Earth Temperatures Calculation Package
1. Solar constant.
Solar Constant and Energy Impacting on the Earth
"The solar energy reaching the periphery of the earth's atmosphere is considered to be constant for all practical purposes, and is known as the solar constant. Because of the difficulty in achieving accurate measurements, the exact value of the solar constant is not known with certainty but is believed to be between 1,353 and 1,395 W/m2 (approximately 1.4 kW/m2, or 2.0 cal/cm2/min). The solar constant value is estimated on the basis of the solar radiation received on a unit area exposed perpendicularly to the rays of the sun at an average distance between the sun and the earth."
[http://almashriq.hiof.no/lebanon/600/610/614/solar-water/unesco/21-23.html]
Radius of the Earth:
The value of 6371 km used here is the Volumic Radius, ie the value giving a fairly exact value for the Earth's volume by the usual formula for a true sphere. Because the Earth is actually an oblate spheroid, other radii have been calculated.
[http://en.wikipedia.org/wiki/Earth_radius]
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The Earth
<http://en.wikipedia.org/wiki/Earth>
Surface area 510,072,000 km©˜
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Calculations:
Taking the solar constant to be 1.4 kW/m2, and the Earth's radius to be 6371 km, the cross-sectional area of the Earth is pi*r^2, ie 3.142*((6371*10^3)^2)=1.2753E14 sq m.
With the Earth at its average distance from the Sun, total energy received (ignoring atmosphere etc) is 1.2753E14 times 1.4 = 1.785E14 kW. This is equal to 178,500,000 GW (gigawatts). (For a world population of ca 6 billion, solar energy per person= ca 30,000 kW.)
1 year=365.25*24 hr =8766 hr. Total solar energy received per year = 8766*1.785E14 kW-hr = 1.564731 * 1018 kW-hr or 5.6330316 * 1024 joules.
Solar energy received per day hours is therefore 1.564731 * 1018 / 365.25 = 4.28400 * 1015 kW-hr or 5.6330316 * 1024 / 365.25 = 1.54224 * 1022 joules. 1 BL unit is one millionth of this, 1.54224 * 1016 joules.
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2. Heat emission from the Earth.
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Global Heat Flow. <http://geophysics.ou.edu/geomechanics/notes/heatflow/global_heat_flow.htm>
"we find that the total, global, [geothermal flux] energy production is 3.8x1013 Watts"
"Although 38 trillion Watts is a lot of energy, when we spread it out over the entire surface of the Earth, the average global heat flow is only about 0.075 Watts/meter2"
"in the United States, our energy consumption averages about 3.0x1011 (300 billion or 0.3 trillion) Watts."
Data above from Pollack et al., Heat flow from the Earth's interior: analysis of the global data set, Rev. Geophys., 31, 267-280, 1991
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Calculations. Since 1 BL Unit is equal to 4.28400 x 109 kWh:
3.8x1013 Watts for 24 hours =24 x 3.8x1010 kWh = 9.12 x 1011 kWh . = 212.885 BL. Say 213 BL.
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3. The atmosphere.
<http://hypertextbook.com/facts/1999/LouiseLiu.shtml>
Mass of the atmosphere=5.3 * 1018 kg.
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<www.nobleednews.com/earth's_atmosphere.htm >
The total mass of the atmosphere is about 5.1 * 1018 kg.
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4. Energy generated by Man.
<http://www.aoi.com.au/Calculations/HydroSolarCalcs.htm>
Whole-world consumption of energy per year =10,000 million tonnes (1 x 1010 tonnes) of oil equivalent. One tonne of oil equivalent equals approximately 12 megawatt-hrs (1.2 x 104 kWh) of electricity.
So: daily consumption is (1 x 1010 x 1.2 x 104) / 365.25 kWh = 1.2 x 1014 / 365.25 = 3.285 x 1011 kWh. Divide by 4.284 x 109 to give 76.690 BL Units. Say 77 BL.
<http://www.enviroliteracy.org/subcategory.php/21.html>
In 2005, more than 3/4 of total world energy consumption was through the use of fossil fuels. Petroleum led with over 43.4 percent of the world's total energy consumption, followed by natural gas (15.6 percent) and coal (8.3 percent). North America is the largest consumer of fossil fuels, utilizing nearly 25 percent of the world's resources.
Energy from fossil fuel per day = 80% of 77 =61.6 Say 62 BL.
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5. Atomic bombs
<http://hypertextbook.com/facts/2000/MuhammadKaleem.shtml>
Nuclear weapons are far more destructive than any conventional (non-nuclear) weapon. They are often called atomic bombs or hydrogen bombs. The energy released by nuclear weapons is measured in tons, kilotons (thousands of tons), or megatons (millons of tons) of TNT. In international standard units (SI), one ton of TNT is equal to 4.184 * 109 joule (J).
Nuclear weapons have a large variety of energy yields. The first detonated on July 16, 1945 near Alamogordo, New Mexico, had a yield of about 19 kilotons or 80 terajoules (1 TJ = 1012 J). The two bombs that were dropped on the Japanese cities Hiroshima and Nagasaki during World War II were comparable in size: 15 and 20 kilotons or 63 and 84 terajoules, respectively. These bombs were only half the volume of the largest aerial bombs in use at the time, but released far more energy. It was said that there was as much energy in each bomb as in a stack of conventional explosives the size of the Washington Monument. Far more powerful bombs were made within a few years. The most powerful American bomb known as "Castle/Bravo"was detonated on February 28, 1954 and released energy equivalent to an astounding 15 megatons or 84,000 terajoules!
Typical yield: 4000 TJ. Most powerful American bomb: 84,000 Tj.
Calculation: 4000 TJ = 4 x 1015 joules = 0.2594 BL.
84,000 TJ = 8.4 x 1016 joules = 5.447 BL.. Say 5 BL.
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6. Tropical Hurricane.
According to Bill Bryson (p.231 in 'A Short History of Nearly Everything', Doubleday, 2003), a tropical hurricane can release, in 24 hours, as much energy as Britain or France uses in a year.
<www.berr.gov.uk/energy/statistics/.../ecuk/page17658.html>
UK energy consumption 1970-2000 approx 220 million tonnes oil equivalent. (4): 10,000 Mt 0E= 77 BL.
Calculation:
(220 x 77) / 10000 = 1.694 BL. Say 2 BL.
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7. Heat capacities. Air, CO2. Melt Ice.
<http://www.engineeringtoolbox.com/spesific-heat-capacity-gases-d_159.html>
Air: 1.01 kJ/kg K.
Carbon dioxide: 0.844 kJ/kg K.
to change 1 kg of ice at 0 deg C to 1 kg of water at 0 deg C, it has to take in 334 kilojoules of energy.
From (3): Mass of the atmosphere=5.3 * 1018 kg.
CO2 content ca 400 ppm.
Calculations: To raise entire atmosphere 1 deg takes 5.3 * 1018 x 1.01 kJ. BL value is (5.3 * 1018 x 1.01) / (1.542 x 1013) = 347,146.563 BL. Say 347,000 BL.
To raise total CO2 in atmosphere 1 deg takes above (x 400 / 106) ie 347,000 x 4 /104 = 138.858. Say 139 BL.
To melt 1 square kilometre of ice 1 metre thick (1,000,000 tonnes) takes 1,000,000 x 103 x 334 kJ, or 0.0216601816 BL. So heat to melt 1,000 sq km =21.66, Say 22 BL.
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8. Energy moved north by Gulf Stream.
Flow amount (from Greenzilla Fig 10) is 1.4 petawatts. Daily energy amount = 1.4 x 24 petawatt-hr = (1.4 x 24) x 1012 kWh = 7843.13725. Say 7840 BL.
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Unit conversion formulas.
1 kilowatt hour = 3 600 000 joules = 3.6E6 joules. 1 kilowatt = 1.0 x 10-6 gigawatts.
In scientific units, 1 BL Unit is equal to 4.28400 x 109 kWh (kilo-Watt-hours) or 1.54224 x 1016 joules (1.54224 x 1013 kJ).
(End)
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