Jo Nova energy balance

SSDD wrote: Bottleneck, by definition, demands a hot spot...where is it?

El Nino
:haha:

El Nino is NOT caused by CO2... The shear ignorance of this post is hilarious..

Please provide evidence for your assumption...

Thats the good thing about assumptions...you don't need no steeenking evidence.....like the assumption that energy spontaneously transfers from cool to warm.

like the assumption that energy spontaneously transfers from cool to warm.

Or the assumption that the 2nd Law says anything about radiation.
 
SSDD wrote: Thats the good thing about assumptions...you don't need no steeenking evidence.....like the assumption that energy spontaneously transfers from cool to warm.

Granny says, "Dat's right...

... ever take a cold one outta the refrigerator an' leave it out?...

... Dat's right - it gets warm...

... it don't get colder...

What do you suppose happens to the air temperature around the bottle granny? Why do you suppose it doesn't get colder? If energy moved from cool to warm, that good old bottle of beer sure would get colder as it transferred its energy to the warmer surroundings. That ole bottle of beer is doing just what the second law says it will do...it is absorbing energy from its warmer surroundings and will keep on absorbing energy from those warmer surroundings till it is the same temperature...or very very close.

What you have there granny is an example of energy moving from warm to cool...if you had an example of energy moving from cool to warm, that bottle would just keep getting colder and colder till it finally got to about absolute zero when at last, it would have no more energy to move to the warmer surroundings.
 
.if you had an example of energy moving from cool to warm, that bottle would just keep getting colder and colder till it finally got to about absolute zero when at last, it would have no more energy to move to the warmer surroundings.

Not true. There are lots of examples of radiant energy moving from colder to warmer. For example a star at 45 thousand degrees will radiate energy to a star at 50 thousand degrees. However the hotter star radiates even more energy the other way. So the net heat flow is from the hotter to the colder as it should be. In short it's a two way energy flow, but a one way heat flow.
 
Wuwei wrote: For example a star at 45 thousand degrees will radiate energy to a star at 50 thousand degrees.

How `bout dat...

... not as hot as a bazillion degrees like Uncle Ferd thought...

... but still pretty hot...

... like Granny says, "Ya learn sumpin' new ever' day."
 
About the OP. There's just something basically wrong with the scientific process when "models" are used that aren't fully discussed and vetted. I know that you can inspect any one of a number of them. But here's what I mean.

You look at other areas that use modeling extensively. For instance in Neurobiology.. You'll find THOUSANDS of papers discussing methodologies, different math treatments, the nuisances of feedbacks, storage and gain specific to that field. Same deal as the Artificial Intell. field I was in. Again THOUSANDS of papers on just the modeling techniques.

Yet -- Climate models are kept close to the vest with VERY little sharing and review and collaboration. Am I wrong? Or is that community now and have been very sensitive to perhaps their shortcomings in modeling expertise?
 
.if you had an example of energy moving from cool to warm, that bottle would just keep getting colder and colder till it finally got to about absolute zero when at last, it would have no more energy to move to the warmer surroundings.

Not true. There are lots of examples of radiant energy moving from colder to warmer. For example a star at 45 thousand degrees will radiate energy to a star at 50 thousand degrees. However the hotter star radiates even more energy the other way. So the net heat flow is from the hotter to the colder as it should be. In short it's a two way energy flow, but a one way heat flow.

Easy to say....now prove it. The SB equation for energy flow is an equation describing a one way flow off energy....and so far as I know...neither the second law of thermodynamics nor the SB equations say anything about net energy flow....energy movement is a gross movement from warm to cool....but if you want to prove otherwise in some observable way, I am sure that there is a nobel in it for you and a rewriting of the second law of thermodynamics.
 
About the OP. There's just something basically wrong with the scientific process when "models" are used that aren't fully discussed and vetted. I know that you can inspect any one of a number of them. But here's what I mean.

You look at other areas that use modeling extensively. For instance in Neurobiology.. You'll find THOUSANDS of papers discussing methodologies, different math treatments, the nuisances of feedbacks, storage and gain specific to that field. Same deal as the Artificial Intell. field I was in. Again THOUSANDS of papers on just the modeling techniques.

Yet -- Climate models are kept close to the vest with VERY little sharing and review and collaboration. Am I wrong? Or is that community now and have been very sensitive to perhaps their shortcomings in modeling expertise?

Being that they aren't modelers they keep the techniques close to the vest because after all, if they make them public...someone will just find something wrong with them.
 
Easy to say....now prove it. The SB equation for energy flow is an equation describing a one way flow off energy....and so far as I know...neither the second law of thermodynamics nor the SB equations say anything about net energy flow....energy movement is a gross movement from warm to cool....but if you want to prove otherwise in some observable way, I am sure that there is a nobel in it for you and a rewriting of the second law of thermodynamics.
Here is a reference from Dartmouth on the SB equation that says that there is a two way flow and it derives the net energy as the difference between the energy emitted minus the energy absorbed..
http://www.dartmouth.edu/~phys17/labs/lab1.pdf

DartmouthSBequation.JPG
 
Easy to say....now prove it. The SB equation for energy flow is an equation describing a one way flow off energy....and so far as I know...neither the second law of thermodynamics nor the SB equations say anything about net energy flow....energy movement is a gross movement from warm to cool....but if you want to prove otherwise in some observable way, I am sure that there is a nobel in it for you and a rewriting of the second law of thermodynamics.
Here is a reference from Dartmouth on the SB equation that says that there is a two way flow and it derives the net energy as the difference between the energy emitted minus the energy absorbed..
http://www.dartmouth.edu/~phys17/labs/lab1.pdf

View attachment 52350


thanks for the effort. it is not the first time cut outs from physics texts, courses or labs have been presented to SSDD. he cannot and will not accept them because if he did then his whole worldview on this topic would collapse.
 
four-pipes-emissions-greenhouse-gas-space-sml.gif


I have been arguing a similar type of explanation for years. a bottleneck at the surface with only 10 micron radiation getting out

Bottleneck, by definition, demands a hot spot...where is it?


obviously at the surface.

are you confusing the predicted mid trophospheric hotspot caused by extra evaporation, hence the positive feedback assumed, for something else? (its not there, btw)

The satellite data shows no surface hot spot..


you claim to be 'all scienced up' but your words say the opposite.

I say there is a radiation bottleneck at the surface-atmosphere boundary. what is my proof?

if the Earth had no atmosphere it would warm up and cool off more quickly as it revolves but the average surface temperature would be lower than it is presently.

if the Earth had an atmosphere of only non-GHGs, the temperature swings from day-to-night would be more moderate because the heatsink of the atmosphere would take up heat during the day and release it during the night. the average surface temp would be higher than the no atmosphere example. already the bottleneck has begun to form, as the atmosphere is returning some of the energy that the surface has imparted to it. at this point remember that all surface radiation is escaping directly into space. the atmosphere is only warming by conduction from the surface, a very limited amount of convection, and some absorption of solar.

now add GHGs, especially H2O, but CO2 and others also have an effect. 90% of the surface radiation is absorbed with only 10% escaping freely. that energy becomes part of the total atmospheric energy and much of it is available as kinetic energy, also known as temperature. we truly have a large bottleneck now. the surface temperature is much higher than the no atmosphere or the non-GHG atmosphere examples. note well that rudimentary equilibrium all three examples have the same amount of energy coming in as going out. the energy to fill the heatsinks has been 'borrowed' from radiation out while moving towards equilibrium.

I say there is a very large bottleneck at the surface/atmosphere boundary, with about 90% of surface radiation used to heat the atmosphere within the first few tens of metres, which in turn returns some of that energy to the surface.


I have said all this many times before. I havent even touched on water vapour and the convection/phase change cycles. Dont believe me? explain how else the surface radiates 400W while only receiving 160W solar input.
 
Easy to say....now prove it. The SB equation for energy flow is an equation describing a one way flow off energy....and so far as I know...neither the second law of thermodynamics nor the SB equations say anything about net energy flow....energy movement is a gross movement from warm to cool....but if you want to prove otherwise in some observable way, I am sure that there is a nobel in it for you and a rewriting of the second law of thermodynamics.
Here is a reference from Dartmouth on the SB equation that says that there is a two way flow and it derives the net energy as the difference between the energy emitted minus the energy absorbed..
http://www.dartmouth.edu/~phys17/labs/lab1.pdf

View attachment 52350

The proper form for the SB equation when a radiator is emitting into its surroundings is
CodeCogsEqn_zps2e7aca9c.gif
. It is the form found in hard physics classes. The form you reference
CodeCogsEqn-2_zpsfee0b3c1.gif
is found in physics for soft sciences and is incorrect. For example, the correct form is found in highly respected texts such as:

Atmospheric Radiation: Theoretical Basis by Goody and Yung
Radiative Heat Transfer by Modes
Radiative Transfer by Chandrasekhar
An Introduction to Radiative Transferby Peraia

The incorrect form can be found in physics for soft sciences such as:

Fundamentals of atmospheric radiation by Bohren-Clothiaux
Assessing Climate Change by Rapp
Advancing the Science of Climate Change 2010, NRC
The Greenhouse Effect by Linden

There are several problems with the version of the SB law that you referenced....adequately overcome them and I will certainly agree with you as you will have the evidence on your side....fail to overcome them and it will be clear that you aren't interested in science so much and are simply another one of the faithful trying to support your religion. The problems are:

  • In your version, you must set T=0 which violates the basic assumption of the SB law which is that T>Tc...
  • Switching the roles alters the description of the physics.. In your version the radiator must become the background. Describe how that might look. Those terms in the equation have actual physical meanings....the radiator simply can not be the radiator and then become the background which is what must happen for your equation to be correct.
  • In physics, when you apply an algebraic law to an equation describing a thing that is happening in reality, one must define a physical meaning associated with the application of the property
  • And finally applying an algebraic property to an already simplified equation is simply poor application of mathematics ...when you have a correct form of the equation
    CodeCogsEqn_zps2e7aca9c.gif
    why would you unnecessarily recomplicate it by writing it as
    CodeCogsEqn-2_zpsfee0b3c1.gif
    . Planck received a nobel for proving the correct version of the SB law when a radiator is radiating into its surroundings...I would imagine that there would also be a prize for proving the altered version of it. Maybe you can prove it yourself or maybe someone has already proven it. Such an accomplishment would be a big deal and would be very easy to look up. So here we stand....me with an equation which has been proven, and you with one which has not and violates the intent of the actual SB Law. Who is more likely right?
I might ask you to answer a couple of questions if I thought you were capable of anything like an honest answer...Hell, lets ask them anyway just to see how honest you are

  1. Which version of the SB equation supports CO2 alarmism?
  2. I can provide Planck's proof of the version of the SB law that describes a gross 1 way energy flow....Can you provide proof of the version that you provide which supposedly describes a net two way flow...we are, after all talking about an equation describing a physical law...proof is necessary if you are going to alter the equation in any way. Got proof?
  3. How do you suppose sting T=0 is valid when the law assumes that the temperature of the radiator is greater than that of the background?
  4. How is applying the SB law twice in the equation (which is what is happening there) either valid physically (the equation is describing a thing that is happening in reality and if you change the equation, you change the reality to unreality without proof) or mathematically?
 
four-pipes-emissions-greenhouse-gas-space-sml.gif


I have been arguing a similar type of explanation for years. a bottleneck at the surface with only 10 micron radiation getting out

Bottleneck, by definition, demands a hot spot...where is it?


obviously at the surface.

are you confusing the predicted mid trophospheric hotspot caused by extra evaporation, hence the positive feedback assumed, for something else? (its not there, btw)

The satellite data shows no surface hot spot..


you claim to be 'all scienced up' but your words say the opposite.

I say there is a radiation bottleneck at the surface-atmosphere boundary. what is my proof?

if the Earth had no atmosphere it would warm up and cool off more quickly as it revolves but the average surface temperature would be lower than it is presently.

if the Earth had an atmosphere of only non-GHGs, the temperature swings from day-to-night would be more moderate because the heatsink of the atmosphere would take up heat during the day and release it during the night. the average surface temp would be higher than the no atmosphere example. already the bottleneck has begun to form, as the atmosphere is returning some of the energy that the surface has imparted to it. at this point remember that all surface radiation is escaping directly into space. the atmosphere is only warming by conduction from the surface, a very limited amount of convection, and some absorption of solar.

now add GHGs, especially H2O, but CO2 and others also have an effect. 90% of the surface radiation is absorbed with only 10% escaping freely. that energy becomes part of the total atmospheric energy and much of it is available as kinetic energy, also known as temperature. we truly have a large bottleneck now. the surface temperature is much higher than the no atmosphere or the non-GHG atmosphere examples. note well that rudimentary equilibrium all three examples have the same amount of energy coming in as going out. the energy to fill the heatsinks has been 'borrowed' from radiation out while moving towards equilibrium.

I say there is a very large bottleneck at the surface/atmosphere boundary, with about 90% of surface radiation used to heat the atmosphere within the first few tens of metres, which in turn returns some of that energy to the surface.


I have said all this many times before. I havent even touched on water vapour and the convection/phase change cycles. Dont believe me? explain how else the surface radiates 400W while only receiving 160W solar input.

Why is the temperature on the surface not steadily increasing....even a little with the ever growing atmospheric CO2....if CO2 created a bottleneck as you claim....even a little one, by definition the temperature would be increasing with the increasing CO2....I might also ask how, if CO2 creates a bottleneck, even a little one how the present ice age ever began with CO2 levels in excess of 1000pm....and previous ice ages began with CO2 levels even higher?
 
SSDD wrote: Thats the good thing about assumptions...you don't need no steeenking evidence.....like the assumption that energy spontaneously transfers from cool to warm.

Granny says, "Dat's right...

... ever take a cold one outta the refrigerator an' leave it out?...

... Dat's right - it gets warm...

... it don't get colder...


oddly

in that sense as it gets warmer

it releases CO2


--LOL
 
four-pipes-emissions-greenhouse-gas-space-sml.gif


I have been arguing a similar type of explanation for years. a bottleneck at the surface with only 10 micron radiation getting out

Bottleneck, by definition, demands a hot spot...where is it?


obviously at the surface.

are you confusing the predicted mid trophospheric hotspot caused by extra evaporation, hence the positive feedback assumed, for something else? (its not there, btw)

The satellite data shows no surface hot spot..


you claim to be 'all scienced up' but your words say the opposite.

I say there is a radiation bottleneck at the surface-atmosphere boundary. what is my proof?

if the Earth had no atmosphere it would warm up and cool off more quickly as it revolves but the average surface temperature would be lower than it is presently.

if the Earth had an atmosphere of only non-GHGs, the temperature swings from day-to-night would be more moderate because the heatsink of the atmosphere would take up heat during the day and release it during the night. the average surface temp would be higher than the no atmosphere example. already the bottleneck has begun to form, as the atmosphere is returning some of the energy that the surface has imparted to it. at this point remember that all surface radiation is escaping directly into space. the atmosphere is only warming by conduction from the surface, a very limited amount of convection, and some absorption of solar.

now add GHGs, especially H2O, but CO2 and others also have an effect. 90% of the surface radiation is absorbed with only 10% escaping freely. that energy becomes part of the total atmospheric energy and much of it is available as kinetic energy, also known as temperature. we truly have a large bottleneck now. the surface temperature is much higher than the no atmosphere or the non-GHG atmosphere examples. note well that rudimentary equilibrium all three examples have the same amount of energy coming in as going out. the energy to fill the heatsinks has been 'borrowed' from radiation out while moving towards equilibrium.

I say there is a very large bottleneck at the surface/atmosphere boundary, with about 90% of surface radiation used to heat the atmosphere within the first few tens of metres, which in turn returns some of that energy to the surface.


I have said all this many times before. I havent even touched on water vapour and the convection/phase change cycles. Dont believe me? explain how else the surface radiates 400W while only receiving 160W solar input.

Why is the temperature on the surface not steadily increasing....even a little with the ever growing atmospheric CO2....if CO2 created a bottleneck as you claim....even a little one, by definition the temperature would be increasing with the increasing CO2....I might also ask how, if CO2 creates a bottleneck, even a little one how the present ice age ever began with CO2 levels in excess of 1000pm....and previous ice ages began with CO2 levels even higher?


good questions. I believe CO2 has had an impact on the temperature of the surface. difficult to discern or tease out of the background of natural variability but it is there. according to Trenberth's cartoon only 25W gets through from the surface to the cloud tops via radiation other than the 10% that leaves directly, unimpeded by GHGs. estimates for CO2's role in the greenhouse effect are about 5-25%. 1W to 6W for the TOTAL CO2 effect from surface to cloudtop. now you have to figure out how much was caused by the previous CO2 concentration and how much by the extra manmade CO2. how much was the original bolus that caused the first 1C increase? are we in the fifth doubling or the tenth?

water, in all its forms, is the joker here. remember the last time you flew to Maui or Barbados? do you recall all the fluffy evenly spaced clouds making shadows on the ocean? Nature's sunglasses. you dont even need to have more of them, just altering the timing of when they form is enough is more than enough to overwhelm any puny change in forcing caused by CO2. Trenberth's cartoon has about 5/8ths of the surface energy getting to the cloudtops via water based routes. they are obviously the most variable and even entities like the IPCC admits they have very little 'certainty' on how they react.

ice ages are triggered by Earth tilts and orbital changes. it is interesting to note that liquid water has existed at the equator throughout history even though the Sun's output was roughly 20% weaker 3 billion years ago.
 
four-pipes-emissions-greenhouse-gas-space-sml.gif


I have been arguing a similar type of explanation for years. a bottleneck at the surface with only 10 micron radiation getting out

Bottleneck, by definition, demands a hot spot...where is it?


obviously at the surface.

are you confusing the predicted mid trophospheric hotspot caused by extra evaporation, hence the positive feedback assumed, for something else? (its not there, btw)

The satellite data shows no surface hot spot..


you claim to be 'all scienced up' but your words say the opposite.

I say there is a radiation bottleneck at the surface-atmosphere boundary. what is my proof?

if the Earth had no atmosphere it would warm up and cool off more quickly as it revolves but the average surface temperature would be lower than it is presently.

if the Earth had an atmosphere of only non-GHGs, the temperature swings from day-to-night would be more moderate because the heatsink of the atmosphere would take up heat during the day and release it during the night. the average surface temp would be higher than the no atmosphere example. already the bottleneck has begun to form, as the atmosphere is returning some of the energy that the surface has imparted to it. at this point remember that all surface radiation is escaping directly into space. the atmosphere is only warming by conduction from the surface, a very limited amount of convection, and some absorption of solar.

now add GHGs, especially H2O, but CO2 and others also have an effect. 90% of the surface radiation is absorbed with only 10% escaping freely. that energy becomes part of the total atmospheric energy and much of it is available as kinetic energy, also known as temperature. we truly have a large bottleneck now. the surface temperature is much higher than the no atmosphere or the non-GHG atmosphere examples. note well that rudimentary equilibrium all three examples have the same amount of energy coming in as going out. the energy to fill the heatsinks has been 'borrowed' from radiation out while moving towards equilibrium.

I say there is a very large bottleneck at the surface/atmosphere boundary, with about 90% of surface radiation used to heat the atmosphere within the first few tens of metres, which in turn returns some of that energy to the surface.


I have said all this many times before. I havent even touched on water vapour and the convection/phase change cycles. Dont believe me? explain how else the surface radiates 400W while only receiving 160W solar input.

A "bottle neck" is a point of resistance.. that point always causes heat. In electrical circuits, water restrictions, air restrictions. Empirical evidence shows, if we had such a bottle neck it must result in heat increase.

Where is this?
 
yes or no.....do GHGs retard in any way the IR radiation given off by the earth's surface?
 
good questions. I believe CO2 has had an impact on the temperature of the surface. difficult to discern or tease out of the background of natural variability but it is there. according to Trenberth's cartoon only 25W gets through from the surface to the cloud tops via radiation other than the 10% that leaves directly, unimpeded by GHGs. estimates for CO2's role in the greenhouse effect are about 5-25%. 1W to 6W for the TOTAL CO2 effect from surface to cloudtop. now you have to figure out how much was caused by the previous CO2 concentration and how much by the extra manmade CO2. how much was the original bolus that caused the first 1C increase? are we in the fifth doubling or the tenth?

Considering the fact that the present ice age began with atmospheric CO2 in the 1000ppm range, logic dictates that the whisp of manmade CO2 had zero effect.

water, in all its forms, is the joker here. remember the last time you flew to Maui or Barbados? do you recall all the fluffy evenly spaced clouds making shadows on the ocean? Nature's sunglasses. you dont even need to have more of them, just altering the timing of when they form is enough is more than enough to overwhelm any puny change in forcing caused by CO2. Trenberth's cartoon has about 5/8ths of the surface energy getting to the cloudtops via water based routes. they are obviously the most variable and even entities like the IPCC admits they have very little 'certainty' on how they react.

As was pointed out in the Nova series...what controls the clouds controls the climate and it isn't CO2...even in a small way.
 
yes or no.....do GHGs retard in any way the IR radiation given off by the earth's surface?

No. Radiatively active gasses are holes in the "blanket" that keeps the earth warm....not the blanket itself. Radiation is a quicker way out than conduction or convection and the simple fact its that radiation is going to move towards cooler...it isn't going to back radiate towards a warmer surface and it isn't going to side radiate and create warmth...it is going to move in the direction of greatest entropy...which is up.

Like it or not, observation bears this out.
 
yes or no.....do GHGs retard in any way the IR radiation given off by the earth's surface?

No. Radiatively active gasses are holes in the "blanket" that keeps the earth warm....not the blanket itself. Radiation is a quicker way out than conduction or convection and the simple fact its that radiation is going to move towards cooler...it isn't going to back radiate towards a warmer surface and it isn't going to side radiate and create warmth...it is going to move in the direction of greatest entropy...which is up.

Like it or not, observation bears this out.

and the simple fact its that radiation is going to move towards cooler...it isn't going to back radiate towards a warmer surface

Smart radiation. I wonder if it would radiate toward the surface if we cooled a sensor with liquid nitrogen? LOL!
 
In your version, you must set T=0 which violates the basic assumption of the SB law which is that T>Tc...

There is no “my version.” It is the version of all scientists. Secondly, T should never be set to absolute zero. T=0 is not found in any natural process under discussion. Thirdly, I have no idea why you would want to set T to zero.

Switching the roles alters the description of the physics.. In your version the radiator must become the background. Describe how that might look. Those terms in the equation have actual physical meanings....the radiator simply can not be the radiator and then become the background which is what must happen for your equation to be correct.

Your statement misses the fact that in a system with an object at any one temperature and a surround at any other temperature, both are radiators and absorbers. The roles are both the same and not altered.

In physics, when you apply an algebraic law to an equation describing a thing that is happening in reality, one must define a physical meaning associated with the application of the property
The difference form of the equation simply means that when the two temperatures are the same, the absorption has the same magnitude as the emission. That idea is in countless physics books.

And finally applying an algebraic property to an already simplified equation is simply poor application of mathematics ...when you have a correct form of the equation why would you unnecessarily recomplicate it by writing it as . Planck received a nobel for proving the correct version of the SB law when a radiator is radiating into its surroundings...I would imagine that there would also be a prize for proving the altered version of it. Maybe you can prove it yourself or maybe someone has already proven it. Such an accomplishment would be a big deal and would be very easy to look up. So here we stand....me with an equation which has been proven, and you with one which has not and violates the intent of the actual SB Law. Who is more likely right?

You have it backwards. The difference form of the equation is a simplification of the two equations that define emission and absorption.

I might ask you to answer a couple of questions if I thought you were capable of anything like an honest answer...Hell, lets ask them anyway just to see how honest you are

Which version of the SB equation supports CO2 alarmism?
Both equations are valid and have been used to define the SB law, as long as you correctly understand what each form means. So, if you want to think that way, both forms of the equation should support both alarmism and skepticism.

I can provide Planck's proof of the version of the SB law that describes a gross 1 way energy flow....Can you provide proof of the version that you provide which supposedly describes a net two way flow...we are, after all talking about an equation describing a physical law...proof is necessary if you are going to alter the equation in any way. Got proof?

Plank refers to a condition of thermodynamic equilibrium, in which
"any two bodies or elements of bodies selected at random exchange by radiation equal amounts of heat with each other."
(Planck, M. (1914). The Theory of Heat Radiation, p. 40 )

How do you suppose sting T=0 is valid when the law assumes that the temperature of the radiator is greater than that of the background?
As I said earlier setting T=0 is not valid. Not in any application in this galaxy.

How is applying the SB law twice in the equation (which is what is happening there) either valid physically (the equation is describing a thing that is happening in reality and if you change the equation, you change the reality to unreality without proof) or mathematically?

A century ago Einstein show a detailed-balance, or reciprocity in absorption and emission of EM energy in atomic systems. It is that reciprocity that requires that the absorption and emission be given by the same mathematical form when it comes to black body radiation. Remember a black body is both a perfect emitter and absorber. In reality emission and absorption are both equally modified in the same way by the emissivity.

If you want to know more, look up “microscopic reversibility” and detailed-balance.”
At equilibrium, each elementary process should be equilibrated by its reverse process.

The short answer is that in the subtractive form the equation can validly represent both absorption and emission, and their roles can be reversed if the temperature difference is reversed.

It is the detailed-balance aspect that is confusing you when the emission and absorption are combined into one equation.
 
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