
• The value of R is defined below.
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Gases
• Thus, the ideal gas equation in terms of moles is
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Gases
• The following example illustrates a calculation
using the ideal gas equation.
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Gases
• A mole of anything has precisely the same
number of particles. What differs from substance
to substance is the mass of 1 mole.
• In general, the molar mass, M, of a substance is
the mass in grams of 1 mole of that substance.
For example, 1 mole of helium atoms has a
mass of 4.00260 g, and 1 mole of copper atoms
has a mass of 63.546 g.
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Gases
• Molar mass provides a convenient bridge
between the macroscopic world, where we
measure the mass of a substance in grams, and
the microscopic world, where the number of
particles in a sample of a substance is typically
1023 or more.
• If you measure out a mass of copper equal to
63.546 g, you have, in effect, counted out
NA = 6.022 x 1023 atoms of copper.
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Gases
• The picture of a gas consisting of innumerable
particles flying about randomly at high speeds is
known as the kinetic theory of gases.
• Experiments show that the average kinetic
energy of the particles in a gas is directly
proportional to the Kelvin temperature. Thus,
when a gas is heated, its particles move faster.
This in turn increases the pressure exerted by the
gas.
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Gases
• Similarly, phase transitions can be understood in
terms of the kinetic behavior of molecules. This
explanation is sometimes referred to as the kinetic
molecular theory.
• For example, as the temperature of a solid is
increased, the molecules oscillate about their fixed
positions with more and more energy. When the
temperature is high enough, the molecules have
enough energy to break free of one another and
move about more or less freely in the liquid state.
• Increasing the temperature even more gives the
molecules enough energy to form the gas phase.
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Fluids at Rest
• Fluids flow from place to place and can change
their shape and hence may seem somewhat
difficult to describe and analyze.
• One of the best ways to describe a fluid is in terms
of amount of mass it has per volume. In general,
the density of a substance (fluid or not) is the
mass m of the substance divided by its volume, V.
• The denser the substance, the more mass it has
in any given volume.
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Fluids at Rest
• Using the Greek letter rho, ρ (pronounced
"row"), to stand for density, the definition of
density is as follows:
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Fluids at Rest
• The cylindrical flask in the figure below contains
three colored liquids with different densities. The
helium-filled blimp floats because helium is less
dense than air.
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Fluids at Rest
• A container 1 meter on a side
encloses 1 cubic meter (1 m3).
It takes 1000 kilograms of water
to fill the container. Therefore,
the density of water is
ρ = 1000 kg/1 m3 = 1000 kg/m3
• The table below gives the
densities of a variety of solids,
liquids, and gases.
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Fluids at Rest
• The following example shows how the density
equation can be used to solve for the mass of a
given volume or for the volume of a given mass.
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Fluids at Rest
• The pressure in a fluid increases with depth. The
increase in pressure is due to the added weight
of the fluid pressing down as the depth
increases.
• The figure below shows the how the force varies
with depth.
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Fluids at Rest
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Fluids at Rest
• The top of the fluid-filled container in the figure is
open to the atmosphere, which has a pressure
Patmospheric.
• If the cross-sectional area of the container is A,
the downward force exerted on the top surface
by the atmosphere is
Ftop = PatmosphericA
• At the bottom of the container, the downward
force is Ftop plus the weight of the fluid, where
the weight of the fluid is
W = mg = ρVg = ρ(hA)g
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Fluids at Rest
• It follows that the total force at the bottom of the
container is
Fbottom = PatmosphericA + ρ(hA)g
• Dividing the force by the area equals the
pressure at the bottom:
Pbottom = Patmospheric + ρgh
• This equation holds not only for the bottom of
the container, but also for any depth below the
surface.
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Fluids at Rest
• The following example illustrates how pressure
can be calculated for a specific depth.
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Fluids at Rest
• The equation Pbottom = Patmospheric + ρgh can be
applied to any two points in a fluid.
• Suppose the pressure at one point is P1 and the
pressure is P2 at a depth h below point 1. As
shown in the figure below, the pressure at point 2
is greater than that at point 1 by the amount ρgh.
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Fluids at Rest
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Fluids at Rest
• The barometer is an interesting application of
the change of pressure with depth.
• The basic idea of the barometer is that the
height difference is directly related to the
atmospheric pressure that pushes down on the
fluid in the bowl.
• The figure below shows that the pressure in the
vacuum at the top of the tube is zero.
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Fluids at Rest
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Fluids at Rest
• Thus the pressure in the tube at a depth h below
the vacuum is ρgh.
• At the level of the fluid in the bowl, the pressure is
1 atmosphere. Therefore, Patmospheric = ρgh.
• Thus, a measurement of the height difference (h)
gives the atmospheric pressure.
• Mercury is a fluid that is often used in a barometer
of the type shown above. Using h = Patmospheric/ρg
and appropriate values for ρ and g, the height of a
column of mercury at normal atmospheric
pressure is found to be 760 mm.
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Fluids at Rest
• The unit in the above result, millimeters of
mercury, is used to define normal atmospheric
pressure:
1 atmospheric = Patmospheric = 760 mmHg
• The table below summarizes the various units in
which atmospheric pressure can be expressed.
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Fluids at Rest
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Fluids at Rest
• Squeezing a balloon causes the pressure to
increase everywhere in the balloon. This is an
example of Pascal's principle.
• Pascal's principle states that an external pressure
applied to an enclosed fluid is transmitted
unchanged to every point within the fluid.
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Fluids at Rest
• A classic example of Pascal's principle is the
hydraulic lift, such as the one shown in the figure
below.
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Fluids at Rest
• Pushing down on the small piston increases the pressure
in that cylinder by the amount ΔP = F1/A1.
• By Pascal's principle, the pressure in cylinder 2 increases
by the same amount: ΔP = F2/A2.
• Combining the two equations, we find
F2 = F1(A2/A1)
• Since the figure shows A2 to be greater than A1, the force,
F1, exerted on the small piston causes a larger force, F2,
on the large piston.
• The lift magnifies force F2, but the distance d2 is smaller
than distance d1. Energy is conserved.
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Fluids at Rest
• As the figure below shows, a fluid surrounding
an object exerts a buoyant force in the upward
direction.
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Fluids at Rest
• The direction of the buoyant force is due to the
fact that the pressure increases with depth, and
hence the upward force on the object, F2, is
greater than the downward force, F1. Forces
acting to the left and to the right cancel out.
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Fluids at Rest
• It can be shown that the buoyant force acting on
the object is equal to the weight of the fluid that
the object displaces. This is referred to as
Archimedes' principle.
• The figure below illustrates an example of
Archimedes' principle. Note that the decrease in
scale reading is equal to weight of the water that
the block displaces.
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Fluids at Rest
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Fluids at Rest
• When an object floats in water, the upward
buoyant force is equal in magnitude to the
downward force of gravity.
• High-density objects can also float. For example,
a steel block that normally sinks will float if is it is
molded into the shape of a bowl (see figure
below). This is the principle that allows ships to
be made of steel and iron.
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Fluids at Rest
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Fluids in Motion
• When the opening of a hose is made smaller
with a nozzle or a thumb, the velocity of flow
increases (see figure below).
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Fluids in Motion
• This increase in speed illustrates what is
referred to as the equation of continuity.
• The equation of continuity states that if the
cross-sectional area through which a fluid flows
is reduced, the speed of the fluid increases.
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Fluids in Motion
• That is,
cross-sectional area 1 x velocity 1 =
cross-sectional area 2 x velocity 2
or
A1v1 = A2v2
• The figure below illustrates the increase in
velocity due to the narrowing of a pipe.
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Fluids in Motion
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Fluids in Motion
• When a fluid flows at high speed, its pressure
is less than when it flows at low speed.
• The fact that the pressure of water—or any
fluid—is reduced when it flows at a higher
speed is referred to as Bernoulli's principle.
• As the figure below shows, blowing across the
top of a piece of paper reduces the pressure
there, resulting in a net upward force that lifts
the paper.
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Fluids in Motion
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Fluids in Motion
• Practical applications of Bernoulli's principle
include:
– the lift provided by the flow over the top of an airplane
wing
– the modification of roof design to prevent high-speed
winds from lifting roofs off houses
– the natural air conditioning provided by the design of
a prairie dog burrow. A burrow typically has a high
mound and a low mound. Greater air speed over the
higher mound reduces the pressure over the higher
mound. The difference in pressure causes air to be
drawn through the burrow.
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Fluids in Motion
• A fluid flowing past a stationary surface experiences a
force opposing the flow. This tendency of a fluid to resist
flow is referred to as the viscosity of the fluid.
• Fluids like air have low viscosities, thick fluids like water
are more viscous, and fluids like honey and molasses
are characterized by high viscosity.
• Real fluids always have some viscosity, and hence work
must be done to force a fluid to flow through the tube.
• This is the reason the blood in our arteries has a
relatively high pressure. If a blood vessel is partially
blocked, the resistance to blood flow increases, resulting
in a higher than normal blood pressure.
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Fluids in Motion
• Real fluids also exhibit surface tension, the force
that tries to minimize the surface area of a fluid.
• It is surface tension that makes the surface of
water behave like an elastic sheet.
• Surface tension enables some insects to walk on
the surface of a pond (see figure below).
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Fluids in Motion
• Even a needle or razor blade can be supported
by surface tension if it is put into place gently.
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Solids
• Unlike fluids, solids maintain their shape.
• A solid may be thought of as a collection of small
balls representing molecules. In this model, the
molecules are connected to one another by
springs (see figure below).
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Solids
• When you pull on a solid rod with a force, you
stretch each of the intermolecular springs in the
direction of the force. The result is that the entire
solid increases in length.
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Solids
• In the case of a spring, the amount of stretch
varies with the force applied. The greater the
force, the greater the stretch.
• The figure below shows how a spring scale
responds to increasing weight.
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Solids
• As the figure indicates, the change in the
spring's length is directly proportional to the
applied force.
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Solids
• The proportionality between stretch and applied
force may be summarized with the following
equation:
F = kΔL
• This equation is known as Hooke's law.
• The change in length ΔL can be either a stretch
or a compression.
• The constant k is called the spring constant, and
its units are newtons per meter (N/m).
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Solids
• The change in length is generally represented
with the symbol x, as is shown in the figure
below.
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Solids
• When x = 0, the spring is relaxed, and there is
no change in length. When stretched or
compressed, x represents the distance from
equilibrium. Replacing ΔL with x yields Hooke's
law for the specific case of a spring: F = kx.
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Solids
• Objects that return to their original shape and
size after being deformed are said to be elastic.
• Stretching a spring too far, however, causes
permanent deformation. In this case, which is
referred to as exceeding the elastic limit of the
spring, the spring never returns to its original
state.
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Solids
• The stretch-force graph in the figure below
shows how a spring responds to forces of
various magnitudes.
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Solids
• As the figure below illustrates, the amount that a
wire, or any object, will stretch is proportional to
the original length of the wire. A convenient way
to increase the initial length of a wire is to wrap it
into a coil of many turns. This is how a spring is
made.
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Solids
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