Chapter 4 Physics of Matter. 2 Matter: Phases, Forms & Forces We classify matter into four categories: Solid: rigid; retain its shape unless distorted

Chapter 4

Physics of Matter

2

Matter: Phases, Forms & Forces We classify matter into four categories:

Solid: rigid; retain its shape unless distorted by a force.

Liquid: flows readily; conforms to the shape of a container; has a well-defined boundary; has higher densities than gases.

Gas: flows readily; conforms to the shape of a container; does not have a well-defined surface; can be compressed readily.

Plasma: has gaseous properties but also conducts electricity; interacts strongly with magnetic fields; commonly exists at higher temperatures.

3

Matter: Phases, Forms & Forces, cont’d

The chemical elements represent the simplest and purest forms of everyday matter. There are currently 114 different elements. 110 of them have accepted names.

Each element is composed of incredibly small objects called atoms. There are 114 different atoms, one for each of the

known elements. Only about 90% of the elements exist naturally on

Earth. The others are artificially produced in laboratories.

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The atom is not indivisible. It has its own internal structure.

Every atoms has a very dense, compact core called the nucleus. The nucleus is composed of two kinds of particles:

Protons: have a positive electric charge. Neutrons: have no electric charge.

The nucleus is surrounded by one or more particles called electrons. Electrons have the same electric charge as protons but

are negatively charged.

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Every atom associated with a particular element has a fixed number of protons. The number of protons distinguishes the element.

Atoms with two protons are helium atoms.

The atomic number of an element specifies the number of protons. The atomic number of helium (He) is 2 because it

has two protons. Each element is given its own chemical symbol.

This is a one- or two- letter abbreviation.

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Atoms can have various numbers of neutrons. Atoms with different numbers of neutrons for a

certain elements are called isotopes. More on this in chapter 11.

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Chemical compounds are the next simplest form of everyday matter.

Examples: water, salt, sugar, etc.

Compounds are made from building blocks called molecules. Every molecule of a particular compound consists

of the same unique combination of two or more atoms.

Each water molecule consists of two hydrogen atoms and one oxygen atom.

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Each compound can be represented by a chemical formula.

water is H2O; salt is NaCl; carbon dioxide is CO2;

sugar is C12H22O11;

ethyl alcohol is C2H5OH.

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Many substances are composed of two or more different compounds that are physically mixed together called mixtures and solutions. Air is a mixture of

several gases. The actual composition

varies widely from day to day and place to place.

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Behavior of atoms and molecules The constituent particles of atoms and

molecules exert electrical forces on each other.

“Static cling” is an example of an electrical force.

The forces depend upon the configuration of the atoms in each atom.

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Behavior of atoms and molecules, cont’d

Solids: Attractive forces between particles are very strong; the atoms or molecules are rigidly bound to their neighbors and can only vibrate.

Liquids: The particles are bound together, though not rigidly; each atom or molecules move about relative to the others but is always in contact with other atoms or molecules.

Gases: Attractive forces between particles are too weak to bind them together; atoms or molecules move freely with high speed and are widely separated; particles are in contact only when they collide.

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Atoms or molecules in a solid arranged in a regular geometric pattern are called crystals.

Solids that do not have a regular crystal structure are called amorphous solids.

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Carbon has two common crystalline forms. Graphite forms crystalline sheets with little

bonding between sheets.

Diamond forms very strong bonds between adjacent carbons — it’s the hardest known natural substance.

14


In liquids, the inter-atomic forces are insufficient to bind the atoms rigidly. The atoms are free to move and vibrate.

In gases, the inter-atomic forces are virtually negligible unless the atoms are very close. Gaseous atoms have rather high speeds: ~1,000 mph.

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Whenever a high-speed gas atom impacts a large force on a container. It is this force that produces a pressure on the

container. As the air molecules strike the inside of a tire, they

produce the pressure that inflates the tire. If the molecules are stationary, there is no pressure.

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Gases are easily compressed because the majority of their volume is the space between the atoms. If you compress it enough, you force the atoms

close enough together that you form a liquid.

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Pressure

Pressure is the force per unit area for a force acting perpendicular to a surface. Since we use the perpendicular component of

the force, pressure is a scalar.

forcepressure

areaF

pA

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Pressure, cont’d

The units of pressure are: Metric:

pascal (Pa; 1 Pa = 1 N/m2) — SI unit; millimeters of mercury (mm Hg).

English: pound per square foot (lb/ft2); pound per square inch (lb/in2 or psi); inches of mercury (in. Hg).

19

Pressure, cont’d

Some pressure conversions: 1 psi = 6,890 Pa.

We also use an atmosphere (atm) as a pressure unit: One atmosphere is the average pressure

exerted by air at sea level: 1 atm = 1.01×105 Pa; 1 atm = 14.7 psi.

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Pressure, cont’d

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ExampleExample 4.1

A 160-pound person stands on the floor. The area of each show that is in contact with the floor is 20 square inches. What is the pressure on the floor?

Assume the person’s weight is shared equally between the two shows.

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ANSWER:

The problem gives us:

Since the shoes support the weight equally, each show must support a weight of 80 lb.

The pressure is

ExampleExample 4.1

2

160 lb

20 in

F

A

2

80 lb4 psi.

20 in

Fp

A

23

DISCUSSION:

If the person stands on only one foot:

If the person wore high heels and stood on only one heel (0.5 in by 0.5 in):

ExampleExample 4.1

2

160 lb8 psi.

20 in

Fp

A

2

160 lb480 psi.

0.5 0.5 in

Fp

A

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ExampleExample 4.2

In the late 1980s, there were several spectacular aircraft mishaps involving rapid loss of air pressure in the passenger cabins.

The cabin pressure of a passenger jet cruising at high altitude (25,000 ft) is about 6 psi (0.41 atm) greater than the pressure outside. What is the outward force on a window measuring 1 foot by 1 foot and on a door measuring 1 meter by 2 meters?

25

ANSWER:

The force on the window is:

The force on the door is

ExampleExample 4.2

6 psi 12 in 12 in

864 lb.

F pA

6 psi 39.4 in 39.4 in

9,310 lb.

F pA

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DISCUSSION:

The force on a window is approximately the weight of four adults.

The force on the door is nearly the weight of five pickups.

ExampleExample 4.2

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Pressure, cont’d

Pressure is a relative quantity. When you measure a pressure, you are

measuring it relative to some other pressure. When you measure your

tire pressure, you are measuring the pressure in the tire above the atmospheric pressure.

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Pressure, cont’d

The gauge pressure is the pressure relative to the current atmospheric pressure.

The absolute pressure is the gauge pressure plus the atmospheric pressure.

absolute gauge atmosphericp p p

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Pressure, cont’d

The standard pen-shaped tire gauge compares the tire pressure against a spring and the atmospheric pressure.

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Pressure, cont’d

An important statement about gases. Consider a gas held at constant temperature.

Increasing the temperature increases the motion of the gas atoms and therefore the pressure.

Under these conditions:

pressure volume constant

constantpV

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Pressure, cont’d

This means: Decreasing the volume increases the

pressure. Imagine squeezing part of an inflated balloon.

Decreasing the pressure increases the volume.

Imagine letting the air out of an inflated balloon.

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Density

Mass density is the mass per unit volume of a substance. It is the ratio of the mass to the volume of the

substance.

massmass density

volumem

DV

33

Density, cont’d

Units of mass density: Metric:

kilogram per cubic meter (kg/m3); gram per cubic centimeter (g/cm3).

English: slug per cubic foot (slug/ft3).

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Density, cont’d

Measure density by finding the mass of a sample and dividing by the volume of the sample.

The actual size of the sample is irrelevant. If you use a sample with twice the volume you

will twice the mass.

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Density, cont’d

You can measure the freezing point of your car’s coolant by measuring the density. The density of water and antifreeze are

different. Water: 1,000 kg/m3. Antifreeze: 1,100 kg/m3.

The overall density depends on the ratio of the amount of water and amount of antifreeze.

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ExampleExample 4.3

The dimensions of a rectangular aquarium are 0.5 meters by 1 meter by 0.5 meters. The mass of the aquarium is 250 kilograms larger when it is full of water than when it is empty. What is the density of the water?

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ANSWER:


The volume is:

ExampleExample 4.3

0.5 m

1 m

0.5 m

250 kg

l

w

h

m

3

0.5 m 1 m 0.5 m

0.25 m .

V l w h

38

ANSWER:

The mass density is then

ExampleExample 4.3

3 3

250 kg kg= =1,000 .

0.25 m m

mD

V

39

DISCUSSION:

If the width of the tank was doubled, the amount of water would be doubled — the density would remain the same.

If filled with gasoline, the mass is 170 kg. The density of gasoline is

ExampleExample 4.3

3 3

170 kg kg= =680 .

0.25 m m

mD

V

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Density, cont’d

If you know the volume and what type of substance you have, you can find the mass:

m V D

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ExampleExample 4.4

The mass of water needed to fill a swimming pool can be computed by measuring the volume of the pool. Let’s say a pool is going to be guilt that will be 10 meters wide, 20 meters long, and 3 meters deep. How much water will it hold?

42

ANSWER:


The volume is:

ExampleExample 4.4

20 m

10 m

3 m

l

w

h

3

20 m 10 m 3 m

600 m .

V l w h

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ANSWER:

Since the density of water is 1,000 kg/m3, the amount of water is:

ExampleExample 4.4

3 31000 kg/m 600 m

600,000 kg.

m D V

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DISCUSSION:

Since a common bathtub is about 0.25 m3 (let’s say 1 m by 0.5 m by 0.5 m), this swimming pool is about 2400 bathtubs of water.

ExampleExample 4.4

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Density, cont’d

Weight density is the weight per unit volume of a substance. It is the ratio of the object’s weight and its

volume.

weightweight density

volume

W

WD

V

46

Density, cont’d

Units or weight density: Metric:

newton per cubic meter (N/m3). English:

pound per cubic foot (lb/ft3); pound per cubic inch (lb/in3).

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ExampleExample 4.5

A college dormitory room measures 12 feet wide by 16 feet long by 8 feet high. What is the weight of the air in it under normal conditions?

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ANSWER:


The volume is:

ExampleExample 4.5

16 ft

12 ft

8 ft

l

w

h

3

16 m 12 m 8 m

1,536 m .

V l w h

49

ANSWER:

The weight of the air in the room is

ExampleExample 4.5

3 30.08 lb/ft 1,536 ft

123 lb.

WW D V

50

DISCUSSION:

Notice that as the temperature increases, the density would decrease.

So the air in the room would weigh less on hotter days.Because there is less air (fewer air molecules) in the

room.

ExampleExample 4.5

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Fluid pressure and gravity

The law of fluid pressure states that the (gauge) pressure at any depth in a fluid at rest equals the weight of the fluid in a column extending from that depth to the “top” of the fluid divided by the cross-sectional area of the column.

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Fluid pressure and gravity, cont’d

Mathematically,

The force is:

The area is:

weight of liquid

area of liquid column

F Wp

A A

W WF W D V D l w h

A l w

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We can write then write the pressure as:

The pressure depends on: the fluid’s density, the gravitational acceleration, and the depth of the fluid

W

W

D l w hFp

A l wD h

Dgh

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Note that this is the gauge pressure at the depth h. To get the absolute pressure, we need to add

the atmospheric pressure pushing down at the top of the fluid column.

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ExampleExample 4.6

Let’s calculate the gauge pressure at the bottom of a typical swimming pool — one that is 10 feet (3.05 meters) deep.

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ANSWER:


The gauge pressure is:

ExampleExample 4.6

3

10 ft

62.4 lb/ft

h

D

3

2

62.4 lb/ft 10 ft

624 lb/ft .

Wp Dgh D h

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DISCUSSION:

To convert this to psi:

ExampleExample 4.6

2

2

lb 1 ft 1 ft624

ft 12 in 12 in624 lb

144 in4.33 psi.

p

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The general result for pressure increase under water is:

The pressure increases 4.33 psi for every 10 ft.

It increases by 1 atm every 10 meters, or about 35 feet.

0.433 psi/ftp h

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ExampleExample 4.7

At what dept in pure water is the gauge pressure 1 atmosphere?

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ANSWER:


The pressure depends on depth according to:

Rearranging for the depth:

ExampleExample 4.7

1 atm 14.7 psip

0.433 psi/ftp h

14.7 psi

0.433 psi/ft 0.433 psi/ft

34 ft.

ph

61

DISCUSSION:

If you went swimming in mercury, which is 13.6 times as dense as water:

ExampleExample 4.7

13.6 0.433 psi/ft

14.7 psi

5.89 psi/ft

2.5 ft.

ph

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The atmosphere exerts a pressure on everything since there is a very high column of air above Earth’s surface. The column height for

air, water and mercury are different because the mass densities are increasingly larger.

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A device to measure air pressure is a barometer. As the air pressure increases, it exerts a larger

pressure on the fluid’s surface. The forces the fluid

farther up the tube. The height of the

column in the tube indicates the air pressure.

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Archimedes’ principle

We’ve found that the force of gravity on a fluid causes the pressure to increase with depth. This means that the mass density of the fluid

actually decreases with depth. We typically neglect this fact to keep things

simple.

This produces something we call a buoyant force that exerts an upward force on an object placed in a fluid.

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Archimedes’ principle, cont’d

The buoyant force is an upward force exerted by a fluid on a substance partly or completely immersed in the fluid. The buoyant

force depends on the density of the fluid and the substance.

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Archimedes’ principle states that the buoyant force acting on an object in a fluid at rest is equal to the weight of the fluid displaced by the object.

This means the object will sink until the weight of the object equals the weight of the water displaced by the object.

weight of displaced fluidBF

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Consider weighing an object in air and then partly immersed in water. In air, the scale must

support the entire weight.

In water, the buoyant force adds an additional upward force.

The scale reads less.

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Mathematically, we can write the buoyant force as:

fluid displaced fluidWDBF V

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ExampleExample 4.8

A contemporary Huckleberry Finn wants to construct a raft by attaching empty, plastic, 1-gallon milk jugs to the bottom of a sheet of plywood. The raft and passengers will have a total weight of 300 pounds. How many jugs are required to keep the raft afloat on water?

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ANSWER:


The buoyant force is:

Rearranging for the necessary volume:

ExampleExample 4.8

1

3

300 lb

62.4 lb/ftW

F

D

B WF D V

B

W

FV

D

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ANSWER:

The necessary volume to just float is:

ExampleExample 4.8

33

33

300 lb4.8 ft

62.4 lb/ft7.48 gal

4.8 f1 ft

36 gal.

V

t

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DISCUSSION:

So Huck needs at least 36 jugs.

Note that he would just float.

For a safety margin, you should probably have many more than just 36 jugs — just in case a wave rolls through or you want to take a friend along.

ExampleExample 4.8

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Pascal’s Principle

Pascal’s Principle states that the pressure applied to an enclosed fluid is transmitted undiminished to all parts of the fluid and to the walls of the container. This principle is used in hydraulic systems.

hydraulic lifts, braking systems,etc.

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Pascal’s Principle, cont’d

The piston on which the force is applied (left) has a small area:

The piston that applies the force (right) has a larger area:

input

input

Fp

A

output

output

Fp

A

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Since the pressures are the same, the output force is:

With the output piston’s area larger than the input piston’s area, the output force is larger than the input force.

input output outputoutput input

input output input

F F AF F

A A A

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A common example is the braking system in your car.

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Bernoulli’s principle

So far we spoke only of static fluids. We now talk about moving fluids. Bernoulli’s principle states that for a fluid

undergoing steady flow, the pressure is lower where the fluid is flowing faster. Steady flow means the fluid flow is smooth.

No random swirling, eddies, or “white water.”

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Bernoulli’s principle, cont’d

One idea behind the Bernoulli principle is: The amount of mass passing through an area

during an amount of time must be the same throughout the pipe.

There additional fluid enters or leaves the pipe so what goes in must come out.

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In order for the same amount of mass to pass through a cross-section of the wide and narrow sections in a certain amount of time, the fluid must flow faster in the narrow section.

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The other idea behind the Bernoulli principle is energy conservation.

We can consider the fluid to have a pressure potential energy. The greater the pressure, the greater the PE.

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Just as with a falling ball, as the PE decreases the KE increases.

So as the pressure decreases, the pressure PE decreases.

By energy conservation, the KE must increase.

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Another example is an atomizer. When you squeeze the bulb, you increase the

pressure in the nozzle. This lowers the pressure in the nozzle. The higher pressure in

the bottle draws the fluid up the tube.

The moving air carries the fluid out of the nozzle.

Documents

Chapter 4 Physics of Matter. 2 Matter: Phases, Forms & Forces We classify matter into four categories: Solid: rigid; retain its shape unless distorted