Transcript ISNS3371_022207_bw - The University of Texas at Dallas

ISNS 3371 - Phenomena of Nature
The Gas Laws
ISNS 3371 - Phenomena of Nature
Properties of gases
•
•
•
•
•
•
Very compressible.
Acquires shape of its container,
Completely fills any closed container.
Very low density compared with a liquid or a solid.
Exhibits a pressure on the walls of its container.
Pressure = force per unit area
P = F/A
Force has direction. Force giving rise to pressure is
always perpendicular to the surface.
ISNS 3371 - Phenomena of Nature
Gas Laws
P = pressure of gas
V = volume of gas
T = absolute (kelvin) temperature of gas
– Boyle's Law:
– Charles’ Law:
– Guy Lussac’s law
– General or ideal gas law
PV = constant, if T is constant
V/T= constant, if P is constant
P/T = constant, if V is constant
PV/T = constant
PV = n RT
• R = general gas constant = 8.314 joules/degree-mole
• n = number of moles of gas - a mole is 22.4 liters of a gas
Ideal gas - one in which we can ignore interactions between the gas
molecules. Most gases behave in the same universal way as long as the
temperature is kept far from the liquefaction temperature.
ISNS 3371 - Phenomena of Nature
Guy Lussac’s Law and Absolute Zero
Remember third law of thermodynamics:
No system can reach absolute zero.
How do you determine absolute zero?
Consider Guy Lussac’s law:
P/T = constant, if V is constant
This is for an ideal gas
Temperature must get smaller as pressure gets smaller
Theoretically, as pressure goes to zero, temperature must go
to some smallest value
This value is absolute zero and can be determined by
measuring the pressure and temperature of a gas at several
values and extrapolating to zero pressure
ISNS 3371 - Phenomena of Nature
Boyle’s Law
PV = constant, if T is constant
ISNS 3371 - Phenomena of Nature
The Law of Adiabatic Expansion (or Compression))
Any gas will cool that is allowed to expand freely from a higher pressure to a
lower pressure without the transfer of external energy to the gas. Similarly,
a gas will heat if compressed from a lower to a higher pressure in the
absence of a transfer of energy from the gas.
Consider gas in a bicycle pump:
Push the pump in quickly - the gas heats up – you are doing work
on the gas.
Pull the pump out quickly - gas will cool down - the gas is doing
work for you.
On a molecular scale.
The gas particles are moving with a speed that is determined by the
temperature of the gas:
Push the pump in - the particles speed up - when they collide with
the oncoming piston, they rebound more quickly - they heat up.
Pull the pump out - the particles slow down - when they collide with
the outgoing piston, they rebound more slowly - they cool down.
ISNS 3371 - Phenomena of Nature
The same reasoning works for a gas that is expanding freely. Rather than
bouncing off a container, the particles bounce off each other. But they are
all moving outwards. So any collisions at the edges of the gas will have the
effect of taking some of the speed off the expanding molecules. Explains
why fog formed in chamber when pressure suddenly reduced:
All air contains water vapor of varying quantities. A state of saturation exists
when the air is holding the maximum amount of water vapor possible at the
existing temperature and pressure.
Dew point - the temperature to which the air would have to cool in order to
reach saturation - indicates the amount of moisture in the air. Condensation
of water vapor begins when the temperature of air is lowered to its dew
point and beyond - results in the formation of tiny water droplets that leads
to the development of fog, frost, clouds, or even precipitation.
When the air in the chamber suddenly expands, the temperature of the air
is suddenly reduced to below the dew point and the water vapor condenses
to form fog in the chamber.
Why is your breath colder when blown out through pursed lips?
ISNS 3371 - Phenomena of Nature
Bernoulli Effect
For horizontal fluid flow, an increase in the velocity of flow will result
in a decrease in the static pressure.
ISNS 3371 - Phenomena of Nature
The Airfoil (Wing) and the Bernoulli Effect
The air across the top of the airfoil
experiences increased air speed
relative to the wing - it must go farther
to reach the back edge of the airfoil.
This causes a decreases in pressure
and provides a lift force.
Increasing the angle of attack gives a
larger lift from the upward component
of pressure on the bottom of the wing.
The lift force can be considered to be a
Newton's 3rd law reaction force to the
force exerted downward on the air by
the wing.
At too high an angle of attack,
turbulent flow increases the drag
dramatically and will stall the aircraft.
ISNS 3371 - Phenomena of Nature
How Does an Airplane Fly Upside Down?
If the greater curvature on top of the wing and the Bernoulli effect are evoked
to explain lift, how is this possible? An increase in airstream velocity over the
top of the wing can be achieved with airfoil surface in the upright or inverted
position - requires adjustment of the angle of attack. Typical asymmetric
shape of airfoil increases efficiency of lift production but not essential for
producing lift.
ISNS 3371 - Phenomena of Nature
The Curve Ball and the Bernoulli Effect
A non-spinning baseball or a
stationary baseball in an
airstream exhibits symmetric
flow.
A baseball which is thrown with
spin will curve because the air
flows faster on one side of the
ball than the other side because
of friction. So one side of the
ball will experience a reduced
pressure.
The roughness of the ball's
surface and the laces on the
ball are important! With a
perfectly smooth ball you would
not get enough interaction with
the air.
ISNS 3371 - Phenomena of Nature
Balancing Ball and the Bernoulli Effect
A ball balances on a stream of air
because of the Bernoulli effect.
If the ball is displaced from the
center of the air stream, it will feel
a force pulling it back into the
center. The air on the right side of
the ball in not moving so pressure
is lower on the left side of the ball
and the ball feels a force toward
the center of the air stream.
No matter which direction the ball
is deflected, it is attracted to the
center of the air stream, and stays
balanced.
ISNS 3371 - Phenomena of Nature
Archimedes’ Principle
Archimedes Principle states that the buoyant force on a submerged
object is equal to the weight of the fluid that is displaced by the object.
Remember from Pascal’s Law - the difference in pressure between any two
places in a single fluid is dependent on tne vertical difference of level of the fluid
and at any place in a fluid, pressure pushes equally in all directions. So, the
sideways forces on an object are balanced and oppose each other equally, but
the upward and downward forces are not the same. The pressure at the bottom
of the object is greater than the pressure at the top of the object, because
pressure increases with increasing depth. The difference between the upward
and downward forces acting on the bottom and the top of the object,
respectively, is called buoyancy.
ISNS 3371 - Phenomena of Nature
Specific Gravity
If the mass of an object is less than the mass of an equal volume of water, the
bouyant force is greater than the weight of the object and it will float.
So the specific gravity is defined as the heaviness of a substance compared
to that of water, and it is expressed without units. If something is 7.85 times as
heavy as an equal volume of water (such as iron is) its specific gravity is 7.85.
Its density (mass per unit volume) is 7.85 grams per cubic centimeter.
(The density of water is 1 gr/cm3.) An object with a specific gravity less than 1
will float. A object with specific gravity greater than 1 will sink.
Suppose you had equal sized balls of cork, aluminum and lead, with
respective specific gravities of 0.2, 2.7, and 11.3 . If the volume of each is 10
cubic centimeters then their masses are 2, 27, and 113 gm. The cork floats
and the aluminum and lead sink.
ISNS 3371 - Phenomena of Nature
A steel rowboat placed on end into the water will sink because the
density of steel is much greater than that of water. However, in its
normal, keel-down position, the effective volume of the boat includes all
the air inside it, so that its average density is then less than that of water,
and as a result it will float.
Hot air balloons rise into the air because the density of the air (warmer
air) inside the balloon is less dense than the air outside the balloon
(cooler air). The balloon and the basket displaces a fluid that is heavier
than the balloon and the basket, so it has a buoyant force acting on the
system. Balloons tend to fly better in the morning, when the surrounding
air is cool.
ISNS 3371 - Phenomena of Nature
Archimedes’ principle is useful for determining the volume and therefore the
density of an irregularly shaped object by measuring its mass in air and its
effective mass when submerged in water.
effective mass under water = actual mass - mass of water displaced
(bouyant force)
The difference between the real and effective mass therefore gives the mass
of water displaced and allows the calculation of the volume of the irregularly
shaped object The mass divided by the volume thus determined gives a
measure of the average density of the object.
Archimedes found that the
density of the king's supposedly
gold crown (14.2 gr/cm3) was
actually much less than the
density of gold (19.3 gr/cm3) -implying that it was either hollow
or filled with a less dense
substance.
440 gr/31cm3 = 14.2 gr/cm3
ISNS 3371 - Phenomena of Nature
Waves
A wave is a pattern which is revealed by its interaction with particles. It is a
vibration - a movement of particles up and down, side-to-side, or back and forth.
Waves on a Pond Animation
Wave is moving up and down but not outward - carries energy but not matter.
Sound and light are both waves - but different.
Sound is the movement of vibrations though matter - solids, liquid,
or gases - no matter, no sound. Cannot travel in a vacuum.
Light is a vibration of electric and magnetic fields - pure energy does not require matter.
ISNS 3371 - Phenomena of Nature
Properties of Waves
Any traveling wave will take the form of a sine wave. The position of an
object vibrating in simple harmonic motion will trace out a sine wave as a
function of time. (Or if a mass on a spring is carried at constant speed
across a room, it will trace out a sine wave.)
This transverse wave is typical of that caused by a small pebble dropped
into a still pool.
Crest - high point
of sine wave
Crest
Trough - low point
of sine wave
Amplitude (a):
maximum
displacement
from equilibrium
Wave length (l):
distance between
successive crests
Trough
ISNS 3371 - Phenomena of Nature
Properties of Waves
Period: time to complete one cycle of vibration - from crest to crest or
trough to trough
Frequency (f): number of crests passing a fixed point
per second
Frequency= 1/period
Example:
Period = 1/100 = 0.01 sec.
Frequency = 100 hertz (cycles/sec.)
Speed (of a wave) (s)= wave length x frequency
s= l x f
ISNS 3371 - Phenomena of Nature
Anatomy of a Wave Animation
ISNS 3371 - Phenomena of Nature
Wavelength and Frequency Animation
ISNS 3371 - Phenomena of Nature
TYPES OF WAVES
Transverse:
Vibration or oscillation is perpendicular to direction of
propagation of wave.
Examples: water wave, vibrating string, light
Longitudinal:
Vibration or oscillation is in the same direction as
propagation of wave.
Examples: sound waves, mass on a spring,
loudspeaker