What is “Density”
Terminology of many uses, with a common thread
• Population Density
– People by region, political party, ethnicity
• Energy Density
– Chemical energy per unit volume
• Optical Density
– Transmission of light, X-rays, radio, nuclear particles
• Ratio of units
– One unit divided by a different unit
– Density goes UP as numerator increases
– Density goes DOWN as denominator increases
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The current Population Density on earth
is 13 people per square kilometer
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Population Density, people/sq.mile
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Homicide Density, murders/location
Santa Cruz sends patrol cars where the crimes most likely
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Economic Density, $/square.km
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Energy Density, watts/kg
most common batteries are cylindrical, “primatic” are rectangular
two density measures, energy per weight, energy per volume
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Bone Density, opacity/volume
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Probability Density, items/location
Apples falling from tree, electrons around Hydrogen
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Dice Probability Density,Value/throw
36 combinations for sum of two die (face value 1 to 6)
Rolling a 7 is highest probability (4+3, 3+4, 2+5, 5+2, 1+6, 6+1)
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Matter & Energy Ratios
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The Common Thread …
measurement quantity using ratios
Chemistry Applications
– Optical Density (absorbance, transmittance)
• IR analysis, spectra photometry
• X-Ray images, optical filters
– Mechanical (or Geometrical) Density
• Intensity per unit area (people/km^2)
• Mass per unit Volume (grams/cm^3)
– Water is reference of 1 gram/cm^3
– This is the subject of today’s experiment
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Seven Basic SI Measurements
•
•
•
•
•
•
•
Mass = Kilogram
Length = Meter
Time = Second
Temperature = degrees Kelvin
Quantity of matter = mole
Energy Rate = Ampere
Light Energy = Candela
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Derived Units
• Area is a 2-dimensional multiplication of lengths. An
acre was defined by length of one furlong (220 yards)
and breadth of one chain (22 yards), or 4,840 square
yards per acre. Square feet are still common in US
• Volume a 3-Dimensional concept, based on (length)3
Early definitions were arbitrary (quart, gallon),
“metric” system is based on 1 Liter = 1000 cm3
• Density is mass per unit volume. The initial metric
system “CGS” (Centimeter, Gram, Second) used
water defined as 1.0 gram per cubic centimeter. CGS
evolved to MKS (Meter, Kilogram, Second), now
called SI (System Internationale) or ISO
(International Standards Organization) units system. 13
Basic CGS metric scheme
Preceded SI / ISO system of units (cm vs meter)
1 cm^3 = 1 milliliter = 1 gram H2O
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Density
• Mass/Volume defined by water
– Grams/cm^3 =1 (1 gm / milliliter)
– Kilograms/liter = 1 (1000 gm /1000 ml)
– 1000 kilogram/meter^3 (1000 liter/meter^3)
• Density is important on a “water planet”
– Objects >1 gm/ml sink in water, <1 gm/ml float
– Ships float due to mass < water displacement
– Ice floats due to expansion <4oC
• If not, ice would sink … life on planet changes
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Ice and Water
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What’s the difference, MKS & CGS
• Kilograms / Meter^3 in MKS units
– MKS = Meter, Kilogram, Second
• Same concept as grams / cm^3 in cgs units
– CGS = Centimeter, Gram, Second
– 1 gram =0.001 kilogram = 10-3 kg
– 1 cm^3 = 0.01m*0.01m*0.01m =10-6 m^3
– 1 g/cm^3 =10-3gram/10-6m^3 = 1000 kg/m^3
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Density of Water
• when water cools, it
tends to stack in a
crystalline lattice
configuration that
stretches the length of
the bond.
• The rigidity of ice
crystalline structure
ensures that each
given H2O molecule
has fewer neighbors,
and thus the solid is
less dense. This
effectively reduces the
density when ice is
formed under standard
conditions.
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Density Triangle
Mass=D*V, Density=M/V, Volume=M/D
(DMV ≠ Dept of Motor Vehicles !)
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Density of material groups
(water is 1000 kg/m^3)
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Table 3-4, p. 82
Balsa, the least dense Wood
internal structure is mostly air, from South America
Density is 0.16 gm/cm^3, a person can carry an entire tree!
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Density of the Earth
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Earth composition by Density
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Detecting mass with density?
• Gravity attracts
objects by distance
and amount of mass.
• For identifying the
location of a more
dense ore body (iron,
uranium) gravitational
acceleration is slightly
greater over the ore
(more mass, same
volume) than not.
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What “floats your boat”?
• Archimedes principle
– Less dense object floats in more dense medium
– Wood therefore floats on water, iron sinks
– Displacement is key concept
• Iron ship full of air, average density <1 gm/cm^3
– so it floats in water of density ≈ 1 gm/cm^3
• Must consider combined mass and volume
– Lead glued to cork … calc the sum of mass + volumes
– Floats if mass/volume < 1 gm/cm^3
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Flotation applies to Gases as well
• You don’t need tables of density values
– Periodic chart has all the data we need
– 1 mole of ANY gas occupies 22.4 liters
• Balloon will float in air with less dense gas
– Hydrogen (H2) is 2.016 gm/(mole=22.4 liters)
– Helium is 4 grams/(mole=22.4 liters)
– Air is about 29 grams/(mole=22.4 liters)
– Carbon Dioxide is 44 gm/(mole=22.4 liters)
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Helium and/or Hot Air
Density difference provides the lift
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Lawn Chair Larry
1993 Darwin Award Honorable Mention Award
(this stunt did not kill him, otherwise a full award)
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Hot Air Balloons more practical
• Helium difficulties
– Expensive material, need lots of it
– must compress to store (or leave balloon full)
– Small molecule leaks easily
• Hot air more practical
– Make it as needed
– Inexpensive (burn propane)
– … but hot air is hard on the balloon
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A hot air balloon is partially inflated with cold air from a petrol-driven
fan, before the propane burners are used for final inflation.
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CS #4 Density Experiment
• You measured density in expt. #3
– Density of Water
– Density of irregular object
• Today we look at relative densities
–
–
–
–
Less dense materials float on more dense
Work with liquids and solids
We’ll make a “column” of varying densities
We’ll sink and float a golf ball
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Density
• Water all around us, a useful reference
– Easy to obtain, purify, & measure
• Density is temperature sensitive
– Usually expand with rising temperature
– Water has a maximum density at 4oC
• Water at < 0oC forms ice, which floats
• Density defined as 1.0000 gm/cm^3 at 4oC
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Density
• Mass/Volume defined by water
– Grams/cm^3 =1 (also defined as 1 milliliter)
– Kilograms/liter = 1 (1000x gm and ml)
– 1000 kilogram/meter^3 (1000 liter/meter^3)
• Density is important on a “water planet”
– Objects >1 gm/ml sink in water, <1 gm/ml float
– Ships float due to mass < water displacement
– Ice floats due to expansion <4oC
• If not, ice would sink … life on planet changes
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Ice and Water
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Density of Water
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Experiment Procedure
• Measure mass and volumes of 4 liquids
– Calculate densities of the liquids
• Carefully pour liquids into graduated cylinder
– Observe which ones float on others
– Blue food color in KBr solution
– Red food color in distilled water bottle
• Place solid objects in layered column
– Where do they float?
– What are likely densities, what are materials?
• Mix liquids in column
– How many layers are left?
– Which ones were soluble in each other?
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Measure densities of 4 liquids
• Liquid Volume
– Milliliters via graduated cylinder
• Liquid Mass
– Grams container with – without liquid
• Density of liquid
– Grams/volume = density
– Dimensions are gms/mL (or gm/cm^3)
• Repeat for 3 other liquid densities
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“Stacked” densities, 50mL grad cyl.
Add liquids, most dense at bottom, others float in order of density
mix the layers … how many layers left, which ones mixed?
Least
Dense
Most
Dense
Material =
Density =
Material =
Density =
Material =
Density =
Material =
Density =
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Densities of solid objects
• Add solid objects to density column
– Which layers does it float between
– Density of those two layers?
– What is density range of floating object?
– What material is it likely to be?
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Mixing the layers
•
•
•
•
•
Hold thumb over top of grad. cylinder
Invert several times to mix liquids
How many layers are left?
Which ones mixed?
How would you tell?
– Hint: try some solid objects
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Golf Ball Flotation
• We will calculate theoretical density
– Specified mass & specified volume
• We will measure actual density
– Weight of ball, displaced volume
• How do the two compare?
• Does ball float on salt solution?
– Try it
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Common Plastics
Arranged by Density
MATERIAL NAME
Shorthand
Polypropylene
Low Density Polyethylene
High Density Polyethylene
PP
LDPE
HDPE
Water
Water
Acrylonitrile Butadiene Styrene
PolyStyrene
Nylon
Polymethyl Methacralate (Acrylic)
Polycarbonate
Polyvinyl Chloride
Polyethylene Terephthalate
ABS
PS
Nylon
PMMA
PC
PVC
PETE
recycle
grams
grams
code
#
per
cm^3
min
0.90
0.91
0.94
1
1.01
1.03
1.06
1.18
1.20
1.32
1.35
per
cm^3
max
0.92
0.93
0.96
1
1.04
1.06
1.15
1.18
1.22
1.42
1.38 48
5
4
2
ABS
6
none
none
7
3
1
Plastics with applications
recycle grams
Arranged by Density
code
#
MATERIAL NAME
Shorthand
Polypropylene
Low Density Polyethylene
High Density Polyethylene
PP
LDPE
HDPE
Water
Water
Acrylonitrile Butadiene Styrene
PolyStyrene
Nylon
Polymethyl Methacralate (Acrylic)
Polycarbonate
Polyvinyl Chloride
Polyethylene Terephthalate
ABS
PS
Nylon
PMMA
PC
PVC
PETE
5
4
2
ABS
6
none
none
7
3
1
per
cm^3
min
0.90
0.91
0.94
1
1.01
1.03
1.06
1.18
1.20
1.32
1.35
grams
per
cm^3
max
0.92
0.93
0.96
1
1.04
1.06
1.15
1.18
1.22
1.42
1.38
applications
lowest density, chem resistant
1% of plastic used, heat sealed bags
47% of plastic bottles
no recycling code, came after definitions developed
foam cups, plastic "keep boxes", brittle but cheap
tough & slippert plastic, combs, some engineering use
"Plexiglas", paint, brittle, poor chem resistance
"7" is a catchall or "others", made from BPA
plastic pipe, 2% of bottles, window frames, automotive
48% of bottles, soft drinks, beer, juice, veg oil
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