Our Earth’s atmosphere is primarily made up of three gases nitrogen (N2) 78%, oxygen (O2) 21% and argon (Ar) .93%. Water vapor is the next most plentiful followed by trace amounts of neon, helium, methane, carbon monoxide, sulfur dioxide, ozone and carbon dioxide which logs in at. 03%
This is the same carbon dioxide which bears the name of the “green house gas” (although water vapor is the most important greenhouse) and which is so important in our photosynthesis cycle. As most will recall from their high school days the definition of photosynthesis is the process by which a plant converts CO2 and H2O into sugars, starches and O2. 6 CO2 + 6 H2O + Sun light Þ C6Hi2O6 + 6O2. Animals and man breathe in air for its oxygen content and expel carbon dioxide as part of their exhaling, this couples with other (CO2) gases which are the bi-product of plant and animal decay. At this point plants absorb this carbon dioxide use it, and then expel their bi-product which turns out to be partially oxygen. And so the cycle goes on. A continuation of this discussion will take place later in this paper in the section on how man can effect some changes on this green house effect.
In our atmosphere we also find small particles of dust, sand, hydrocarbon carbons (from the burning of fossil fuels) as well as amounts of sulfuric acid which spew forth from our ever present and always erupting volcanoes, marine organisims and fossil burning generators.
Three of the most important properties which describe our atmosphere are its pressure, humidity and temperature. Our atmospheric pressure is a mathematical description of the pressure which a column of air exerts on a square unit of area. This column rises from sea level up through to the top of our atmosphere which is called the thermoshpere. While there are several ways to demonstrate the effect of such pressure I think the most graphic way is to collect the following items. A three foot long glass rod, which has been sealed at one end, a dish or a soup bowl, a stand and finally a quantity of mercury. Next we take and partially fill the bowl with mercury and we fill our glass tube with the same. Taking care not to spill any mercury we place a finger over the open end of the glass tube, invert it and place it up right in the bowl, secure it to its stand.
At this point we observe that the mercury has dropped down a bit in its tube, but it has not left the tube. In the top of the tube we have formed a vacuum. The height of the tube can be measured using a metric ruler and hopefully the reading will be close to 760 mm. What keeps the mercury up in the tube? Pressure from the atmosphere should be the reply.
Figures available in print form
Why did we not use water in this experiment? By a simple conversion, based on the densities of the two liquids, we can show that if we had used water we would have needed a 34 foot long tube, this is most impractical for classroom work. As an application of the law of atmospheric pressure I should point out that those of us who rely on wells (shallow) can only draw water from 29 to 30 feet below the surface of the earth. These pumps create a vacuum and the atmosphere “pushes” the water up the pipe. These pumps can create a partial vacuum but they will never be able to “pull” 34 feet of water.
While still on the topic of air pressure it would be interesting to look at a graphical representation of air pressure which is listed as 1000 millibars for the height at sea level. As we examine the greater heights the pressure drops off as seen in the graph below.
Figure available in printed form
Humidity has been described as the amount of water vapor which a given volume of air has in it. Air’s ability to hold water vapor depends to a great degree on air temperature, warm air can hold more water vapor than an equal volume of cold air. When we use the word humidity we are giving a percentage which tells us how much water vapor a particular volume of air has in it, also it says just how much more it could hold.
If we had remained planet bound we would have the following impressions. Its warmer at ground level and much colder on a mountain top. These impressions are still valid if we stay on the ground (troposphere). Today we have a wide range of tools which help us “read” our atmosphere. These tools are weather balloons and rockets which probe the outer limits and beyond and send back data. A small part of these data will be seen in the next graph which describes middle latitude atmospheric temperatures. The data found in these tables comes from Goody and Walker’s
Atmospheres
(pages 44Ð46).
Figure available in print form
At the troposhpere we find the temperature at 288 kelvin (15°C) which we would have expected but in the far reaches we find that the temperature rises to 1000°K. The molecules at this height are few so the warming effect on a surface is imperceptible. This great temperature is caused by the thermosphere’s absorption of solar radiation which bombards the Earth in the form of extreme ultraviolet wave lengths.
In our work it would be good to stop and look at how the positioning of the planets in the solar disk affects their reception of solar energy. If we take a look at some simple ideas we can get a better understanding of that which is to follow. Take and compare the surface area of two spheres. The first has a radius of one and the second a radius of 2. To compare them through a ratio we will get 4X pi X r
2
/4X pi X r
2
. We see that both contain 4 and pi which will go out as a unity factor, the real thing we must look at are the radii. So we write 1
2
/2
2
= 1/4. This tells us that the area of the second sphere is four time larger, which implies that each unit of its cross section gets but one fourth of the radiation which the first had received. We can look at the next sketch and see how this looks in the form of a picture.
Figure available in print form
Our thoughts now turn to the Earth and the planets which are circling the Sun. How do they compare in amounts of radiation received? Take Earth’s distance as one and compare the others to it we would get the following table.
Planet Kilometers From Sun Compared to Earth Decimal
(10
6
km) Equivalent
Mercury 58 150
2
/58
2
6.680
Venus 108 150
2
/108
2
1.9290123
Earth 150 150
2
/150
2
1.0000000
Mars 228 150
2
/228
2
0.4328254
Jupiter 778 150
2
/778
2
0.0371726
Saturn 1430 150
2
/1430
2
0.0110029
Uranus 2870 150
2
/2870
2
0.00273161
Neptune 4500 150
2
/4500
2
0.00111111
Pluto 5900 150
2
/5900
2
0.00064636
A table such as this tells us a lot at a glance. Care to move to Mercury? Their solar radiation is almost 7 times Earth’s radiation per square mile. At the other end of the spectrum we find Pluto. Pluto’s temperature of -230°C, is connected to its .00064636 on the chart above.
We all have experienced the Sun’s radiation in one form or another. At this point it would be interesting to look at the electromagnetic waves and learn something about them. The energy which is generated in the Sun’s core needs anywhere from one to ten million years to pass through to the Sun’s surface. The next part of the trip runs a little more than 8 minutes.
We take 9.3 X 10
7
miles (Earth‘s distance from the Sun) and divide by 1.86 X 10
5
miles/sec (which is the speed of light) and we get 500 (seconds). This 500 seconds divided by 60 seconds/min. will give us 8 minutes and 20 seconds, this is a very short sprint to Earth.
This flow of radiant energy takes many forms. To distinguish one form from another we have but to study their wavelengths and compare them to a rule or chart. A wavelength is the distance between successive wave crests, the sine waves which we did in high school are a good way to think of this. Mentally picture such a symmetrical wave pattern and measure the distance from the top of one wave to the top of the next and you will have a wave length. Each form of radiation has it peculiar wavelength. The following graph gives typical wavelengths in meters.
Figure available in print form
A major portion of our Sun’s radiant energy is seen by us as white light, which when passed through a prism spreads to form a rainbow. All of this is related to a law known as Wien’s Law which states that there is a relationship between a body’s temperature and the peak wavelength which it emits. The rule is as follows:
Peak Wavelength (m) = 2.88 X 10
-3
Temperature °C + 273
Wien’s Law applies to ‘’black body” objects which absorb all of the energy (radiation) which falls on them and then in turn emits all of the radiation which it should give off at that temperature. It is a law which describes ideal or laboratory conditions but can be used in the class room. Wien’s Law has some interesting applications. If we already know that the temperature of the surface of the Sun is about 5700° C. Then we can plug this into the formula and find the wave length of this light.
Peak Wavelength (m)= 2.88 X 10
-3
/(5700° + 273) = 4.821697639 X 10
-7
When we refer back to our spectrum of electromagnetic chart we see that this reading falls between in the visible light range or between the ultraviolet and the infra-red sections. This law can be used to show that our own body temperature falls not in the visible range but rather in the infra-red range of radiation. When we take this law and solve for temperature we get new problems like the following. If we observe the flame on a propane torch and see that it gives off a blue-violet light. We will be able to match that color to the chart and come up with its approximate wave length, which we then plug into the formula to get its temperature.
T(C°) = 2.88 X 10
-3
x -273
Peak wavelength (m)
T(C°) = 2.88 X 10
-3
-273 =6927°C
4 X 10
-7
Bodies emit many forms of heat and therefore more than one wavelength. We can’t see infra-red in such an experiment but we know its there.
Next our thoughts turn to the examination of the effective temperature of planets. As we follow our path around the Sun we present a side or a face to it (Sun). From a distance the Earth looks like a disk in space, as do all of the other planets. We have some dark areas which readily receive the Sun’s radiation and we have some large areas which reflect incoming radiation (ice caps, desserts, clouds). Thus we only absorb about (1 -.33) or .67% of the incoming radiation. The reflected percentage is referred to as albedo. The albedo rating is different for each planet.
When our planet is seen from the Sun its disk area may be computed using the formula, Area = pi X r
2
(1- albedo). To determine just how much Sun generated energy is hitting the planet we must multiply all of this by our planets solar flux. This flux rating is 1.4 x 10
6
erg. cm.
-2
sec
-1
for Earth. This spells out as Energy absorbed (Earth)= 3.14159 x 6371
2
x 10
10
x 1.4 x 10
6
x .67. Over the year a planet’s energy balance is in steady state, that is the amount of energy (solar flux) which a planet receives is equal to the amount it radiates back out to space.
According to two scientists (Stefan and Boltzmann) who worked on this problem, the outgoing radiation from a surface of unit area in unit time is proportional to the fourth power of the temperature. They computed a constant which is referred to as the Stefan-Boltzmann Constant (s)and it equals 5.67 x 10
-5
cm
-2
x sec
-1
. In this work the planet is treated as a sphere which is emitting radiation from its total surface, so the formula we use to compute the energy which is being radiated to space is. Energy radiated = 4 x pi x r
2
x 5.67 x 10
-5
x erg x cm
-2
x T
4
. Equate the two formulas and we get following:
Temperature =
4
Solar Flux X (1- albedo)
4 x s
Temperature =
4
1.4 X 10
6
X erg X (.67) X 10
5
X cm
2
X deg
4
X sec
4 X 5.67 X cm
2
X sec X erg
Temperature =
4
4135802469deg
4
= 253.59455 deg °K
This is the Te of the Earth. ( Atmospheres pages 46Ð48)