Energy Theory for Global Warming
Aubrey E Banner firstname.lastname@example.org
11th May 2019
Global warming is certainly happening.
This has been proved by many measurements of the Earth’s temperature, and the resulting consequences are manifest. A popular explanation is that this effect is due to the carbon dioxide in the Earth’s atmosphere, and it is known as the “Greenhouse Gas Effect.” It claims that anthropogenic burning of fossil fuels continually increases the amount of carbon dioxide, and so causes the temperature of the atmosphere to increase. However, many physicists disagree with this theory because they say that it violates the Second Law of Thermodynamics.
I should like to offer a new, simple idea which shows that the rise in temperature of the Earth’s atmosphere is due to two combined causes which have nothing to do with the Greenhouse Gas effect. They are :-
(1) Primary Energy
(2) Energy from the Oceans
The larger of these effects is due to the vast amount of energy we generate and consume. The energy we get from burning fossil fuels, or from nuclear power, eventually ends up as heat put into the Earth’s system, and this heat energy causes the temperature to rise. It’s fairly obvious, really. Most of the energy goes into the oceans, but a small proportion remains in the air, and is enough to cause the effect. It should be realized that although the amount of energy involved on a daily or yearly basis is relatively small, nevertheless the total amount accumulated over a period of years is sufficient to explain the temperature increase. Moreover, once the energy has arrived in the atmosphere, it does not escape to space as many might think. Please refer to the Appendix for the explanation.
Information for primary energy consumption has been obtained from the British Petroleum website at https://www.bp.com/en/global/corporate/energy-economics/statistical-review-of-world-energy/primary-energy/energy-and-the-environment.html
and the following total figures have been calculated for the Northern and Southern Hemispheres separately, over the 50 years from 1965 to 2015.
The BP figures are given in units of million tons of oil equivalent (mto equiv), but are expressed below in Joules, where the conversion factor 1 mto equals 4.187*1016 Joules has been used. This data shows that the annual energy consumed in the Northern Hemisphere increases each year in an approximately linear way.
The graph below shows the increase in the aggregate (accumulated) Primary Energy in the Earth’s system from 1965 to 2015, calculated from the BP data.
Primary Energy over 50 years 1965 -2015
Most of the energy is consumed in the Northern Hemisphere.
The energy in the atmosphere stays in its hemisphere of origin because of the well-known circulation of the currents in the atmosphere. BP data, after conversion.
Northern Hemisphere 8.8510*1021 Joules
Southern Hemisphere 5.2513*1020 Joules
This is the primary energy consumption over 50 years.
Initially all the energy enters the atmosphere.
I have had some difficulty in obtaining a definitive figure for the proportion of this energy which remains in the atmosphere. Most of it enters the oceans; some enters the land mass and the ice. However, from the IPCC report
and scroll to 18.104.22.168 we find for the period 1961 to 2003 that the total energy entering the oceans was 89.3% of the total energy from all sources, and the energy remaining in the atmosphere was 3.14%, this latter figure being subject an error of +or – 40%. This means that the proportion of the total energy remaining in the atmosphere was between 1.89% and 4.40% of the total. The following calculations use the value 3.14%.
Oxygen and nitrogen molecules do not radiate, so the increase in energy of the atmosphere is
0.0314 * 8.8510 * 1021 Joules, that is 2.77921 * 1020 Joules, over 50 years.
0.0314 * 5.2513 * 1020 Joules, that is 1.64891 * 1019 Joules, over 50 years.
Now, the surface area of the Earth is 5.1*1014 m2
So, the area of each hemisphere = 2.55 * 1014 m2
Therefore energy consumption = (2.7792*1020) / (2.55*1014 )
= 1.08988 * 106 Joules per square metre, over 50 years.
From www.theweatherprediction.com/habyhints3/976/ we find that the number of molecules in the Earth’s atmosphere is 1.09*1044
So, the number of “air” molecules in the standard column based on 1m2 of the surface = (total number of molecules in the atmosphere) / (surface area of Earth)
= (1.09*1044) / 5.1*1014
= 2.137 * 1029 molecules in column (on 1 m2)
It has been assumed that the added energy is confined to half of the troposphere, which contains 75% of the atmosphere. ( Refer to https://web.physics.ucsb.edu/~lgrace/chem123/troposphere.htm
So the number of participating molecules in the column is 0.5*0.75*2.137*1029
= 8.0138*1028 molecules per m2
The increase in energy is shared between these molecules in the column.
So the increase in energy per molecule = (1.08988*106) / (8.0138*1028)
= 1.36*10-23 Joules per molecule
From the kinetic theory of gases,
the kinetic energy of a molecule moving in a gas is (3/2)*k*T where k is the Boltzmann constant 1.38*10-23 J/K, and T is the Absolute temperature of the molecule.
So, increase in energy = 1.5*k*(increase in temp)
So, increase in temperature = (increase in energy) / (1.5*1.38*10-23) K
Therefore, for the Northern Hemisphere
increase in temperature = (1.36*10-23 ) / (2.07*10-23) K = 0.657 K
So, increase in atmospheric temperature = 0.657 K over the 50 year period.
From https://earthobservatory.nasa.gov/world-of-change/DecadalTemp we find measured values for atmosphere temperature increases from 1965 to 2015, and these are shown in blue in the graph below. The graph for the calculated values is in red. The equation for this curve is
Temp.Anomaly = (7.423*10-23 )*(Primary Energy Aggregate (gross) in Joules) o C
From this graph, it is clear that the effect of the Primary Energy is not sufficient to explain the measured increase in temperature of the atmosphere in the Northern Hemisphere. But the effect of warming by the Oceans has still to be considered. For this we must first deal with the temperature rise in the Southern Hemisphere.
we find the measured temperature anomalies for the Southern atmosphere, and these are shown in blue in the graph below. The effect of the Primary Energy in the Southern Hemisphere is shown ingreen. The difference between the two is shown in red.
The increase in atmospheric temperature in the Southern hemisphere over the 50 years 1965 to 2015 was 0.43 oC.
The energy theory gives a value of only 0.039 oC. For 2015, the difference, 0.391 oC, is explained by means of the energy emitted from the oceans.
This difference provides crucial information about the amount of energy transferred from the oceans to the atmosphere.
Assuming that the warming occurs in a similar way in the Northern Hemisphere, but allowing a factor of 0.75 for the smaller area of the Northern Oceans, the contribution of the oceans to the total temperature increase in the North can then be readily calculated, as shown in the graph below. This is the “Ocean Effect”.
Northern Hemisphere, revisited, including the Ocean Effect
It will be seen that the sum of the temperature anomalies for the Primary Energy and the Ocean effects gives a value slightly in excess of the measured temperature anomaly.
Projection for the Northern Hemisphere until 2065
If annual energy consumption and ocean warming were to increase at the same rate as the average value over the last 20 years, the increase in atmospheric temperature from 1965 to 2065 levels would be 2.37o C, as shown in the graph below
It would seem that energy considerations alone could account for global warming, so the problem is far more serious than the enhanced greenhouse gas effect attributed mainly to carbon dioxide. Even if continuing increases in concentrations of greenhouse gas levels were to be reduced to zero, temperature rises would still continue unabated because of the continuing energy increases here considered.
It follows that in order to limit temperatures to present levels, it is vital to avoid adding any further energy to the system. This means that all present methods of energy generation must be discontinued, except for the renewables such as solar, wind and wave.
The renewable energy is derived from the Sun, and is ultimately absorbed into the Earth’s system. In using this energy, we are simply diverting it first for our own use, so it does not cause any increase in temperature.
To estimate the possible loss of energy from the atmosphere
Consider a standard column of the atmosphere based on an area of 1square metre of the Earth’s surface.
As before, the number of nitrogen molecules in the column = 2.15*1029 Therefore, for carbon dioxide at 400ppm, number of CO2
molecules = 8.6*1025
From the PNNL spectra at http://vpl.astro.washington.edu/spectra/co2.htm we find that the absorption cross section of a CO2 molecule for a 15 micron photon is 5*10-22 m2 per molecule.
So, in a standard column on 1 m2 surface, the number of photons absorbed = (8.6*1025 )*(5*10-22 )
= 4.3*104 photons / m2
Now, the energy per 15 micron photon = 1.3252*10-20 Joule.
Therefore, the sum total of the absorbed energy
= (4.3*104 )*(1.3252*10-20 )Joule
= 5.7*10-16 Joule
Let us suppose that this energy can be transported to space, and so lost.
But, the collision relaxation time of the carbon dioxide molecule is taken to be 2*10-10 second, so the absorption process can be repeated 5*109 times per second.
So the total energy lost to space by carbon dioxide per square metre of the Earth’s surface could be (5.7*10-16 ) * 2*109 Joule per second
= 1.14*10-6 Joule per second per m2
= 1.14*10-6 Watts per m2
Similarly, for the same repetition rate, it can be shown that the total energy lost to space by water per square metre of the Earth’s surface could be 1.14*10-9 Joule per second
= 1.14*10-9 Watts per m2
These figures must be compared with the rate of supply of energy to the atmosphere from anthropogenic sources.
In the Northern Hemisphere, the energy entering the atmosphere
= 5.148*1020 Joules over 50 years
= 3.265*1011 Joule per second
The surface area of the hemisphere = 2.55*1014 m2
Therefore, the input rate = (3.265*1011) / (2.55*1014) Joule/sec/m2
= 1.28*10-3 Watts per m2
Therefore, although a very small proportion of energy might be lost to space, the re-supply rate at average consumption over the 50 years period is much greater, by a factor of 2.2*105