HOW THE EARTH SEQUESTER HEAT FROM SUN

Earth receives 697.04 W/m^2 of infrared radiation from 1367 W/m^2 of the incoming energy (light, ultraviolet, radio, etc.) from the Sun. (Maoz. 2007. Page 36). 14% of incoming heat to Earth is absorbed by air.

Data from the meteorological station in Monterrey, Mexico located at 25º 48´ North latitude and 100º 19' West longitude and an altitude of 513 meters ASL: On 31 March 2007 at 18:15 UT the soil absorbed approximately 453 W/m^2 of IR radiation causing a ground temperature of 318.15 K (45°C). The air temperature was 300.15 K (27 °C), what was the tropospheric ΔT due to the absorptivity-emissivity of air?

For the answer, first we need to know the load of heat transferred from the soil to the mixed air. Principally, we need to obtain the Grashof Number and the Conductive Heat Transfer Coefficient for those particular conditions:

Grashof Number

When we are calculating the load of heat transferred from the surface to the air we need to know the flux of the air toward the warm surface and toward the upper levels. The rate of flux is known as the Grashof number (Gr), and it describes a ratio involving buoyancy and viscosity: buoyancy/viscosity. As a fluid adjacent to a warmed surface starts to increase in temperature, the density of that fluid decreases. The buoyancy causes the less dense fluid to lift up, so the adjacent colder fluid is conveyed into contact with the warmer surface.

Gr L = g β (Ts – T ∞) D^3 / v^2

Where,

g is the gravitational constant (9.8 m/s^2)
β is the volumetric expansion coefficient (1/T)
T1-T2 is the difference of temperature between two adjacent systems expressed in Kelvin (18 K).
D^3 is the distance between two systems to the third power (1 m)
v^2 is the kinetic viscosity (2.076 x 10^-5 m^2 / s) to the second power.

Introducing magnitudes:

Gr L = (9.8 m/s^2) (3.332 x 10^-3 K^-1) (18 K) (1 m)^3 / (2.076 X 10^-5)^2 m^4 /s^2 =
= 5.877648e-1 m^4/s^2 / 4.309776^-10 m^4 /s^2 = 1.36 x 10^9

Heat Transfer Coefficient

The Heat Transfer Coefficient (Ћ) is the rate of heat transferred from a warmer system to a colder system. It relates to the Grashof number, the Prandtl number and the thermal conductivity of the fluid. The Prandtl number is dimensionless and refers to the ratio of momentum diffusivity (v, or dynamic viscosity) and the thermal diffusivity (a). The heat transfer coefficient is determined by the next formula:

k
Ћ =  ---------- (C) [(Gr) (Pr)]^a
D^3

Where,

k is the thermal conductivity (dry air k = 0.03003 W/m*K)
D or L is the distance between the two systems
C is a factor of correction for irregular surfaces facing up (soil)
Gr is the Grashof Number (obtained in the previous calculus Gr = 1.36 x 10^5)
Pr is the Prandtl Number (0.697 for air)
a is the constant of proportionality for laminar natural systems (1/3 for surfaces facing up).

Introducing magnitudes:

0.03003 W/m*K
Ћ =  ---------------------------------- (0.14) [(1.36 x 10^9) (0.697)]^1/3 = 4.13 W/m^2*K
1 m^3

The heat transfer from soil to mixed air is:

q = Ћ A (Ts – T∞)

Where,

q is the heat absorbed by the colder system
Ћ is the convective heat transfer coefficient (obtained in the previous formula = 4.13 W/m^2*K)
A is the implied Area (1 square meter)
Ts - T∞ is the difference of temperature between the heated system and the colder system.

Introducing magnitudes:

q = 4.13 W/m^2*K (1 m)^2 (18 K) = 74.4 W (rate of heat transfer or heat flow rate)

74.4 W = 74.4 J/s (http://www.iprocessmart.com/techsmart/conversions.htm)

E = 74.4 (J/s) (1 s) = 74.4 J  = 17.782 cal-th

If m of mixed air = 1.18 Kg/m^3 and the Cp of mixed air at 300.15 K = 1005.7 J/kg*K (240.37 cal/Kg*K), then:

ΔT = q/m (Cp) = 17.8 cal/(1.18 Kg) (240.37 cal/Kg*°C) = 17.8 cal/ 283.64 cal*°C= 0.063 °C

0.063 °C was the ΔT caused by thermal transfer by conduction-convection from the ground to the air mixture. Let's see what happened in 1998:

The heat absorbed by dry air from incoming Solar radiation is 697.04 W/m^2 X 0.14 (absorptivity of dry air at T = 300.15 K, and P = 1 atm) = 18.7 W/m^2 = 4.47 cal/s*m*K.

Considering the whole mixture of dry air and despising the absorbency of soils and oceans the Δ T by Solar Irradiance, absorbed-emitted by the CO2, would be of only 0.029 °C. However, the change observed in the tropospheric temperature is 0.52 °C; then, the discrepancy is 0.491 °C. This means that the oceans and the soils are the true cause of the Earth’s warming, not the atmosphere alone.

If you do not apply heat to the pot, the fababeans never will cook. If the Sun were not brighter, the Earth would not be warming up. Favorably, our Sun now is shining more than 400 years ago, and we do not have to fear a natural cycle that has occurred through the whole existence of our Solar System.

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CARBON DIOXIDE AND LIFE

Without light, life would not be possible on Earth. The same applies to water and carbon dioxide.

Carbon Dioxide is an organic compound formed by one atom of Carbon and two atoms of Oxygen (O=C=O).

Carbon Dioxide (CO2) is a natural constituent of the atmosphere and its density is of 747 mg/cubic meter of air. Its concentration in the composition of air is roughly 0.032%; however, it is the most important organic compound for the sustainability of the biosphere (the whole of living beings on Earth).

Without CO2 the life of the photosynthetic organisms and the animals would not be possible, given that the CO2 is used as the base for the synthesis of organic compounds that are nutrients for plants and animals.

Through photosynthesis, the organisms with chlorophyll take the atmospheric or dissolved in water CO2 to form more complex molecules, like carbohydrates, lipids, proteins and nucleic acids.

The general formula of photosynthesis is as follows:

6CO2 + 6H2O + Light = C6H12O6 (Glucose) + 6O2

Carbon Dioxide is fixed in the chloroplast stroma. Then the fixed carbon dioxide is used in the cytoplasm to synthesize sucrose. (See a Graphic Outline of Photosynthesis Here).

The organism with chlorophyll absorbs light, CO2 and water from its surroundings. The water molecule is broken and the Hydrogen of this molecule adheres to carbon dioxide molecules to form glucose. The Oxygen of water molecules is released to the atmosphere, whereas the energy provided by photons is stored in the bonds of the glucose molecule.

Any nutritional chain begins with producer organisms; that is, with those organisms that produce their own food. These organisms are called autotrophs. The plants are autotrophs because they produce their own food; the raw materials for photosynthesis are water, carbon dioxide and light.

It has been determined experimentally that the density of carbon dioxide for the optimal development of all kinds of plants is 895 mg/cubic meter of air (about 500 ppmv).

Some plants grow better in atmospheres with VHD of carbon dioxide; for example the pteridophyte and certain species of conifers are developed better in humid atmospheres with 5000 ppmv of carbon dioxide.

Carbon Dioxide is not an environmental polluting agent because it is not detrimental or poisonous. The carbon dioxide does not work physiologically like the oxygen, but it does not intoxicate; this means that carbon dioxide cannot be placed by the cells instead the oxygen, but the CO2 does not kill them, as carbon monoxide makes it.

A single difference exists between carbon dioxide and carbon monoxide, an oxygen atom less in the molecule of carbon monoxide. By that small difference, one of them is toxic, the carbon monoxide, whereas the other is vital for living beings, the carbon dioxide.

If you lock yourself into a totally sealed room with an ignited stove (NEVER DO IT!), it is not the carbon dioxide what kills you, but the carbon monoxide and the asphyxia by the depletion of the oxygen consumed through the ignition of the fuel. If you accumulate carbon dioxide in the same room until having a density of 5 grams by cubic meter of air you will not asphyxiate as much the density of oxygen in the room remains normal and stable.

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®
®
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Sun and Life on Earth © 2007, by Biology Cabinet.
Biology Cabinet Organization ® 1997.

 Web www.biocab.org
Title: SUN AND LIFE ON EARTH
Authors: Nasif Nahle and Adip Said.
©January 28, 2007 by Biology Cabinet. New Braunfels, TX.

HOW THE EARTH SEQUESTER HEAT FROM SUN

PHOTOSYNTESIS

DIAGRAM OF PHOTOSYNTHESIS

THE SUN AND OTHER HABITABLE STARS

BIBLIOGRAPHY

Published: January 28, 2007Update: None
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THE SUN AND OTHER HABITABLE STARS

Living beings must receive a stable and continuous supply of energy from a star. Earth receives a continuous and stable tide of energy from a G2V star (the Sun); besides, Earth is positioned at an suitable distance from the Sun (the Earth is placed at 1 AU far from the Sun), not too near as to be scorched by the intense solar radiation (as Mercury and Venus), neither too far as to be frozen in the cold sidereal space (as the outer planets like Mars, Jupiter, Saturn, etc.). The source of energy may not be necessarily a star. The planet that shelters living forms can be itself the source of that energy needed for life.

We think that the G class stars (yellow-white, with nuclear reactions by fission of Hydrogen and with effective temperatures of 5300-6000 K. G Class are Sun-like stars) and belonging to the main sequence (V or dwarf) are the most possible stars to have planets with optimal conditions for the origin and evolution of living beings. The Sun is a star of class G2V (surface effective temperature of 5800 K):

Classification of Stars: See Table # 1

The star Alpha Centauri is also a G2V star.  This makes it to be a star very similar to the Sun. It is an accessible candidate for exploration through our instruments because it is relatively near to our Solar System (4.36 light years from here). There is only a problem that darkens the scene: it has a star companion, this is to say that the system is a double star. Its companion is a dwarf of the class K1V (5300 K).  If there were in that system a planet with intelligent living beings, they would see our Sun as a star of first magnitude near the constellations of Perseus and Cassiopeia. Our Sun would be their sidereal point of reference…

For stars to be included like appropriate for generating and to maintaining living beings, the astrobiologists make a record of the physic characteristic of the stars, like size, electromagnetic spectrum, brightness, temperature, rotation, nuclear stability and metallicity.

Very hot or very cold stars should not be excluded from the catalogue because they may have planets that could be orbiting at such distance that they would not experience the pounding of high amounts of cosmic radiation. The problem proposed by some scientists to exclude hot stars from the habitable stars is that hot stars extinguish more quickly than the stars of low or medium temperature; however, most biologists think that the usual life of a star is not a critical impediment for the emergency of life on any of its planets. It is possible that the living beings have emerged in a world with the appropriate conditions and that they have continued their evolution through hundreds of millions of years, whenever the star that provides the energy have remained active and steady down such a time.

An understandable example comes from the history of life on Earth where, although the biodiversity scaled through 3.3 billion years, the highest point of biodiversity occurred in the course of 500 million years (at the Paleocene). Thus, any star of F, G and perhaps K classes, which had habitable planets -in a system where the fundamental abiogenesis may have occurred- and that still were active and steady at this time, will be a suitable star for our list of habitable stars.

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BIBLIOGRAPHY

Boyer, Rodney. Concepts in Biochemistry. 1999. Brooks/Cole Publishing Company: Thomson Corporation; Stamford, CT.

Callen, Jean-Claude. Biologie Cellulaire. Des Molécules aux Organisms. Cours et questions de révision. 1999. Dunod. Paris, France.

Campbell, Neil A., et al. Biology. Addison Wesley Longman, Inc. 1999, Menlo Park, CA.

Krupp, Marcus A. and Chatton, Milton J. Current Medical Diagnosis and Treatment. 1984; Lange Medical Publications. New York, NY.

Lodish, H., Berk, Arnold, et al. Molecular Cell Biology. 1999. W. H. Freeman and Company; New York, New York.

McGrew, Jay L., Bamford, Frank L and Thomas R. Rehm. Marangoni Flow: An Additional Mechanism in Boiling Heat Transfer. Science. Vol. 153. No. 3740; pp. 1106 - 1107. 2 September 1966.

Pitts, Donald and Sissom, Leighton. Heat Transfer-Second Edition. © 1998 McGraw-Hill Companies Inc.

Wilson, Jerry D. College Physics-2nd Edition; Prentice Hall Inc. 1994.

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