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Dr. Eder's MEA-130 Lectures
Chapter 2: Warming the Earth and Its Atmosphere
>> Energy, Temperature and Heat
Energy (E): the capacity to do work on some form of matter.
E = m c2 Kg m 2 [Joule]
s2
Potential Energy (PE)
PE = m g h [Joule]
Kinetic Energy (KE)
KE = ˝ m v2 [Joule]
Where: m is mass (Kg); c is speed of light (m/s);
g is gravity (m/s2); h is height (m); v is velocity (m/s)
First Law of Thermodynamics
Energy can take many forms, however it can neither be destroyed nor created...energy is always conserved!
Temperature (T): is a form of Kinetic Energy,
or a measure of the average speed of all of the molecules of an object (air)
as their speed increases, the T increases
The lowest temperature possible (theoretically) is the temperature at which all atoms/molecules stop moving...
Absolute Zero (AZ)
At AZ we start a temperature scale called the
Kelvin Scale (K).
Kelvin is convenient for scientific computations because it is never negative; however, non-scientist generally either:
Celsius (oC) (Centigrade)
Fahrenheit (oF)
At AZ, the temperature is equal to: 0 K
-273 oC
-459 oF
Temperature Conversions
K = oC + 273
oC = (5/9 (oF - 32))
oF = (9/5 (oC) + 32)
Cartoon Example:
oF = (9/5 (oC) + 32)
= (9/5 (36) + 32)
= 96.8
Comparison of Scales
Freezing Boiling
K 273 373
oC 0 100
oF 32 212
Heat: is energy in the process of being transferred between or within substances - because of a difference in temperature.
measure in Calories (1 cal = 4.2 Joules)
Specific Heat: the amount of heat required to raise the temperature of 1 gram of a substance 1o C
Table 2.1
Example: Water has a high Specific Heat value (1.0):
1.0 cal
1 gram 1o C
(If we heat 1 gram of water, it takes 1 cal of heat to raise its temp. 1o C)
Sand has a low Specific Heat value (0.19):
0.19 cal
1 gram 1o C
(If we heat 1 gram of sand it takes only 0.19 cal of heat to raise its temp 1o C)
Given the same amount of heat applied, the sand’s temperature would increase 5 times that of the water [1/0.19] .
Just as we had two types of energy……
we also have two types of Heat:
Latent Heat
Sensible Heat
Water is unique in that it is the only substance that can exist in all three phases or states in the atmospheric Figure 2.3 :
gas (invisible vapor) : highest state
liquid : middle state
solid (ice) : lowest state
Latent Heat: heat that is hidden or locked-up by water molecules when they go to a higher state
Sensible Heat: heat that is released by water molecules when they go to a lower state
we can feel (or sense) and measure with a thermometer.
Air will cool when Sensible Heat is converted to Latent Heat
Melting: ice water
Evaporation: water gas
Sublimation: ice gas
Air will warm when Latent Heat is converted to Sensible Heat
Freezing: water ice
Condensation: gas water
Deposition: gas ice
Example: 1 gram of liquid water requires 600 cal of heat in order to evaporate.
The heat required to do this is “taken” from the air and “locked up” within the water vapor.
This heat is thus stored or hidden, hence the name Latent.
Going from a lower state (liquid) to a higher state (gas) requires energy
Because of this - evaporation cools the air
If this same 1 gram of water vapor were to condense, 600 cal of heat would be released back to the air.
Going from a higher state (gas) to a lower state (liquid) releases heat:
Because of this - condensation warms the air
Four Types of Sensible Heat Transfer
Conduction
Convection / Advection
Radiation
Conduction: transfer of heat by molecular activity from one substance to another or within a substance
transfer is always from hot to cold
the larger the T, the faster the transfer
solids, especially metals are excellent conductors Table 2.2
air, however is a poor conductor of heat
as a result: conduction of heat within the atmosphere only occurs at the earth’s surface, where the Ts are very large
Convection: transfer of heat by the mass movement of air (in the vertical direction) Figure 2.6
- thermals
Advection: transfer of heat by the mass movement of air (in the horizontal direction)
- warm, cold advection
Radiation: transfer of heat through the propagation of electromagnetic waves
only release heat when striking an object
transfer occurs at the speed of light (3 x 108 m/s)
transfer does not need a medium (molecules), therefore it can occur in the vacuum of space
We measure these electromagnetic wavelengths () using:
microns (µ)
= 1 x 10-6 meters
micrometers
1
As the wavelength () of the radiation decreases, the amount of energy it carries increases Figure 2.7
for example: X-rays 1 x 10-3 µ
uv rays 1 x 10-1 µ
are all short , therefore the carry a lot of energy and can be harmful to humans; while
TV 1 x 106 µ
radio 1 x 108 µ
are long , carry less energy and are harmless.
Radiation and Temperature
All objects (whose T > 0 K) emit radiation.
The higher the temperature, the greater the amount of radiation emitted.
This association is described by the:
Stefan - Boltzmann Law
E = T4
E : is the energy emitted by the body Watts
m2
: is the Stefan Boltzmann constant: 5.67 x 10 -8 Watts m2 K4
T: is the temperature of the body (K)
Notice that since T is raised to the fourth power, even a small increase in T will result in a large increase in emitted energy.
Using the Stefan - Boltzmann Law , we can calculate the amount of energy emitted by the sun and the earth:
Sun has a T = 6000 K, therefore:
E sun = 5.67 x 10 -8 Watts (6000 K)4
m2 K4
= 7.35 x 10 7 Watts
m2
Earth has a T = 288 K, therefore:
E earth = 5.67 x 10 -8 Watts (288 K)4
m2 K4
= 3.90 x 10 2 Watts
m2
The sun emits ~2 x 105 (200,000) times more energy
than the earth, per square meter!
Another Radiation Law, allows us to calculate the wavelength () at which the sun and earth emit the maximum amount of radiation:
Wien’s Displacement Law
max = 2897 µ K
T
Where: max : wavelength at which maximum radiation is emitted (µ)
T : body’s Temperature (K)
as the temperature of the body increases, the of maximum emission decreases!
The value 2897 µ K is a constant developed by Wien, which the book rounds to 3000 µ K
Sun: max = 3000 µ K = 0.5 µ
6000 K
Earth: max = 3000 µ K = 10.0 µ
300 K
This difference (displacement) between 0.5 and 10.0 µ allows us to refer to:
Earth’s (Terrestrial) Radiation as Longwave Radiation
Sun’s (Solar) Radiation as Shortwave Radiation
Although the sun emits at a maximum rate around 0.5 µ, it also emits radiation at other wavelengths as seen in the:
Solar Electromagnetic Spectrum
Figure 2.9
Human’s eyes are sensitive to radiation at wavelengths between 0.4 and 0.7 µ, this is called the:
Visible Range
The visible range can be further divided into the colors of the spectrum (rainbow):
> 0.7 0.70 0.65 0.60 0.55 0.50 0.45 0.40 < 0.4
(IR) R O Y G B I V (UV)
>> Balancing Act : Absorption, Emission and Equilibrium
Both the Earth and the Sun function like a:
Black Body: an object or body that is both:
a perfect emitter (emits the maximum radiation possible for a given T) , and
a perfect absorber (absorbs all of the radiation incident upon it)
The Earth and Sun are said to be in:
Radiative Equilibrium
when the rate of absorption of shortwave radiation by the Earth
is equal to the rate of emission of longwave by the Earth.
This Radiative Equilibrium provides the Earth with an average:
Radiative Equilibrium Temperature
255 K
-18 oC
0 oF
However; this temperature is much colder that the average:
Actual Temperature
288 K
15 oC
59 oF
WHY?
Because unlike the Earth and the Sun, the Atmosphere does not act like a Black Body!
Rather...all of molecules of gases that comprise the atmosphere each act like:
Selective Absorbers/Emitters
they absorb/emit well at some s but poorly at other s
Kirchhoff’s Law: gases that are good absorbers of a given of radiation tend to be good emitters at that same .
Figure 2.11 illustrates the selective absorption/emission characteristics of the various gases that comprise the atmosphere.
with the exception of O3, most gases are “transparent”
to the short emitted by the sun
i.e. they do not absorb the short ;
but, most absorb some of the long emitted by the earth
especially H20 and CO2
As H20 and CO2 absorb the longwave (earth) radiation, they
gain Kinetic Energy, causing them to warm and
re-radiate (Kirchhoff’s Law) some of this energy back to the earth.
the Earth’s lower atmosphere is 33o C (59 o F) warmer than it would be w/o the gases that comprise it! Fig. 2.12
This phenomenon is called the: “Greenhouse Effect”
“Greenhouse Effect”
much like the glass in a greenhouse, the gases in the atmosphere allow shortwave (solar) radiation to penetrate....but absorb or trap the longwave (terrestrial) radiation.
Unfortunately, as we saw earlier, the concentration of several
Greenhouse Gases:
CO2, CH4, N20 and CFCs
have been increasing due to the anthropogenic emissions.
Chapter 2 is nicely summarized in Figure 2.13, illustrating how the atmosphere is warmed from below.
Short (solar) radiation passes through the atmosphere unimpeded and heats the ground upon impact.
The ground then warms the first few cms of the atmosphere through conduction.
As the surface air warms, it becomes less dense and rises, carrying heat vertically through convection, which can then moved horizontally through advection.
Additionally warming of the atmosphere occurs through:
the radiation of long (terrestrial) energy
which is captured by Greenhouse gases;
The conversion of latent heat into sensible heat through condensation and deposition as clouds and precipitation form.
Calculation of Earth’s Radiative Equilibrium Temperature
(Ignoring the Atmosphere and its Greenhouse Effect)
Area of a Sphere: 4 r2
Area of a Disk: r2
S = Solar Radiation constant 1367 watts m-2
re = Radius of the earth
A = Albedo (% of solar radiation reflected (i.e. not absorbed by earth))
E = Earths Radiation = ????????
Disk Sphere
(1-A) S ( r2) = E (4 r2)
(1-A) S ( r2) = E
(4 r2)
(0.7) (1367 watts m-2)) = E
(4)
239 watts m-2 = E
Use Stephan-Boltzmann’s Law (E = T4) and solving for T we get:
T = (E/)1/4 =
= 254.8 K
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