Atmospheric Vortex Engine

Frequently Asked Questions 



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9. Earth Energy and Entropy budgets – Advanced Topics 

9.1 How much energy does the earth receive from the sun? How is the energy budget of the earth balanced?

The figure below based on Kiehl and Trenberth shows the earth’s energy budget. Figures are in watts per square meter of earth surface.

trenberth

Link to presentation containing the figures of Energy and Entropy Section 9 of the FAQ in PDF format

The earth receives of 342 W/m2 of short wave solar radiation. The earth reflects 107 W/m2 of solar radiation to space and emits 235 W/m2 of long wave infrared radiation to space. The earth’s surface absorbs 168 W/m2 of solar radiation. The heat absorbed by the earth’s surface is carried upward by convection and by infrared radiation. The total heat carried by convection is 102 W/m2 of which 78 W/m2 is carried as latent heat of water vapor and 24 W/m2 is carried as sensible heat of air. The remaining 66 W/m2 is carried upward by infrared radiation.

9.2 What are some of the earth's major stored energy resources, and how much energy is stored in each?

The earth has numerous stored energy resources. Probably the best known energy resources is crude oil. However, there are also other energy resources which contain even more energy than crude oil reserves.  One of these resources is the latent heat released when the water vapor in air condenses.  Another abundant energy resource is the heat stored in warm tropical oceans.  The figure below shows a relative comparison of magnitude of each of these stored energy resources, including an estimation of the replenishment time for each resource.

These resources are significant since the atmospheric vortex engine process is capable of using latent heat stored in water vapor and also heat stored in warm ocean water as heat sources to fuel the process.

earth energy resources

Higher resolution version of the above figure - PNG (410 KB)

Link to Earth Energy Resources calculation details

9.3 What is entropy?

Entropy is a measure of energy degradation; entropy increases as the quality of an energy source degrades. The entropy of a system can be received or given up from external sources or can be produced internally. The entropy received from an external source can be positive or negative. The internally produced entropy, which is also called internally generated entropy, must always be positive. Entropy received from an external source is essentially equal to heat received or given up divided by the absolute temperature at which the heat is received or given up.

The yellow reflected solar radiation on the left of the energy budget figure of section 9.1 has the same wave length as the as the incoming solar radiation and there is no change in its entropy. The long wave infrared radiation on the right is emitted at a longer wave length than the incoming short wave solar radiation and therefore has more entropy than the incoming solar radiation.

9.4 How is the entropy budget of the Earth balanced?

The next two figures show the overall entropy budget of the Earth. The top figure shows the extrenal entropy fluxes and the overall internal entropy production. The bottom figure shows where the entropy is produced.


earth entropy budget

High resolution version of the above image - PNG 551 KB


earth entropy budget internal production

High resolution version of the above image - PNG 366 KB

The entropy numbers in the above figures were based the figure below from Ozawa et al..

The equation under the figure shows how entropy production is calculated. The sun emits radiation short wave radiation at 5800 K; the earth surface emits infrared radiation at an average temperature of 288 K; and the upper troposphere and the earth as a whole emits infrared radiation at an average temperature of 255 K.

ozawa

The Ozawa figure is redrawn below to make it easier to see where the entropy is produced.

entropy budget

Energy fluxes are shown in square brackets; external entropy fluxes are shown in parenthesis; and entropy production is shown in curly brackets. The numbers in the figure below are the same as in the Ozawa figure except that the entropy units were changed to mW/(K m2) to give whole numbers rather than with fraction.

The external entropy fluxes are shown in red. The overall entropy production can readily be calculated as shown by the first line of the calculation in the Ozawa et al. budget. The entropy emitted by the earth, -940 mW/(K m2), is much higher than the entropy received by the earth, 40 mW/(K m2). The difference is made up by internally generated entropy. The total internally generated entropy shown in orange is 900 mW/(K m2). There are four internal entropy production terms: three absorption terms shown in yellow and one turbulence term shown in green. The orange number is the total entropy production, the three yellows plus the green. The internally generated entropy must make up for the difference between the entropy received and the entropy given no matter where this entropy is produced.

The numbers in yellow are the entropy produced when radiation is absorbed. 95% of the entropy is produced by absorption. Whenever radiation is absorbed, entropy is produced instantly. Energy degradation is instantaneous except for a small part, less than 0.5% which is converted to organic matter by photosynthesis. Nonetheless the organic matter produced over billion of years will be sufficient to meet human energy need for a few centuries.

The green number is the entropy produced when heat is carried upward by convection. Osawa et al. used the name turbulent entropy production to distinguish it from the three absorption entropy production terms. Turbulent entropy production is not an instantaneous process; it occurs when the heat is carried upward by convection as opposed to when the heat is received.

The entropy production that occurs when radiation is absorbed is largely unavoidable. This section of the FAQ will focus on the convection process shown in the following figure. Note that the quantity of entropy produced is the same whether the heat is carried by convection, radiation, or conduction.

ave budget convection 9.5 Can entropy production be avoided?

There is a way of avoiding entropy production and that is to transfer the heat via an engine. The figure below shows what happens if the heat is transferred with a Carnot engine. If the work leaves the system, as shown by the left hand side of the figure, no entropy is produced. If the work is allowed to dissipate, as shown on the right hand side of the figure, the internally generated entropy is the same as without the Carnot engine.

carnot

The engine does not have to be a Carnot engine other ideal cycles can be used. The gravity cycle shown on the figure below accomplishes essentially the same result as a Carnot engine. The cycle is called the gravity cycle because its operation requires gravity; the gas expands as it rises and is compressed as it descends. The operating conditions and the vertical extent of the cycle were selected to make the average temperatures at which heat is received and given up correspond to those in the Osawa et al. entropy budget. Subsiding air is compressed naturally as it descends. The gravity cycle is reversible; there is no entropy produced.

gravity cycle

The reversible gravity cycle in the above figures operates on pure air for illustration purpose but the concept that the work production principle remains valid irrespective of whether the cycle operates on pure air or on humid air. There is potential for converting approximately 12% of the heat carried by convection from an average temperature of 288 K to 255 K irrespective of whether the working fluid is dry air or humid air.

The energy production potential of upward heat convection is enormous. The Energy Production Potential figure below shows that converting 12% of the heart carried upward by convection could produce 3000 times more energy than the total electrical energy produced by humans.

energy production potential

High resolution version of the above figure - PDF 336 KB

9.6 How is the entropy produced? What processes are responsible for producing the entropy? How can the entropy produced always equal the difference between the entropy received and the entropy given up?

An expander must have a shaft to get the work out of the system. Replacing the expander with a restriction, as shown in the next figure, is sufficient to make the process irreversible and restores entropy production. There can be more than one restriction or none. The quantity of entropy produced is the same whether there is one restriction, several restrictions, or no restriction. A turbine is a nozzle wherein the kinetic energy of the exit jet is captured; a restriction is a nozzle wherein the kinetic energy of the exit jet is not captured and is allowed to dissipate. What distinguishes an engine from a dissipation process is the expander – no expander no work. Without an expander entropy must be produced.Without a shaft to get the work out of the system there can be no work - thus the term shaft work.

gravity cycle irreversible

The word expander is used instead of turbine because the expander can be either a turbine or a cylinder and piston. Expansion of a gas in anything except an expander is called free or unrestrained expansion. Expansion in an expander is isentropic; expansion in a restriction or expansion without an expander is isenthalpic.

The temperature of the air at the upper level, at point 4, is higher in the irreversible case than in the reversible case. Frictional dissipation in the atmosphere is generally estimated to be around 2 W/m2, a small fraction of the 12 W/m2 that would be produced by a Carnot engine. Numerical models of the atmosphere usually calculate the temperature of updrafts assuming isentropic expansion. Most atmospheric models have energy deficits of 20 to 35 W/m2 because they do not consider the energy dissipated in unrestrained expansion; see for example Emanuel and and Zivkovic-Rothman .

The primary entropy production process is unrestrained expansion. There are additional slides in the associated presentation below explaining how entropy is produced in unrestrained expansion. The presentation also has slides showing earlier entropy budgets.

Link to a presentation containing the figures in this Energy and Entropy Section 9.0 of the FAQ plus additional figures

For more information on entropy production, see:
Michaud 1996: Heat to work conversion during upward heat convection.Part II: Internally generated entropy method.


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