# The Second Law of Thermodynamics and the Stefan-Boltzmann Law

• jackdale
In summary: Light comes in from the sun and is re-emitted at longer wavelengths, so the absorption profile is different on the way out vs the way in.
jackdale
I have a question about the Second Law of Thermodynamics and the Stefan-Boltzmann law.

“The Stefan-Boltzmann law, a fundamental law of physics, explains the relationship between an object's temperature and the amount of radiation that it emits. This law (expressed mathematically as E = σT4) states that all objects with temperatures above absolute zero (0K or -273°C or -459°F) emit radiation at a rate proportional to the fourth power of their absolute temperature. "

Heat is energy in the process of being transferred from one substance (or object) to another. This process occurs when there is a temperature difference between the two substances. Heat is always transferred from a warmer object to a cooler one." (this is, I think, the gist of the Second Law of Thermodynamics.)

The first statement says that all bodies above 0 K emit heat energy, in all directions I presume.

The second seems to say that when two objects are in close proximity only the warmer body emits heat energy, the cooler body would only absorb heat energy.

Somehow it seems to me that both bodies would emit heat energy, the cooler body would only emit less. What would matter is NET HEAT TRANSFER.

I have found very few mentions of NET heat transfer in reference to the Second Law of Thermodynamics. I keep getting claims from those dismissive of climate science that the GHE violates the Law, because a cool body cannot transfer heat energy to a warm body.

Have I missed something?

BTW - I am not a physicist, so the question might seem naïve.

The Stefan-Boltzmann law was initially empirical, but it can be derived by integrating Planck's blackbody spectrum over all wavelengths. The derivation of Planck's law explicitly uses entropy-maximization to figure out how energy is distributed between different electromagnetic wave modes, so in a sense, the Stefan-Boltzmann law is a consequence of the second law of thermodynamics.

Your question seems to be angling at something else though. If you consider two "blackbodies" that are near each other at different temperatures, both would radiate, and both would absorb energy emitted by the other. However, the cooler one would absorb more energy from the hotter one than vice versa. This has the long-term effect of either both of them converging on a temperature between them and then cooling, or both of them cooling towards the same temperature but the hotter one cooling faster.

I'm not sure I see the connection with climate science here...the greenhouse effect has to do with the emissivity of certain wavelengths of infrared light that are absorbed by atmospheric gasses. Light comes in from the sun and is re-emitted at longer wavelengths, so the absorption profile is different on the way out vs the way in.

Greg Bernhardt
jackdale said:
Somehow it seems to me that both bodies would emit heat energy, the cooler body would only emit less. What would matter is NET HEAT TRANSFER.

I have found very few mentions of NET heat transfer in reference to the Second Law of Thermodynamics. [snip]

Have I missed something?
You haven't. The second law of thermodynamics is indeed statistical in nature. I'm an engineer, not a physicist, so I'm not sure if/how that applies on a QM level with light emission/absorption. However it applies in other places as well, such as a glass of water in a 100% humid room: molecules of water are continuously, spontaneously jumping off of the water surface while others are joining it from the air, remaining in net equilibrium.
I keep getting claims from those dismissive of climate science that the GHE violates the Law, because a cool body cannot transfer heat energy to a warm body.
My morbid curiosity is getting the better of me: what is the argument? Surely there is an obvious misunderstanding in it because it is indeed true that in the net, a cool body can't transfer energy to a warm body, but no such thing happens with the greenhouse effect.

klotza said:
The Stefan-Boltzmann law was initially empirical, but it can be derived by integrating Planck's blackbody spectrum over all wavelengths. The derivation of Planck's law explicitly uses entropy-maximization to figure out how energy is distributed between different electromagnetic wave modes, so in a sense, the Stefan-Boltzmann law is a consequence of the second law of thermodynamics.

Your question seems to be angling at something else though. If you consider two "blackbodies" that are near each other at different temperatures, both would radiate, and both would absorb energy emitted by the other. However, the cooler one would absorb more energy from the hotter one than vice versa. This has the long-term effect of either both of them converging on a temperature between them and then cooling, or both of them cooling towards the same temperature but the hotter one cooling faster.

I'm not sure I see the connection with climate science here...the greenhouse effect has to do with the emissivity of certain wavelengths of infrared light that are absorbed by atmospheric gasses. Light comes in from the sun and is re-emitted at longer wavelengths, so the absorption profile is different on the way out vs the way in.
That's what I thought; what matters is NET transfer. Very few physics sites on the web make that distinction. It seems to be assumed, this creating confusion.

Here is one site that argues that the Greenhouse Effect violates the Second Law of Thermodynamics.
http://hockeyschtick.blogspot.com/2010/07/why-greenhouse-theory-violates-2nd-law.html

Here is paper often cited as proving the GHE violates the SLOT.
https://arxiv.org/pdf/0707.1161v4.pdf

russ_watters said:
You haven't. The second law of thermodynamics is indeed statistical in nature. I'm an engineer, not a physicist, so I'm not sure if/how that applies on a QM level with light emission/absorption. However it applies in other places as well, such as a glass of water in a 100% humid room: molecules of water are continuously, spontaneously jumping off of the water surface while others are joining it from the air, remaining in net equilibrium.

My morbid curiosity is getting the better of me: what is the argument? Surely there is an obvious misunderstanding in it because it is indeed true that in the net, a cool body can't transfer energy to a warm body, but no such thing happens with the greenhouse effect.
Here is a paper often cited as proof that the GHE violates the SLOT:
https://arxiv.org/pdf/0707.1161v4.pdf

jackdale said:
Here is one site that argues that the Greenhouse Effect violates the Second Law of Thermodynamics.
http://hockeyschtick.blogspot.com/2010/07/why-greenhouse-theory-violates-2nd-law.html

Here is paper often cited as proving the GHE violates the SLOT.
https://arxiv.org/pdf/0707.1161v4.pdf
Other moderators may get upset with me for asking, but in any case, thanks. The paper is too long and dense for me to bother with (though it seems to be arguing that the Stefan Boltzmann law itself is wrong). The blog article makes a clear argument:
Since "greenhouse" gases cannot add any energy to the system, or "work input", and are colder than the surface of the earth, they cannot cause additional warming of the earth; they just slow the rate of cooling.
This is obviously nonsense, since "slow the rate of cooling" and "warming" are of course functionally equivalent. Anyone who puts on a jacket before going outside on a cold day knows this!

anorlunda
russ_watters said:
Other moderators may get upset with me for asking, but in any case, thanks. The paper is too long and dense for me to bother with (though it seems to be arguing that the Stefan Boltzmann law itself is wrong). The blog article makes a clear argument:

This is obviously nonsense, since "slow the rate of cooling" and "warming" are of course functionally equivalent. Anyone who puts on a jacket before going outside on a cold day knows this!
Thanks for the confirmation. Even the abstract of Gerlich and Tscheuschner is enough to read. One of my concerns is the number of physics websites that simplify the heat transfer by neglecting the fact that it is NET transfer that matters. Do you know of anything out there that deals with net transfer?

## What is the Second Law of Thermodynamics?

The Second Law of Thermodynamics states that the total entropy of a closed system will always increase over time. This means that energy will always flow from areas of higher concentration to areas of lower concentration, and that it is impossible to create a perfectly efficient machine.

## What is the Stefan-Boltzmann Law?

The Stefan-Boltzmann Law is a physical law that states the total energy emitted by a blackbody is proportional to the fourth power of its absolute temperature. This means that as an object's temperature increases, the amount of energy it radiates also increases exponentially.

## How are the Second Law of Thermodynamics and the Stefan-Boltzmann Law related?

The Second Law of Thermodynamics and the Stefan-Boltzmann Law are related in that they both deal with the transfer and transformation of energy. The Second Law of Thermodynamics explains the direction of energy flow, while the Stefan-Boltzmann Law quantifies the amount of energy emitted by an object based on its temperature.

## What are some real-world applications of the Second Law of Thermodynamics and the Stefan-Boltzmann Law?

The Second Law of Thermodynamics and the Stefan-Boltzmann Law have many real-world applications, such as in the design of engines, power plants, and refrigeration systems. They also play a crucial role in understanding the Earth's climate and the behavior of stars and other celestial bodies.

## Are there any exceptions to the Second Law of Thermodynamics?

While the Second Law of Thermodynamics is a fundamental law of nature, there are some exceptions to it. For example, in certain systems that are not in equilibrium, it is possible for the total entropy to decrease temporarily. However, this decrease in entropy is always accompanied by an increase in entropy in the surrounding environment, thus preserving the overall increase in entropy as dictated by the Second Law.

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