Section 3
Density
A few things to remember
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The mass of different materials cannot be compared unless certain properties and conditions are specified
A mass of lead is not necessarily heavier than a mass of feathers, enough feathers can have a greater mass
than a small piece of lead
Quantity makes the comparison of mass more meaningful – reason is DENSITY
Density – measure of how tightly compressed the particles of a material is
Density – defined as mass per unit volume
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ρ = m/V
m = mass (usually) in g
V = volume (usually) in cm3
ρ = density (usually) in g/cm3
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Density of a substance remains constant, not matter what size of shape
Density of solids higher than density of liquids – solids more closely packed
For irregularly shaped objects we can use the displacement of a volume of water in a container to determine
the volume of the object
When water is cooled, molecules closer together, density increases
Water molecules closest at 4oC – density greatest at 4oC
Density decrease when temperature drops below 4oC
Happens because water molecules re-arrange themselves into a pattern where there are larger spaces between
them
When water reaches 0oC re-arrangement is complete and water becomes solid (ice)
Therefore ice is less dens than water and can float in water
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Pressure
Introduction to pressure
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When discussing pressure it is important to take into account force exerted and area on which force is exerted
When an object rests on a surface it exerts a pressure
Reason – it has weight
Weight acts as a downwards force
Pressure also depends on size of contact area
Pressure – define as force per unit area
F = force in N
A = area in m2
p = pressure in Pa
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p = F/A
Pressure is directly proportional to the force that is applied
Area is inversely proportional to the pressure
Pressure in a liquid
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Like solids, liquids exert pressure because they have weight
Unlike solids, liquids exert pressure in all directions, not just downward (on the bottom of the container)
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Liquids exert pressure on the side of the container it is in
Liquids exert pressure upward on a object that is placed in the liquid
Pressure exerted by liquids depend on the following:
Depth of the liquid – pressure directly proportional to depth, liquid weight increases with depth
Density of the liquid – pressure directly proportional to density, more dense liquids are heavier
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Deriving the equation for pressure exerted by a liquid – Method 1
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consider a liquid with a density of ρ that is in a container with a depth of h and let us look at a column of this
liquid which has a base length and breadth of x
the pressure exerted by the column of liquid on the bottom of the container is p = F/A………..1
the weight of the column of water is given by F = mg………..2
using the formula for density ρ = m/V, make m the subject thus m = ρV
substitute into equation 2 and then F = ρVg
remember that volume = l x b x h thus V = x2h (for the column of water)
now the formula becomes F = ρg(x2h)
substitute this now into equation 1 then we see p = ρg(x2h) / A (but the area for the column of water is x2)
thus p = ρgh
p = pressure in Pa
ρ = density of the liquid in kg/m3
g = gravitational acceleration in m/s2
h = depth of the liquid in m
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Deriving the equation for pressure exerted by a liquid – Method 2
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Atmospheric pressure
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Pressure exerted on objects by the AIR
Highest at sea level
Effects of altitude change on atmospheric pressure
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Atmospheric pressure decreases when altitude increases
Atmospheric pressure has an effect on the boiling and melting point of liquids
Atmospheric pressure keeps particles of liquids together
Lower atmospheric pressure – lower boiling point
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Instruments for measuring atmospheric pressure
Mercury Barometer
• Hollow glass tube approximately 0,9 m long
• Closed at one end and filled with mercury
• Open end is placed in an open vessel of mercury - cistern
• Mercury column in the tube will drop until the weight of the air pushing down on the mercury in the cistern is
equal to the weight of the mercury remaining in the tube
• The higher the atmospheric pressure, the higher the mercury will stand in the tube
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Manometer
• Typically used to measure the pressure of fluids under relative low pressure in a container
• Used to obtain precise measurements in laboratory experiments
• Used to obtain blood-pressure readings
• U-shaped glass tube partially filled with a liquid
• One end of the tube is open to the fluid in the container
• Other end is open to atmosphere
• Height difference of column corresponds to difference between pressure of fluid in container and atmospheric
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Aneroid Barometer
• Used for home weather forecasting
• Not as accurate as mercury barometers
• Inside is a flexible metal capsule, tightly sealed after some air has been removed
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When atmospheric pressure increase, the sides of the capsule is even more squeezed in and the pointer moves
further around the scale
Lower atmospheric pressure allow capsule to expand
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Bourdon Gauge
• Bourdon tube is a hollow metallic tube sealed at one end that flexes when pressure is applied
• It flexes because it naturally wants to straighten out, but cannot because it is linked to a geared movement
• As it tries to flex, the linear movement is changed to rotational by means of small gears
• They in turn cause the pointer to indicate the measured pressure
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Gauges like these are designed for clean, non-clogging liquids and gases
Units: 1 bar = 1 atm = 760 mmHg (Torr) = 101325 Pa
Let’s Revise
1. The density of water is 1000 kg/m3. Determine the pressure at the bottom of a 2 m deep swimming pool.
2. A regular storage tank with dimensions 4 m x 3 m is filled with paraffin to a depth of 2 m. Given that the
paraffin’s density is 800 kg/m3, calculate the mass of paraffin and the pressure at the bottom of the tank.
3. If the atmospheric pressure on a certain day is 880 mmHg, what is the pressure in Pa and Bar?
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