Why do some people think the atmospheric Greenhouse Effect violates the Second Law of Thermodynamics?

The atmospheric Greenhouse Effect (GHE) refers to the phenomena in which the presence of certain substances in the atmosphere of a planet (e.g., CO₂) tends to increase the average temperature of the surface of the planet.

Some people assert that:

The atmospheric Greenhouse Effect (GHE) “can’t be real because it violates the Second Law of Thermodynamics (2nd LoT).”

As a physicist, I can tell you that this assertion is absolutely wrong.

We might call this erroneous belief the “GHE-2LoT Fallacy.”

If it’s wrong, why do some people believe it?

I’ve been examining that question for a while, and I think I have some insights into how this mistaken belief arises.

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Misinterpretations of descriptions of the Greenhouse effect

When scientists analyze how temperatures behave in a physical system, they do this by applying the fundamental principles of physics, using the language of mathematics.

However, most people don’t understand mathematics. So, when scientists want to describe what their analysis has revealed, they are forced to use verbal descriptions.

Most people prefer a verbal description that is short and avoids technical language. That’s a problem, when scientists are trying to describe something that’s unfamiliar and a little complicated. Short, informal descriptions aren’t good at conveying precise meanings, or including all the details of how things work. This makes it easy for misinterpretations to arise.

Short, informal descriptions of the Greenhouse Effect are often misinterpreted, especially by people who are skeptical about the whole idea in the first place.

Descriptions of the Greenhouse effect tend to include two ingredients that seem to lead to confusion: the word “warms” (or variations) and the term “thermal radiation” (or longwave radiation). It appears to me that people who end up believing the GHE-2LoT Fallacy misinterpret descriptions of the GHE because they:

  • Assume that the word “warms” implies a simple, direct warming mechanism.
  • Fail to distinguish the concepts of “thermal radiation” and “radiant heat transfer.”

I’ll talk about these two issues separately, in the following sections.

Mistakenly assuming a simple direct warming mechanism

People who believe the GHE-2LoT Fallacy seem to read statements such as “The greenhouse effect warms the surface of the planet” and mistakenly conclude that “warming” MUST mean that heat flows from the atmosphere to the surface, raising the temperature of the surface.

This interpretation has the virtue of being very simple. Unfortunately, it’s NOT the meaning that those who understand the GHE intended to convey.

This erroneous interpretation of the GHE is illustrated below.

There is a serious problem with the GHE (as it is misinterpreted): It involves heat flowing from a cool atmosphere to a warm planetary surface.

Yet, the Clausius formulation of the Second Law of Thermodynamics says (glossing over fine points that aren’t important to this discussion):

“Heat cannot spontaneously flow from matter that is cooler to matter that is warmer.”

So, anyone who believes the GHE works as assumed above will understandably conclude that “The GHE can’t be real, because it violates the Second Law of Thermodynamics.”

Thus, belief in the GHE-2LoT Fallacy is a natural consequence of having a mistaken understanding of how the GHE “warms” the Earth’s surface.

* * *

If the picture above was a misinterpretation of the GHE, how does the actual GHE “warm” the surface of a planet?

It’s not a simple, direct process, as was assumed above.

Instead, the GHE increases the surface temperature via an indirect process.

I think it’s helpful to think of that warming process as involving several steps. The first step—before increasing the concentration of “greenhouse gasses” (GHGs) in the atmosphere—is illustrated in the diagram below.

This diagram depicts two overall energy flows:

  • Absorbed Sunlight increases the internal energy of the surface, providing a warming influence on its temperature.
  • Heat flows away from the surface into the atmosphere (via convection, evaporation/latent heat transport, and radiant heat exchange) and into space (via thermal radiation). This heat flow decreases the internal energy of the surface, providing a cooling influence on its temperature.

(The diagram is simplified a bit to support learning. In reality, on Earth, there are also energy flows associated with Sunlight being scattered or reflected, or being absorbed in the atmosphere. This diagram depicts energy flows between the realms of space, planetary surface, and atmosphere; energy flows within individual realms are not included.)

The temperature of the surface will be stable to the extent that the warming influence of Sunlight is balanced on average by an equal cooling influence associated with heat flowing away from the surface.

The “warming” that results from the GHE is most easily understood in terms of a before-and-after comparison: You look at the average temperature of the planetary surface before any changes, you increase the concentration of “greenhouse gasses” (GHGs) in the atmosphere, allow things to adjust, and look at the average surface temperature after those changes. The surface is said to “warm” if the average surface temperature after is higher than it was before.

The above diagram for Step 0 depicted the situation “before” any changes.

The diagram below for Step 1 depicts the situation immediately “after” the concentration of greenhouse gasses in the atmosphere has been increased.

“Greenhouse gasses” (GHGs) are gasses that are capable of absorbing and emitting thermal radiation. GHGs have the effect of reducing the efficiency of heat transport up through the atmosphere and into space. As a result, the surface is cooled less efficiently than it was before the GHG levels were increased.

(Explaining how GHGs have this effect is outside the scope of this essay. I hope to address that issue elsewhere. I’ll provide a link when I do.)

Technically, what I mean by a “reduced efficiency of heat transport” is that, for a given surface temperature, the total upward heat flux away from the surface is reduced. (The idea of “reduced efficiency of heat transport” is similar to the idea of increased thermal resistance.)

As one can see in the Step 1 diagram above, the effect immediately after the concentration of GHGs has been increased, is that the rate at which heat leaves the surface will be less than it had been.

This creates an imbalance between the warming effect of Sunlight arriving and the cooling effect of heat leaving. As a result, the temperature of the planet’s surface starts to rise.

The process concludes with Step 2, as illustrated below.

As the temperature of the planetary surface increases, this increases the rate at which heat flows upward into the atmosphere and out to space.

In particular, the Stephan-Boltzmann Law tells us that the power of thermal radiation emitted grows as the fourth power of temperature. So, radiant heat transport away from the surface increases with temperature. The rate of heat loss via other heat transport mechanisms may also increase.

Eventually, the average surface temperature rises enough that the cooling influence of heat flow away from the surface once again balances the warming influence of Sunlight being absorbed by the surface.

Once this happens, the average surface temperature stabilizes at a new, higher temperature relative to the surface temperature that existed in Step 0.

* * *

One way to crudely summarize the process I’ve described would be to say that:

Greenhouse gasses only warm a planet’s surface indirectly. What GHGs do directly is make radiant cooling less efficient. That less efficient cooling fails to keep up with heating by the Sun, with the result that the planetary surface gets warmer, until it becomes warm enough that heat loss once again balances the arriving Sunlight.

It’s a little bit like being inside on a hot day and turning down the cooling power of your air conditioner. Less cooling leads to a warmer room.

* * *

The three diagrams above summarize the indirect process by which the GHE leads to a warmer planetary surface.

The way I’ve described this might seem a little different than other descriptions of the GHE you’ve seen. There are different ways of thinking and talking about it all. But, this description and other descriptions of the GHE by scientists are equivalent. They’re all offering a view of the same underlying process.

For purposes of this essay, it’s important to notice that in all the diagrams, heat always flows from the warm planetary surface to the cool atmosphere. Yes, as expected, heat always flows from warm to cool! In other words:

  • The Second Law of Thermodynamics is honored by the actual GHE.

As should now be evident, the GHE-2LoT Fallacy is, in fact, a fallacy.

The GHE-2LoT Fallacy is a mistaken belief that only arises when one jumps to a mistaken, oversimplified interpretation of how the GHE warms the surface.

* * *

What we’ve talked about so far explains quite a bit.

However, there is an additional piece of the puzzle which helps to explain why people jump to misinterpretations about the GHE and the 2nd LoT.

Failing to distinguish the concepts of “thermal radiation” and” radiant heat transfer”

This will be a bit more technical than what I wrote about in the preceding section.

Many people don’t understand the relationship between “thermal radiation” (which is often mentioned in descriptions of the GHE) and “radiant heat transfer” (which must obey the 2nd LoT).

Failures to differentiate between these two concepts leads to incorrectly assessing whether or not situations involving thermal radiation satisfy the Second Law of Thermodynamics.

To illustrate the relationship between these concepts, let’s look at radiant heat transfer between two objects. This is depicted below, for object S at temperature Tₛ and object A at temperature Tₐ. The diagram assumes object S is warmer than object A, i.e., Tₛ > Tₐ.

Radiant heat transfer has been well-understood for over a century. The rate at which this mechanism transfers heat from object S to object A is given by the radiant heat transfer rate formula:

dQ/dt = f𝜎𝐴 (Tₛ⁴ – Tₐ⁴)

In this formula, dQ/dt is the radiant heat transfer rate (measured in Watts).

The leading constants aren’t of much importance to our current discussion. But, for completeness, 𝐴 is the surface area of object S, 𝜎 is the Stefan-Boltzmann constant, and f is a dimensionless value called the “radiation configuration factor” (which takes into account the emissivity of the two bodies and the fraction of radiation emitted by one object that reaches the other object).

The most important part of this formula is the factor (Tₛ⁴ – Tₐ⁴), which depends on the fourth power of the absolute temperature of each object. Considering this factor reveals that:

  • If the two temperatures are equal, there is zero net heat transfer.
  • As long as the temperature of S is higher than the If the temperature of A, the heat transfer rate is positive, meaning heat flows from S to A.
  • If the temperature of A ever became higher than the temperature of S, then heat transfer rate would become negative, meaning that heat transfer would occur in the other direction.

Thus, the formula guarantees that heat always flows from the warmer object to the cooler object, i.e., it guarantees that:

  • Radiant heat transfer always honors the Second Law of Thermodynamics.

* * *

“Radiant heat transfer” is a bit of an abstract concept. The underlying physical mechanism for this heat transfer is the exchange of “thermal radiation” (i.e., electromagnetic radiation which is spontaneously emitted by matter at any temperature above absolute zero).

If you examine the above formula for the radiant heat transfer rate, you’ll see that there are two terms. These two terms correspond to the power carried between objects S and A by thermal radiation in each of the two directions.

The power carried by thermal radiation from object S to object A (i.e., emitted by S and absorbed by A) is:

Ps➔a = f𝜎𝐴⋅Tₛ⁴

The power carried by thermal radiation from object A to object S (i.e., emitted by A and absorbed by S) is:

Pa➔s = f𝜎𝐴⋅Tₐ⁴

This exchange of power carried by thermal radiation is illustrated below.

Each object, because it is at a finite temperature, emits thermal radiation with an intensity proportional to the fourth power of its temperature (T⁴), as is required by the Stefan-Boltzmann Law. The object at a higher temperature will emit more radiation. Each object absorbs some of the radiation emitted by the other object.

Thus, thermal radiation carries power (energy/time) in both directions, but more power is carried in the direction from hot to cold than in the direction from cold to hot.

* * *

The radiant heat transfer rate is related to the the power carried by power carried by thermal radiation in each direction as follows:

dQ/dt = (Ps➔a) – (Pa➔s)

In other words, the “heat transfer rate” is the net amount of power transferred, after one subtracts the power flowing backwards from the power flowing forwards.

The first term is proportional to the fourth power of the temperature of object S (i.e., Tₛ⁴), while the second term is proportional to the fourth power of the temperature of object A (i.e., Tₐ⁴).

* * *

The flow of thermal radiation in a single direction is not “heat transfer” – it’s a component of heat transfer. The Second Law of Thermodynamics specifically applies to “heat transfer”, not to the components that add up to heat transfer.

The 2nd LoT is analogous to a guideline advising that “To be financially healthy, your net worth should be positive.” That does NOT mean one can’t have any debts, such as a home mortgage. It just means that to be financially healthy, your assets (such as the value of your home) should be larger than your liabilities.

Similarly, although this surprises some people, the 2nd LoT does NOT mean that thermal radiation cannot carry energy from a cold object to a hot one! The 2nd LoT simply means that the thermal radiation power flowing from hot to cold must be larger than the thermal radiation power flowing from cold to hot.

The bi-directional flow of thermal radiation is essential; it’s nature’s elegant solution to how radiant heat transfer always honors the 2nd LoT.

It’s wonderfully simple: the relationship between thermal radiation and radiant heat transfer guarantees that the 2nd LoT is always honored:

  • Thermal radiation carries power in BOTH directions.
  • The power in a given direction is larger when the temperature of the source object is higher. So, more radiation always flows from hot to cold than from cold to hot.
  • “Heat transfer” is the net power when power in one direction is subtracted from power in the other direction.

This very simple combination of facts combine in an elegant and straightforward way to ensure that radiant heat transfer always occurs in the direction from hot to cold.

* * *

Some people seem to imagine that the above ideas about radiant heat transfer amount to “unproven” ideas drummed up recently as part of a conspiracy to justify the idea of the Greenhouse Effect. Such beliefs ignore the long history of these concepts.

The principles I’ve shared can be verified in any physics or engineering text book that addresses heat transfer.

Everything I’ve reported here about “radiant heat transfer” and “thermal radiation” and how these relate to the Second Law of Thermodynamics has been an established part of the foundations of modern physics for over a century.

In addition to having been verified by countless physics experiments, every single day, the theory of radiative heat transfer is applied and verified in engineering contexts, in situations ranging from industrial processes to managing the temperature of satellites and space probes.

The principles of radiant heat transfer are just as well-established and integral to the foundations of modern physics as the Second Law of Thermodynamics itself.

* * *

How does all of this relate to the GHE-2LoT Fallacy?

As I described previously, the Greenhouse Effect (GHE) involves certain substances in the atmosphere (clouds and greenhouse gasses) reducing the efficiency of radiative cooling of the planetary surface.

The full details of how that works are complicated enough that brief descriptions of the GHE typically offer just a few highlights about how things work.

One detail that descriptions do often allude to relates to radiant heat exchange between the surface and the atmosphere. That heat exchange means that thermal radiation flows both upwards (from the surface into the atmosphere) and downward (from the atmosphere to the surface).

That downward flowing thermal radiation is sometimes referred to as “back-radiation.”

As I’ve described above, a bi-directional flow of thermal radiation is essential to the way that radiant heat transfer works.

However, whenever “back-radiation” is mentioned, people who don’t appreciate the important difference between “radiant heat transfer” and “thermal radiation” freak out.

If one doesn’t understand the elegant relationship between “radiant heat transfer” and “thermal radiation”, it’s easy to look at something like the diagram of “thermal radiation” above, and jump to the incorrect conclusion that:

“Something fishy is going on here! Heat isn’t supposed to flow from cold to hot! That violates the Second Law of Thermodynamics. What I’m being told must be a lie!”

This happens because people don’t understand that thermal radiation in a single direction is NOT heat transfer, and doesn’t and shouldn’t obey the laws of heat transfer.

When someone who is already suspicious about the idea of Anthropogenic Global Warming (AGW) sees radiation flowing in what they believe to be the “wrong” direction, they mistakenly take that as a confirmation of their suspicions.

* * *

Things get even worse if a description of the GHE says something like “radiation emitted downward warms the surface.”

This triggers the type of misunderstanding that I talked about in the previous section.

To someone who doesn’t distinguish between “radiant heat transfer” and “thermal radiation”, words suggesting that “downward radiation warms the surface” is often mistakenly seen as

a “clear and unambiguous” outrageous claim of direct warming, via “heat flow” downward to the (warm) surface from the (cool) atmosphere.

If that belief about what was claimed of was accurate (it isn’t), the claim would violate the Second Law of Thermodynamics—so mistaken interpretation again leads directly to believing the GHE-2LoT Fallacy.

No scientist who understands the GHE would ever intend for such words to be understood in that way. From the perspective of one who understands the science, those words have two reasonable interpretations:

  1. Radiation emitted downward is a key part of a web of dynamical processes which ultimately lead to the average surface temperature becoming warmer; or
  2. Radiation emitted downward is one of the “warming terms” which counterbalance the “cooling terms” in the equations that govern energy balance at the surface.

Either usage of the term “warms” would be technically correct. Unfortunately, neither usage is likely to be fully understood by most readers.

Final thoughts

I think the root problem is that full, precise descriptions of the GHE would be too long and complex to be useful. Such descriptions would tend to exceed the patience and perhaps comprehension abilities of most readers.

So, those offering descriptions of the GHE often must settle for offering a few key pieces of how it all works, with many omissions. This offers an impression or sketch of how things work, rather than a true map.

These informal descriptions get relied on in inappropriate ways. Readers who find it very important to assess the merits of what is being claimed, but are unwilling or unable to examine the underlying physics and mathematics, pour over these descriptions and make false inferences about what is meant. In the absence of trust, those false inferences never get checked and corrected.

Unfortunately, believing that “studying a brief informal description of a complex scientific phenomenon will lead to proper understanding” is a recipe for disaster.

I believe the problem of people believing in the GHE-2LoT Fallacy is ultimately a consequence of the extreme difficulty of communicating about complex technical topics in a context where trust is absent.

* * *

Perhaps belief in the GHE-2LoT Fallacy could be slightly reduced if those describing the GHE avoided the descriptive patterns that I’ve identified as particularly prone to triggering misinterpretations.

However, the GHE-2LoT Fallacy is now so firmly entrenched in the climate-skeptic subculture that it’s unlikely to disappear.

* * *

I hope this essay has been in some way helpful.