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Intro to Weather and Climate – EART 80C Summer 2008
Lecture 1: July 28
Lecture 1:
Scientific Quantities and SI Units
Mass – kg
Distance – m
Time – s
Temperature – K
Force – Newton, N, kg*m/s2 (Mass times acceleration)
Velocity – m/s (Distance per unit time)
Acceleration – m/s2 (Velocity per time, change in velocity/change in time)
Energy – Joules, J = Nm = kg*m/s2 * m (Force times distance)
Pressure – N/m2 = Pascale, Pa (Force divided by area) kg*m/s2 *1/m2
Density (ρ) – kg/m3 (Mass per volume)
Area – m2
Volume – m3
Power – Watt = J/s (energy per time)
Mole – 6.023*1023 Things
Scientific Notation
Scientific notation is the way that scientists easily handle very large numbers or very small
numbers. So, how does this work? W e can think of 5.6 x 10-9 as the product of two numbers: 5.6
(the digit term) and 10-9 (the exponential term).
Here are some examples of scientific notation.
10000 = 1 x 104
1000 = 1 x 103
100 = 1 x 102
10 = 1 x 101
1 = 100
1/10 = 0.1 = 1 x 10-1
1/100 = 0.01 = 1 x 10-2
1/1000 = 0.001 = 1 x 10-3
1/10000 = 0.0001 = 1 x 10-4
24327 = 2.4327 x 104
7354 = 7.354 x 103
482 = 4.82 x 102
89 = 8.9 x 101 (not usually done)
0.32 = 3.2 x 10-1 (not usually done)
0.053 = 5.3 x 10-2
0.0078 = 7.8 x 10-3
0.00044 = 4.4 x 10-4
As you can see, the exponent of 10 is the number of places the decimal point must be shifted to
give the number in long form. A positive exponent shows that the decimal point is shifted that
number of places to the right. A negative exponent shows that the decimal point is shifted that
number of places to the left.
In scientific notation, the digit term indicates the number of significant figures in the number.
The exponential term only places the decimal point. As an example,
46600000 = 4.66 x 107
Intro to Weather and Climate – EART 80C Summer 2008
Lecture 1: July 28
This number only has 3 significant figures. The zeros are not significant; they are only holding a
place. As another example,
0.00053 = 5.3 x 10-4
This number has 2 significant figures. The zeros are only place holders.
Significant Figures
- no more than 3 sig figs usually
Scientific notation is the most reliable way of expressing a number to a given number of
significant figures. In scientific notation, the power of ten is insignificant. For instance, if one
wishes to express the number 2000 to varying degrees of certainty:
2000
2 x 103 is expressed to one significant figure
2000
2.0 x 103 is expressed to two significant figures
When handling significant figures in calculations, two rules are applied:
Multiplication and division -- round the final result to the least number of significant figures
of any one term, for example:
The answer, 36.8, is rounded to three significant figures, because least number of significant
figures was found in the term, 4.87.
Addition and subtraction -- round the final result to the least number of decimal places,
regardless of the significant figures of any one term, for example:
The answer, 14.4587, was rounded to two decimal places, since the least number of decimal
places found in the given terms was 2 (in the term, 13.45).
Suppose more than one mathematical operation is involved in the calculation? Such a calculation
may be "deceptive" as to how many significant figures are actually involved. For instance:
The subtraction in the numerator must be performed first to establish the number of significant
figures in the numerator. The subtraction results in:
Intro to Weather and Climate – EART 80C Summer 2008
Lecture 1: July 28
Since the subtraction in the numerator resulted in a number to two significant figures the final
result must be rounded to two significant figures.
The Atmosphere
A. Composition
78% Nitrogen (N) – basically inert so it was able to build up in the atmosphere
21% Oxygen (O)
1%
Argon (Ar) – also inert
Carbon Dioxide (CO2) – from respiration, combustion, GHG
Methane (CH4) – cows, wetlands, rice patties, low oxygen environments, GHG
Ozone (O3) – in both the stratosphere (good) and troposphere (bad)
Water (H2O) – 0-5% variable over the surface of the earth
Hydrogen (H2)
Helium (He)
Carbon Monoxide (CO)
Ammonia (NH3)
Nitrogen Oxide (NO)
Nitrous Oxide (N2O)
Sulfur Dioxide (SO2)
Nitrogen Dioxide (NO2)
Particles – Aerosols, dust, smoke
B. Vertical Structure of the Atmosphere
1. Mostly true – Sun warms the earth, the earth warms the air! (Not at fact!)
a. suggests that T decreases as height from the surface increases
2. The vertical structure of the atmosphere is defined by temperature
Figure 1: The vertical structure of the atmosphere
Intro to Weather and Climate – EART 80C Summer 2008
Lecture 1: July 28
c. Troposphere – warmed by earth decreases with height
d. Stratosphere – sun warms ozone, ozone warms the air, temperature increases with
height
e. Mesosphere – returns to normal temperature decrease with height
f. Thermosphere – very high temperatures, the sun warms N2 and O2 and heats up the
rarefied “air”. The molecules have lots of energy and that energy is not necessarily in ‘heat’
energy. Thus, the temperature is high due to the interactions of the energized molecules
bumping into one another.
C. Temperature
a. Gas – molecules bouncing off each other and “walls” and boundaries
b. How fast the molecules are moving
c. Kinetic energy of each molecule
d. Has nothing to do with the number of the molecules
e. Units
1. Kelvin, K, absolute zero is 0 K = -273.15 °C
2. Celsius, °C
3. Fahrenheit, °F (°F=(1.8*°C)+32)
4. Rankine, R (°F = R - 459.67)
D. Pressure
a. Pressure is Force per Area, the units are Pa = N/m2
b. 1 atm = 101325 Pa, 1.013*105 Pa
c. 1kPa = 1000Pa
d. 1 atm = 101.3kPa = 1.01 bar
e. 1 bar = 100kPa
f. 1 bar = 1000mb
g. 1 bar = 100kPa = 1000mb = 105 Pa
h. Pressure associated with fluid – force the fluid exerts on the walls.
i. Pressure is the force/area exerted on a surface caused by the molecules colliding with
the surface.
h. Pressure does not require gravity
EX 1: How much pressure does a standing person exert on the floor
a) Find area:
7in *10in  70in 2 *
2.54cm 2.54cm
1m
1m
*
*
*
 0.045m 2
1in
1in
100cm 100cm
b) Find Force: N = kg * m/s2
F = mass*acceleration (in this case acceleration is gravity)
Weight = mass * 9.8 m/s2
Intro to Weather and Climate – EART 80C Summer 2008
mass  155lb *
Lecture 1: July 28
1kg
 70kg (go over conversion of lb to kg)
2.2lbs
m

F  (70kg) *  9.8   700 N
s

P
700 N
 1.5 * 10 4 Pa
2
0.045m
D. Pressure (con’t)
a. Pressure is Force per Area, the units are Pa = N/m2
1. Pressure = Force/Area
Example: Why aren’t we crushed by the weight of the air above us?
1) We developed under this pressure.
2) Pressure force of air is exerted in all directions
Pressure force is exerted in all directions
Pressure in only one direction
3) If you lower the pressure drastically the cells of our bodies would burst!!
(Hickies)
b. Pressure Profile (From text)
For every 5km you go up the pressure
Decreases by 50%
From 0 to 5km = 50%
From 5 to 10km = 25%
From 10 to 15km = 12.5%
Intro to Weather and Climate – EART 80C Summer 2008
Lecture 1: July 28
E. Ideal Gas Laws
PV  nRT where
P = Pressure R = Universal gas constant, 8.314
V = Volume
N = Number of moles
PV 
mRT
where
M
J
in SI units
mol * K
T = Temperature in Kelvin
m = mass of gas
M = Molecular weight of gas (from periodic table)
Of air = 29 g/mole in a mole of normal air
O2 = 32g/mol, N2 = 14g/mol, H2O = 18g/mol
P
RT
M
ρ = density of gas (density is in units of kg/m3 Mass per Volume!)
where
P  cRT where c = concentration of gas (unites are moles/m3)
Example: What is the density of air at Room Temperature?
P
RT
M

PM
J
  using the values: R = 8.314
RT
mol * R
M = 29 g/mol = 0.028 kg/mol
T = 20C = 20 + 273 K = 293K
P = 1atm = 100kPa = 100000Pa = 1.0*105Pa
Plug in the values:

kg
mol  1.2 kg
m3
* 293K
(1.0 *10 5 Pa) * 29
8.314
J
mol * K
Unit conversion within the problem!
kg * m
2
N
Pa  3  s 3
m
m
J  Nm 
kg * m
*m
s2
N
kg * m
s2
F. Buoyancy
a) Does it sink or float??
b) Density – big ships float but a little pebble sinks – density determines buoyancy
Intro to Weather and Climate – EART 80C Summer 2008
Lecture 1: July 28
1. Less dense rises
2. More dense sinks
c) Density of air at the ground at STP is about 1.2 kg/m3
1. Objects with density greater than the surrounding water or air will sink
2. Objects with density less than the surrounding water or air will rise
3. Objects with density equal to the surrounding water or air will stay suspended.
People think of hot air rising, and cold air sinking…..
Better: Low density rises!!
High density sinks!!
Temperature isn’t the only factor; pressure has to also be taken into account!