Transcript DENSITY AND PRESSURE

Density is how much something of a set volume weighs. This is generally measured by taking
a cubic centimeter of a substance (cm^-3). If we take a cubic centimeter of some commonly
known substances, we can see that they weigh different amounts:
DENSITY is a physical property of matter, as each element and compound has a unique density
associated with it. Density defined in a qualitative manner as the measure of the relative
"heaviness" of objects with a constant volume.
For example: A rock is obviously more dense than a crumpled piece of paper of the same size.
A Styrofoam cup is less dense than a ceramic cup.
Density may also refer to how closely "packed" or "crowded" the material appears to be - again
refer to the Styrofoam vs. ceramic cup.
Calculating Density
The best way to calculate the density of any material is to take a cubic centimeter of it and weigh
it. That will give you the mass of the substance per cubic centimeter. For lead (Pb), each cubic
centimeter of it weighs 11.35 grams, making its density 11.35 grams per cubic centimeter, or g /
cm^-3 if you're scientifically minded.
For lead, 1 cubic centimeter weighs 11.35 grams, while 2 grams weighs 22.70 grams and so on; so
we see that the ratio of 11.35 grams per cubic centimeter holds fast. The definition of density
functions.
The Formula For Density
We calculate density by dividing mass by volume as shown to the right. The units can actually
be of any kind, as long as they are the same between substances to be compared. We could
measure density in milligrams per cubic mile, or kilotons per cubic nanometer, it makes no
difference. As long as the units are clearly stated, conversion to standard units is easily
achieved.
Mass vs. Weight: Although the terms mass and weight are used almost interchangeably, there is
a difference between them. Mass is a measure of the quantity of matter, which is constant all
over the universe. Weight is proportional to mass but depends on location in the universe.
Weight is the force exerted on a body by gravitational attraction (usually by the earth).
Example: The mass of a man is constant. However the man may weigh: 150 lbs on earth, 25 lbs
on the moon (because the force of gravity on the moon is 1/6 that of the earth), and be
"weightless" in space.
HOW TO FIND THE DENSITY OF A LIQUID?
Apparatus: 100ml graduated cylinder, triple beam balance, calculator, 2 unknown
liquids.
Procedure:
1) Find the mass of the empty graduated cylinder.
2) Pour unknown liquid #1 into the graduated cylinder to the 50 ml. level.
3) Find the mass of the graduated cylinder with 50ml of unknown liquid #1.
4) Repeat steps 1-3 for unknown liquid #2.
We can calculate density of a liquid using the formula:
Density= Mass/Volume
where mass is that for just the liquid (you must subtract out the mass of the
graduated cylinder).
To find the density of air the mass of a sample of air is measured and compared to the
volume it occupies. A problem with giving a value for the density of air is that there is
no set value. The density of air will change with height and with a change in the
weather. The density of air is going to depend on the air pressure, the temperature of
the air and how much moisture is in the air.
The density of air under standard conditions is only 1.239 milligrams per cubic
centimeter under standard conditions. Measuring the density is done by finding the
mass of an evacuated glass sphere, letting the air back into the sphere, and finding
the new mass. This is done with the sphere on one pan of an equal-arm balance.
The outside diameter of the sphere is then measured, the thickness of the wall
estimated, as well as the volume of the neck, and the volume of the air
computed. Sometimes smaller, metallic spheres were used in this experiment. An
example can be seen mounted on the vacuum pump.
Pressure is defined as force per unit area. It is usually more convenient to use pressure rather than
force to describe the influences upon fluid behavior. The standard unit for pressure is the Pascal,
which is a Newton per square meter.
For an object sitting on a surface, the force pressing on the surface is the weight of the object, but
in different orientations it might have a different area in contact with the surface and therefore
exert a different pressure.
There are many physical situations where pressure is the most important
variable. If you are peeling an apple, then pressure is the key variable: if the
knife is sharp, then the area of contact is small and you can peel with less
force exerted on the blade. If you must get an injection, then pressure is the
most important variable in getting the needle through your skin: it is better
to have a sharp needle than a dull one since the smaller area of contact
implies that less force is required to push the needle through the skin.
When you deal with the pressure of a liquid at rest, the medium is treated as
a continuous distribution of matter. But when you deal with a gas pressure, it
must be approached as an average pressure from molecular collisions with
the walls.
Pressure in a fluid can be seen to be a measure of energy per unit volume by
means of the definition of work. This energy is related to other forms of fluid
energy by the Bernoulli equation.
Liquids exert pressure due to distribution of their own weight. To see how liquids exert pressure,
try the following experiment. Take three tins of different sizes or diameters. On tin number I, make
three holes at the same height. On tin numbers II and III, make three holes at different heights.
Place three long tapes to close the three holes on each on the tins. Now fill the tin with water.
Remove the tapes quickly and observe the streams coming out of each of the holes.
You will observe the following :
•Water stream will start pouring out through the holes. This means that water is exerting pressure
in all direction.
•In tin I, the water stream comes out evenly irrespective of the direction of the hole. This means
that the pressure is equal at the same height or depth.
•In Tin II and III, the water stream coming out of the lowest hole reaches the farthest. This shows
that the pressure exerted by liquid increases with depth. Also the pressure is acting perpendicular
to the liquid surface.
•Since there is no difference between the streams coming out of tins II and III, the pressure
exerted by liquid is independent of the size of the container, but depends only on the height or the
depth of the liquid. (This is markedly different from what happens when a solid is applying pressure
or weight, as seen in the earlier section).
Atmospheric pressure is the force per unit area exerted against a surface by the weight of air
above that surface in the Earth's atmosphere. In most circumstances atmospheric pressure is
closely approximated by the hydrostatic pressure caused by the weight of air above the
measurement point. Low pressure areas have less atmospheric mass above their location,
whereas high pressure areas have more atmospheric mass above their location. Similarly, as
elevation increases there is less overlying atmospheric mass, so that pressure decreases with
increasing elevation. A column of air one square inch in cross-section, measured from sea level to
the top of the atmosphere, would weigh just over a stone (and a column one square centimetre
in cross-section would weigh just over a kilogram).
Standard Atmospheric Pressure
Force per unit area exerted by the air above the surface of the Earth. Standard sea-level
pressure, by definition, equals 1 atmosphere (atm), or 29.92 in. (760 mm) of mercury, 14.70
lbs per square in., or 101.35 kilopascals, but pressure varies with elevation and temperature.
It is usually measured with a mercury barometer (hence the term barometric pressure), which
indicates the height of a column of mercury that exactly balances the weight of the column of
atmosphere above it. It may also be measured using an aneroid barometer, in which the action
of atmospheric pressure in bending a metallic surface is made to move a pointer.
A barometer is a scientific instrument used to measure atmospheric pressure. It can measure the
pressure exerted by the atmosphere by using water, air, or mercury. Pressure tendency can forecast
short term changes in the weather. Numerous measurements of air pressure are used within surface
weather analysis to help find surface troughs, high pressure systems, and frontal boundaries.
Water-based barometers
It consists of a glass container with a sealed body, half filled with water. A narrow spout connects
to the body below the water level and rises above the water level, where it is open to the
atmosphere. When the air pressure is lower than it was at the time the body was sealed, the
water level in the spout will rise above the water level in the body; when the air pressure is
higher, the water level in the spout will drop below the water level in the body. A variation of this
type of barometer can be easily made at home
Mercury barometers
A mercury barometer has a glass tube of at least 33 inches in height, closed at one end, with
an open mercury-filled reservoir at the base. The weight of the mercury creates a vacuum in
the top of the tube. Mercury in the tube adjusts until the weight of the mercury column
balances the atmospheric force exerted on the reservoir. High atmospheric pressure places
more force on the reservoir, forcing mercury higher in the column. Low pressure allows the
mercury to drop to a lower level in the column by lowering the force placed on the reservoir.
Since higher temperature at the instrument will reduce the density of the mercury, the scale
for reading the height of the mercury is adjusted to compensate for this effect.
The mercury barometer's design gives rise to the expression of atmospheric pressure in inches
or millimeters: the pressure is quoted as the level of the mercury's height in the vertical
column. 1 atmosphere is equivalent to about 29.9 inches, or 760 millimeters, of mercury.
Barometers of this type normally measure atmospheric pressures between 28 and 31 inches of
mercury.
A manometer measures the difference in air or liquid pressure by comparing it to an outside source, usually a
sample of Earth's atmosphere. Common manometers are U-shaped and have interconnected tubes.
Manometers are used in atmospheric surveys, weather studies, gas analyses and research of the atmospheres
of other planets.
They are usually made of glass or plastic, and while most are scored for measurement, some can measure
changes digitally. The single-tube manometer measures only the pressure of a liquid, since there is no
alternate place to compare gases. A U-shaped manometer essentially pits two different gas pressures against
one another, and measures the strength of the captured gas. The free-flowing gas is usually air at the current
atmospheric level.
How it works
A liquid is placed in the tube, usually a responsive liquid like mercury that is stable under
pressure. One end of the U-tube is then filled with the gas to be measured, usually pumped in
so the tube can be sealed behind it. The other end is left open for a natural pressure level.
The liquid is then balanced in the lower section of the U, depending on the strength of the
gas. The atmospheric pressure pushes down on the liquid, forcing it down and into the closed
end of the tube. The gas trapped in the sealed end also pushes down, forcing the liquid back
to the other side.
Then a measurement is taken to see how far the liquid in the sealed end has been pushed
either below the point of the liquid in the open end or above it. If the liquid is level, straight
across in both tubes, then the gas is equal to outside air pressure. If the liquid rises above
this level in the sealed end, then the air's pressure is heavier than the gas. If the gas is
heavier than the air, it will push the liquid in the sealed end below the equal point.
Assumptions of theory
The Kinetic Theory of Matter is a prediction of how matter should behave, based on certain assumptions and
approximations. The assumptions are made from observations and experiments, such as the fact that materials
consist of small molecules or atoms. Approximations are made to keep the theory from being too complex. One
assumption is that the size of the particles is so small that it can be considered a point.
Matter consists of small particles
The first assumption in this theory is that matter consists of a large number a very small particles—either
individual atoms or molecules.
Large separation between particles
The next assumption concerns the separation of the particles.
In a gas, the separation between particles is very large compared to their size, such that there are no attractive
or repulsive forces between the molecules.
In a liquid, the particles are still far apart, but now they are close enough that attractive forces confine the
material to the shape of its container.
In a solid, the particles are so close that the forces of attraction confine the material to a specific shape.
Particles in constant motion
Another assumption is that each particle is in constant motion.
In gases, the movement of the particles is assumed to be random and free. In
liquids, the movement is somewhat constrained by the volume of the liquid. In
solids, the motion of the particles is severely constrained to a small area, in
order for the solid to maintain its shape.
The velocity of each particle determines its kinetic energy.
Collisions transfer energy
The numerous particles often collide with each other. Also, if a gas or liquid is
confined in a container, the particles collide with the particles that make up the
walls of a container.
No energy change
Thus, an assumption is that the particles transfer energy in a collision with no
net energy change. That means the collisions between the particles are
perfectly elastic and no energy is gained or lost during the collision. This follows
the Law of the Conservation of Energy.
In reality, the collisions are not perfect, and some energy is lost. But for the
sake of simplicity in drawing conclusions, this theory makes the collisions
elastic.
BOYLE’S LAW
Boyle's law is one of many gas laws and a special case of the ideal gas law. Boyle's law describes the
inversely proportional relationship between the absolute pressure and volume of a gas, if the
temperature is kept constant within a closed system. The law was named after chemist and physicist
Robert Boyle, who published the original law in 1662. The law itself can be stated as follows:
For a fixed amount of an ideal gas kept at a fixed temperature, P [pressure] and V [volume] are
inversely proportional (while one increases, the other decreases).
The mathematical equation for Boyle's law is:
where:
p denotes the pressure of the system. V denotes the volume of the gas. k is a constant value
representative of the pressure and volume of the system.
So long as temperature remains constant the same amount of energy given to the system persists
throughout its operation and therefore, theoretically, the value of k will remain constant. However,
due to the derivation of pressure as perpendicular applied force and the probabilistic likelihood of
collisions with other particles through collision theory, the application of force to a surface may not
be infinitely constant for such values of k, but will have a limit when differentiating such values over
a given time.
Forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially
measured temperature, the pressure p must decrease proportionally. Conversely, reducing the volume
of the gas increases the pressure.
Boyle's law is used to predict the result of introducing a change, in volume and pressure only, to the
initial state of a fixed quantity of gas. The before and after volumes and pressures of the fixed
amount of gas, where the before and after temperatures are the same (heating or cooling will be
required to meet this condition), are related by the equation:
CHARLES’S LAW
A modern statement of Charles's law is:
At constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same
factor as its temperature on the absolute temperature scale (i.e. the gas expands as the temperature
increases).
which can be written as:
where V is the volume of the gas; and T is the absolute temperature. The law can also be usefully
expressed as follows:
The equation shows that, as absolute temperature increases, the volume of the gas also increases in
proportion.
PRESSURE LAW
The pressure of a fixed mass of gas is directly proportional to absolute temperature, provided the volume
of gas is constant.
P
Or P/T = constant
P1/ T1 = P2/ T2