2. Unit 8: Matterand Energy
27.1 Properties of Solids
27.2 Properties of Liquids and Fluids
27.3 Properties of Gases
Chapter27 The Physical Properties of Matter
3. Chapter27 Objectives
1. Performcalculations involving the density of solids, gases, and
liquids.
2. Apply the concepts of force, stress, strain, and tensile strength to
simple structures.
3. Describe the cause and some consequences of thermal expansion in
solids, liquids, and gases.
4. Explain the concept of pressure and calculate pressure caused by
the weight of fluids.
5. Explain how pressure is created on a molecularlevel.
6. Understand and apply Bernoulli’s equation to flow along a
streamline.
7. Apply the gas laws to simple problems involving pressure,
temperature, mass, and volume.
4. Chapter27 Vocabulary Terms
stress
density
strain
tensile strength
cross section area
pressure
volume
tension
compression
elastic, elasticity
fluid
brittle
ductile
safety factor
modulus of
elasticity
alloy
airfoil
buoyancy
fluid mechanics
ideal gas law
Boyle’s law
streamline
laminarflow
turbulent flow
Bernoulli’s
equation
pascal (Pa)
Charles’ law
gas constant (R)
composite
material
thermal expansion
5. 27.1 Properties of Solids
Key Question:
How do you measure the
strength of a solid
material?
*Students read Section 27.1
AFTER Investigation 27.1
6. 27.1 Properties of Solids
The density of a
material is the ratio of
mass to volume.
Density is a physical
property of the material
and stays the same no
matter how much
material you have.
7. 27.1 Density
ρ = m
V
Mass (kg)
Volume (m3
or L)
Density (kg/m3
)
Most engineers and scientists use the greek letter
rho (ρ) to represent density.
8. 27.1 Densities of Common Materials
Which materials are less dense than water?
9. 27.1 Properties of Solids
The concept of physical
“strength” means the
ability of an object to hold
its form even when force is
applied.
To evaluate the properties
of materials, it is
sometimes necessary to
separate out the effects of
design, such as shape
and size.
10. 27.1 Stress
The stress in a material is the ratio of the force acting
through the material divided by the cross section area
through which the force is carried.
The metric unit of stress is the pascal (Pa).
One pascal is equal to one newton of force persquare
meterof area (1 N/m2
).
σ = F
A
Force (N)
Area (m2
)
Stress (N/m2
)
12. 26.1 Properties of Solids
A thicker wire can
support more force
at the same stress
as a thinner wire
because the cross
section area is
increased.
13. 26.1 Tensile strength
The tensile strength is the stress at which a
material breaks under a tension force.
The tensile strength
also describes how
materials break in
bending.
15. 27.1 Properties of solids
The safety factor is the ratio of how strong
something is compared with how strong it has to
be.
The safety factor allows for things that might
weaken the wire (like rust) or things you did not
consider in the design (like heavier loads).
A safety factor of 10 means you choose the wire
to have a breaking strength of 10,000 newtons, 10
times stronger than it has to be.
16. 27.1 Evaluate 3 Designs
Three designs have been proposed forsupporting a section of road.
Each design uses three supports spaced at intervals along the road.
A total of 4.5 million N of force is required to hold up the road.
Evaluate the strength of each design.
The factorof safety must be 5 orhighereven when the road is bumper-
to-bumperon all 4 lanes with the heaviest possible trucks.
20. 27.1 Properties of solids
Elasticity measures the ability of a material to
stretch.
The strain is the amount a material has been
deformed, divided by its original size.
21. 27.1 Strain
The Greek letter epsilon (ε) is usually used to
represent strain.
ε = ∆l
l
Change in
length (m)
Original length (m)
Strain
22. 27.1 Properties of solids
The modulus of elasticity
plays the role of the
spring constant for solids.
A material is elastic when
it can take a large
amount of strain before
breaking.
A brittle material breaks
at a very low value of
strain.
24. 27.1 Stress forsolids
Calculating stress forsolids is similarto using
Hooke's law forsprings.
Stress and strain take the place of force and
distance in the formula:
σ = -E ε
Modulus of
elasticity (pa)
Strain
Stress (Mpa)
25. 27.1 Properties of solids
The coefficient of thermal
expansion describes how much a
material expands foreach
change in temperature.
Concrete bridges always have
expansion joints.
The amount of contraction or
expansion is equal to the
temperature change times the
coefficient of thermal expansion.
26. 27.1 Thermal Expansion
∆l = α (T2-T1)
l
Change in
temperature (o
C)
Original length (m)
Coefficient of thermal expansionChange in
length (m)
27. 27.1 Thermal Expansion
Which substances will
expand orcontract
the most with
temperature changes?
28. 27.1 Plastic
Plastics are solids formed from long chain
molecules.
Different plastics can have a wide range of
physical properties including strength, elasticity,
thermal expansion, and density.
29. 27.1 Metal
Metals that bend and stretch easily without
cracking are ductile.
The properties of metals can be changed by
mixing elements.
An alloy is a metal that is a mixture of more than
one element.
Steel is an alloy.
30. 27.1 Wood
Many materials have different properties in
different directions.
Wood has a grain that is created by the way trees
grow.
Wood is very difficult to
break against the grain, but
easy to break along the
grain.
A karate chop easily breaks
wood along its grain.
31. 27.1 Composite materials
Composite materials are made
from strong fibers supported
by much weaker plastic.
Like wood, composite
materials tend to be strongest
in a preferred direction.
Fiberglass and carbon fiber
are two examples of useful
composite materials.
32. 27.2 Properties of Liquids and Fluids
Key Question:
What are some implications of Bernoulli’s equation?
*Students read Section 27.2 AFTER Investigation 27.2
33. 27.2 Properties of Liquids and Fluids
Fluids can change shape and flow when forces
are applied to them.
Gas is also a fluid because gases can change
shape and flow.
Density, buoyancy and pressure are three
properties exhibited by liquids and gases.
34. 27.2 Density vs. Buoyancy
The density of a liquid is the ratio of mass to
volume, just like the density of a solid.
An object submerged in liquid feels an upward
force called buoyancy.
The buoyancy force is exactly equal to the weight
of liquid displaced by the object.
Objects sink if the buoyancy force is less than
their own weight.
35.
36. 27.2 Pressure
Forces applied to fluids
create pressure instead
of stress.
Pressure is force per
unit area, like stress.
A pressure of 1 N/m2
means a force of one
newton acts on each
square meter.
37. 27.2 Pressure
Like stress, pressure is a ratio of force per unit
area.
Unlike stress however, pressure acts in all
directions, not just the direction of the applied
force.
38. 27.2 Pressure
The concept of pressure is
central to understanding how
fluids behave within
themselves and also how fluids
interact with surfaces, such as
containers.
If you put a box with holes
underwater, pressure makes
waterflow in fromall sides.
Pressure exerts equal force in
all directions in liquids that are
not moving.
39. 27.2 Properties of liquids and gases
Gravity is one cause of
pressure because fluids
have weight.
Air is a fluid and the
atmosphere of the Earth
has a pressure.
The pressure of the
atmosphere decreases with
altitude.
40. 27.2 Properties of liquids and gases
The pressure at any
point in a liquid is
created by the weight
of liquid above that
point.
41. 27.2 Pressure in liquids
The pressure at the same depth is the same
everywhere in any liquid that is not moving.
P = ρ g d
Density (kg/m3
)
Depth (m)
Pressure
(pa or N/m2
)
Strength of gravity
(9.8 N/kg)
42. 27.2 Calculate pressure
Calculate the pressure 1,000 meters
below the surface of the ocean.
The density of wateris 1,000 kg/m3
.
The pressure of the atmosphere is
101,000 Pa.
Compare the pressure 1,000 meters
deep with the pressure of the
atmosphere.
43. 27.2 Properties of liquids and gases
Pressure comes from collisions between atoms or
molecules.
The molecules in fluids (gases and liquids) are not bonded
tightly to each otheras they are in solids.
Molecules move around and collide with each otherand
with the solid walls of a container.
44. 27.2 Pressure and forces
Pressure creates force on surfaces.
The force is equal to the pressure times the area
that contacts the molecules.
F = P A
Pressure (N/m2
)
Area (m2
)
Force
(N)
45. 27.2 Calculate pressure
A car tire is at a pressure of
35 psi.
Four tires support a car that
weighs 4,000 pounds.
Each tire supports 1,000
pounds.
How much surface area of
the tire is holding up the
car?
46. 27.2 Motion of fluids
The study of motion of fluids is called fluid
mechanics.
Fluids flow because of differences in pressure.
Moving fluids usually do not have a single speed.
47. 27.2 Properties of liquids and gases
A flow of syrup down a
plate shows that
friction slows the syrup
touching the plate.
The top of the syrup
moves fastest because
the drag from friction
decreases away from
the plate surface.
48. 27.2 Properties of liquids and gases
Pressure and energy
are related.
Differences in
pressure create
potential energy in
fluids just like
differences in height
create potential
energy from gravity
49. 27.2 Properties of liquids and gases
Pressure does work as
fluids expand.
A pressure of one
pascal does one joule
of work pushing one
square meter a
distance of one meter.
50. 27.2 Energy in fluids
The potential energy is equal to volume times
pressure.
E = P V
Pressure (N/m2
)
Volume (m3
)
Potential
energy
(J)
51. 27.2 Energy in fluids
The total energy of a small mass of fluid is equal
to its potential energy from gravity (height) plus its
potential energy from pressure plus its kinetic
energy.
52. 27.2 Energy in fluids
The law of conservation of
energy is called Bernoulli’s
equation when applied to
a fluid.
Bernoulli’s equation says
the three variables of
height, pressure, and
speed are related by
energy conservation.
53. 27.2 Bernoulli's Equation
If one variable increases, at least one of the othertwo
must decrease.
If the fluid is not moving (v =0), then Bernoulli’s equation
gives us the relationship between pressure and depth
(negative height).
54. 27.2 Properties of liquids and gases
Streamlines are imaginary lines drawn to show
the flow of fluid.
We draw streamlines so that they are always
parallel to the direction of flow.
Fluid does not flow across streamlines.
55. 27.2 Applying Bernoulli's equation
The wings of airplanes are made in the shape of
an airfoil.
Air flowing along the top of the airfoil (B) moves
faster than air flowing along the bottom of the
airfoil (C).
56. 27.2 Calculating speed of fluids
Water towers create
pressure to make water
flow.
At what speed will water
come out if the water
level in the tower is 50
meters higher than the
faucet?
57. 27.2 Fluids and friction
Viscosity is caused by forces
that act between atoms and
molecules in a liquid.
Friction in fluids also
depends on the type of flow.
Water running from a faucet
can be either laminar or
turbulent depending on the
rate of flow.
58. 27.3 Properties of Gases
Key Question:
How much matter is
in a gas?
*Students read Section 27.3 AFTER Investigation 27.3
59. 27.3 Properties of Gases
Air is the most important
gas to living things on the
Earth.
The atmosphere of the
Earth is a mixture of
nitrogen, oxygen, water
vapor, argon, and a few
trace gases.
60. 27.3 Properties of Gases
An object submerged in gas feels an upward
buoyant force.
You do not notice buoyant forces from air
because the density of ordinary objects is so
much greater than the density of air.
The density of a gas depends on pressure and
temperature.
61. 27.3 Boyle's Law
If the mass and temperature are kept constant, the
product of pressure times volume stays the same.
P1V1 = P2V2
Original volume (m3
)
Original pressure
(N/m2
)
Final pressure (N/m2
)
Final volume (m3
)
62. 27.3 Calculate using Boyle's law
A bicycle pump creates
high pressure by squeezing
airinto a smallervolume.
If airat atmospheric
pressure (14.7 psi) is
compressed froman initial
volume of 30 cubic inches
to a final volume of three
cubic inches, what is the
final pressure?
63. 27.3 Charles' Law
If the mass and volume are kept constant, the pressure
goes up when the temperature goes up.
Original temperture
(k)
Original pressure
(N/m2
)
Final pressure (N/m2
)
Final temperature
(K)
P1 = P2
T1 T2
64. 27.3 Calculate using Charles' law
A can of hairspray has a pressure
of 300 psi at room temperature
(21°C or294 K).
The can is accidentally moved too
close to a fire and its
temperature increases to 800°C
(1,073 K).
What is the final pressure in the
can?
65. 27.3 Ideal gas law
The ideal gas law combines the pressure, volume,
and temperature relations for a gas into one
equation which also includes the mass of the gas.
In physics and engineering, mass (m ) is used for
the quantity of gas.
In chemistry, the ideal gas law is usually written in
terms of the number of moles of gas (n) instead of
the mass (m ).
66. 27.3 Gas Constants
The gas
constants are
different because
the size and
mass of gas
molecules are
different.
67. 27.3 Ideal gas law
If the mass and temperature are kept constant, the
product of pressure times volume stays the same.
P V = m R T
Volume (m3
)
Pressure
(N/m2
)
gas constant (J/kgK)
Temperature (K)
Mass (kg)
68. 27.3 Calculate using Ideal gas law
Two soda bottles contain the same
volume of airat different pressures.
Each bottle has a volume of 0.002 m3
(two liters).
The temperature is 21°C (294 K).
One bottle is at a gauge pressure of
500,000 pascals (73 psi).
The otherbottle is at a gauge
pressure of zero.
Calculate the mass difference
between the two bottles.
Even thought the stress is the same, the tensile strength of the thicker wire is higher
314 N/0.8 mm2 = 400N/mm2
1256N/3.1 mm2 = 400N/mm2
The stress is 1,500,000 N ÷ 0.015 m2 = 100 MPa.
The tensile strength of the steel is six times greater (600 MPa) than the stress in the tube, so the safety factor is 6.
Design #1 is acceptable for strength.
Design #2:
The stress is 1,500,000 N ÷ 0.015 m2 = 100 MPa. The tensile strength of the aluminum alloy is
only 2.9 times greater (290 MPa) than the stress in the tube, so the safety factor is only 2.9.
Design #2 is NOT acceptable because the safety factor is too low.
Design #3:
The stress is 1,500,000 N ÷ 0.03 m2 = 50 MPa.
The tensile strength of the steel in the cables is 8 times greater (400 MPa) than the stress in the cable, so the safety factor is 8.
Design #3 is acceptable for strength.
1) You are asked for the pressure and to compare it to one atmosphere.
2) You are given the density and depth.
3) Use the pressure formula P= ρgd and add the atmospheric pressure to water pressure.
4) P = (1,000 kg/m3)(9.8 N/kg)(1,000 m) + 101,000 Pa = 9,800,000
9,800,000 Pa + 101,000 Pa = 9,901,000 Pa, or 99 times atmospheric pressure.
1) You are asked for area.
2) You are given force and pressure.
3) Force is pressure times area, so area is force divided by pressure.
4) A = F÷P = (1,000 lbs)÷(35 psi) = 28.5 in2.
This is about equal to a patch of tire measuring 5-by-5.7 inches.
1) You are asked for the speed.
2) You are given height.
3) The Bernoulli equation relates speed and height in a fluid.
4) Choose a streamline from A to B and note that speed and pressure at A are zero, while height and pressure at B are zero.
5) (pgh)A = (1/2pv2)B
v = 31 m/s
1) You are asked for pressure.
2) You are given initial and final volume.
3) Apply Boyle’s law: P1V1 = P2V2
4) P2 = (V1/V2) × P1 = (30÷3) × 14.7 = 147 psi.
NOTE: Your tire pressure gauge will read 132.3 psi (147 - 14.7) because most pressure gauges
measure the pressure DIFFERENCE between inside the gauge and the atmosphere outside.
Boyle’s law and the other gas laws use “absolute pressure,” which is pressure relative to zero.
Gauges read “gauge pressure,” which is pressure above the pressure of the atmosphere.
1) You are asked for pressure.
2) You are given initial and final temperatures.
3) Apply the pressure - temperature relation P1÷T1 = P2÷T2.
4) P2 = (T2÷T1) × P1 = (1,073÷294) × 300 = 1,095 psi. …!
This is why you should NEVER put spray cans near heat.
The pressure can increase so much that the can explodes.
The values for the gas constant in Table 27.7 are in metric units.
To use these values with the ideal gas law, pressure is in pascals, volume in meters cubed, mass
in kilograms, and temperature in Kelvin.
Since the law applies to the total amount of gas, pressure needs to be absolute pressure, not gauge pressure.
Absolute pressure is gauge pressure plus the pressure of the atmosphere (101,000 pascals).
1) You are asked for a mass difference.
2) You are given the volume, temperature, gauge pressure, and the gas is air.
3) Use the ideal gas law, PV = mRT with R = 287 J/kg.K.
Convert gauge pressure to absolute pressure by adding 101,000 Pa.
4) First bottle: m = PV/RT = (601,000 x.002)÷(287 x 294) = 0.0143 kg
Second bottle: m = PV/RT = (101,000 x .002)÷(287 x 294) = 0.0024 kg
The difference is .0121 kg, or 12.1 grams.