Transcript lecture_2_2010

EPS 5 Framework
0. Physics Basics: The fundamentals --the driest-1. Atmospheric Radiation: Energy Balance &
Climate
2-3. Atmospheric Physics and Physical Climate
4.Biogeochemical Cycles and Biosphere-Climate
Interactions
5. Stratospheric Chemistry
6.Tropospheric Chemistry
7.Bringing it all together: Synthesis
Demonstrations
Meter Stick
Basketball
Spring Scales
Ball on a String
Golf-Ball Atmosphere
U-tubes: water-air; water paint thinner
Collapsing Drum
January
July
What causes the patterns of wind and pressure?
(What is pressure?)
Pressure anomaly scale (mb)
Structure of Lecture 2, EPS 5:
27 January 2010
1. Define the basic quantities of physics that will be used in the course.
2. Discuss the origin of "units" (needed to make quantitative
measurements).
3. Introduce derived quantities and distinguish between scalar quantities
(not intrinsically directional) and vector quantities (directional).
4. Focus attention on force, and then on pressure, because of the
central role of these quantities in atmospheric processes.
5. Examine the magnitude of the pressure exerted by the atmosphere.
6. Introduce pressure as a phenomenon associated with molecules of a
fluid (gas or liquid) hitting a solid object.
The relationship between pressure as the weight of overlying fluid and
as the force exerted by molecular collisions will lead us, in a later
lecture, to understanding why atmospheric pressure decreases with
altitude, and will start us towards understanding winds and storms.
Fundamental quantities of physics
MKS
cgs
()
Time
s
s
1
Length
m
cm
100
Mass
kg
g
1000
MKS units = "SI" (standard international units)
Once we have defined units (standard measures) for these quantities
we can derive for all other quantities of physics.
How are standards for fundamental quantities defined?
A standard meter (m) was defined by a metal rod in a vault in
Paris. It was supposed to be designed so that 1 m was
1/40,000,000 of the polar circumference. It is now defined by a
certain number of wavelengths of laser light from a particular laser.
The definitions were required to be such that anyone, anywhere,
could set up a way to insure that his/her measurements were
equivalent to measurements made by someone in the vault in Paris.
The laser is obviously easier to replicate than the piece of metal in
Paris, and the light won't change in the future whereas the bar could
be destroyed.
Initially a standard mass (kg) was a block of metal in Paris,
selected so that 1 m3 of water had a mass of about 1000 kg (a
metric ton).
The standard time (s) was an average day divided by 86400 (24
hours, 3600 seconds in each hour).
Once the standards are defined, the quantity in any object (mass,
dimension) or time span can be determined using devices that
compare the object to the standard.
Structure of Lecture 2, EPS 5:
1. Define the basic quantities of physics that will be used in the course.
2. Discuss the origin of "units" (needed to make quantitative
measurements.
3. Introduce derived quantities and distinguish between scalar quantities
(not intrinsically directional) and vector quantities (directional).
4. Focus attention on force, and then on pressure, because of the
central role of these quantities in atmospheric processes.
5. Examine the magnitude of the pressure exerted by the atmosphere.
6. Introduce pressure as a phenomenon associated with molecules of a
fluid (gas or liquid) hitting a solid object.
The relationship between pressure as the weight of overlying fluid and
as the force exerted by molecular collisions will lead us, in the next
lecture, to understanding why atmospheric pressure decreases with
altitude, and will start us towards understanding winds and storms.
Derived quantities: important combinations of fundamental quantities
Quantity, definition
distance
velocity=
time
change of velocity
acceleration =
time
force=mass ´ acceleration
weight= mass ´ acceleration of gravity
= force exerted by gravity on an
object
work = force ´ distance
kinetic energy = energy of motion
Temperature (related v ia Boltzmann's
constant, k, to the mean kinetic energy
of a gas molecule)
pressure = force per unit area
Formula
Dimensions (units)
L/t
m s -1
v/t
m s -2
F=m a
kg ms -2  Newtons (N)
F=mg
(same as force; g=9.8 ms -2)
E=F L
1
E= mv2
2
kg m 2 s-2  Joules (J)
1
mv 2 = kT
2
P = F/A
(same as work)
[non-dimensional,
units=degrees Kelvin;
k=1.38 10 -23 J/K]
kg m -1 s-2
The relationships between fundamental and derived quantities are
intimately tied to the laws of physics. For example, Newton's laws relate
familiar quantities (force, energy) to the fundamental quantities. vectors
Some physical quantities are vector quantities. In order to use these
quantities in studying a physical phenomenon, both the magnitude
and the direction must be specified.
If equal forces act on an object in
opposite directions, it will not start
to move (a = 0 ).
If equal forces act on an object in
same direction, it will start to move
(a  0 ).
Vector quantities include length, velocity, acceleration, force, and
pressure.
Quantities that do not have an associated direction ("scalar" quantities)
include energy, mass, and time.
In EPS-5 we need to understand the concept of a vector but we will not
do "vector algebra" involving adding, multiplying, etc.
A related quantity is the "number of atoms of an element that have mass
equal to the elemental mass in grams", Avogadro's number:
N0 = 6.02  1023
In the 18th centrury, the concepts of mass and density (mass/vol) were
known, but atoms were not. However knowledge of atoms came rather
early, and by the 19th century chemists has determined the relative
amount of mass needed to make a chemical compound from its
components—for example, 12 g of carbon + 32 g of Oxygen to make a
gas now known to be CO2. Atomic or molecular weights were defined,
with H as 1 (approximately) and carbon as 12 (exactly). Then the
“indivisible” mass was determined, and the number of atoms in a “mole”
(number needed to make up the atomic or molecular mass) was
determined- Avogadro’s number. 6.02 x 1023. It is a derived quantity.
mass of 1 mole of an element in grams = "molecular weight"
=mass of N0 atoms
Pressure is a particularly important concept for studying the
atmosphere. It is related to force and weight.
Force and Weight
The weight of an object is the force caused by the gravitational
acceleration (g) acting on the object, which is proportional to its
mass (m), weight = mg. g = acceleration of gravity = 9.8 m/s/s.
The distance a spring extends with a given weight on it depends on
the acceleration of gravity acting on the object attached to the spring.
If we take the spring to the moon, where the gravitational
acceleration is much small than on the earth, the object will weigh
less, even though its mass has not changed. As a result, the spring
will not extend as much as it did on the earth. Weight is not an
intrinsic property of an object. Mass is the intrinsic property.
Density = mass/unit volume = r = M/V (kg/m3).
Density is an intrinsic property specific to a particular material (air,
brass, steel, etc) at a given temperature and pressure. It is an
intensive quantity as opposed to mass being an extensive property.
Pressure
Pressure means the force (F), or weight, of an object distributed over a
surface area (A) equal to 1 meter (Force per unit area). (The acceleration
of gravity is 9.8 m s-2, and the force F = mg). We often refer to the
pressure of the earth's atmosphere at the surface as 1 atmosphere (atm).
A container of water 10 m high, by 1 m wide, by 1 m deep holds 10
cubic meters of water, or 10,000 kg of mass. Thus the pressure of the
water on the bottom of this container would also be about 1 atm. This
means that an individual swimming 10 m underwater would feel a
pressure of 2 atm (1 atm from the weight of the atmosphere and 1 atm
from the weight of the water) on his/her body.
10m
1m2
Structure of Lecture 2,EPS 5:
1. Define the basic quantities of physics that will be used in the course.
2. Discuss the origin of "units" (needed to make quantitative
measurements.
3. Introduce derived quantities and distinguish between scalar quantities
(not intrinsically directional) and vector quantities (directional).
4. Focus attention on force, and then on pressure, because of the
central role of these quantities in atmospheric processes.
5. Examine the magnitude of the pressure exerted by the atmosphere.
6. Introduce pressure as a phenomenon associated with molecules of a
fluid (gas or liquid) hitting a solid object.
The relationship between pressure as the weight of overlying fluid and
as the force exerted by molecular collisions will lead us, in the next
lecture, to understanding why atmospheric pressure decreases with
altitude, and will start us towards understanding winds and storms.
The weight of the atmosphere exerts a pressure on the surface of the
earth. This pressure is 100,000 Newtons (N)/sq meter, corresponding to a
mass m of slightly more than 10,000 kg of air over every square meter of
the earth's surface.
A city bus might weigh about
10,000 kg, and your desk might
have an area of roughly 1 m2.
Thus the weight of the
atmosphere on your desk is
about 10 metric tons.
Why doesn't the desk collapse?
Since the atmosphere is not falling down, there must be an upward force that
balances its weight. What is that?
To answer this we have to understand how a gas (the atmosphere) exerts
pressure on a surface. Suppose we have air molecules in a container. The
molecules in the gas are moving all the time. When they hit a solid
surface, they bounce off. This change in direction of motion is a change
in the velocity, equivalent to an acceleration and hence a force is exerted
on the surface. The force depends on the mass and velocity (temperature)
of each molecule, and on the number of molecules. (The “golf ball
atmosphere" demonstration in class illustrates this effect.)
Experiments carried out in the 19th century showed that there is a very
simple formula that expresses the relationship between the temperature,
pressure, and number of molecules in a volume:
Perfect gas law (a.k.a. Boyle's and Charles' Laws) PV = NkT
where P is pressure, V volume, N the number of molecules in the
volume, and T the absolute temperature (Kelvin; T(K)=T(C)+273.15); k
is Boltzmann's constant (1.38 x 10-23 Joules/Kelvin).
N = number of molecules in the volume V
The Perfect Gas Law relates pressure to temperature (the kinetic
energy of the molecules) and "number density".
Since we don't have confined
volumes in the atmosphere, we
usually use this very important
relationship in the form,
P = nkT,
where n (= N/V, the number
density) is the number of molecules
per unit volume.
n = number of molecules m -3
Pressure in a fluid--can cause the fluid to move! In both tanks the
atmosphere exerts a pressure of 1 atm on the surface of the water (blue)
in each tank, and the weight of the water provides additional pressure, so
the pressure on the bottom is the sum of atmospheric and water pressure.
The picture on the left side illustrates that, since pressure is a measure of
force per unit area, it doesn't matter how wide the the arm of the tank is!
It only matters how much fluid is resting above a unit area of the bottom
of the tank. Therefore, in the experiment on the left, where the height of
the fluid in the two tanks is the same, the pressures at the bottom of the
tanks are equal, forces are balanced, and the fluid does not move.
air
water
fluid will start to move
On the other hand, in the experiment on the right, the side of the tank
which has a higher column of fluid will exert a greater force on the
bottom than the side with the lower column of fluid. This is not a stable
situation. We would expect the fluid to flow from high pressure to low
pressure (from the tank on the left to the tank on the right) until the
pressures are equal - when the height of the fluid in the two tanks are
the same.
air
water
fluid will start to move
Structure of Lecture 2, EPS 5:
27 January 2010
1. Define the basic quantities of physics that will be used in the course.
2. Discuss the origin of "units" (needed to make quantitative
measurements.
3. Focus attention on force, and then on pressure, because of the
central role of these quantities in atmospheric processes.
4. Examine the magnitude of the pressure exerted by the atmosphere.
5. Introduce derived quantities and distinguish between scalar quantities
(not intrinsically directional) and vector quantities (directional).
6. Introduce pressure as a phenomenon associated with molecules of a
fluid (gas or liquid) hitting a solid object.
The relationship between pressure as the weight of overlying fluid and
as the force exerted by molecular collisions will lead us, in the next
lecture, to understanding why atmospheric pressure decreases with
altitude, and will start us towards understanding winds and storms.