Is there a conflict between Greenhouse Effect and the Second Law of Thermodynamics?

From the editor
July, 2011

Sporadically we are challenged over the reality of Earth’s Greenhouse Effect (GE) on the grounds this represents a heat flow from a cooler to a warmer body and hence violates the Second Law of Thermodynamics (2nd Law).

A superficial reading of the Clausius statement apparently gives some support to the contention of “greenhouse doubters” (I had “deniers” here earlier but I just don’t like that term).

No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.

There are a couple of ways of interpreting that statement. The absolutist (and incorrect) version reads this as meaning every and all conveyance of thermal energy is unidirectional from warmer to cooler and no feedback is possible. The more common generalist version is that net heat transfer is always from warmer to cooler because higher temperature bodies emit more intensely than do lower temperature bodies (i.e., energy export of warmer bodies will always exceed energy import) and thus the sole result of energy exchange is always in compliance with the 2nd Law.

The One Minute Answer:

For Greenhouse Effect to be in violation of the Second Law of Thermodynamics certain conditions must be met:

  1. the atmosphere would need to be a discrete body in order to qualify as a “body of lower temperature” and clearly it is not when considering electromagnetic transmission from sun to earth to space and;
  2. the 2nd Law would have to preclude any feedback (return of energy in any form from atmosphere to non-gaseous surface) that could slow the cooling of the “body of higher temperature”.

Self evidently then all that is required to show that our greenhouse doubters are misdescribing the world and/or misreading the 2nd Law is to show any energy transfer from atmosphere to non-gaseous surface since that would invalidate their concept of discrete bodies with strict mono-directional energy flow.

Since the immediate concern is electromagnetic radiation let’s point first to a visible example of electromagnetic transfer from atmosphere to non-gaseous surface – lighting strikes.

While lightening is a flashy example (sorry) it’s actually trivial when compared with kinetic transfer – think wind-driven waves and sand dunes with atmospheric motion delivering kinetic energy from atmosphere to non-gaseous surface.

Q.e.d. energy feedback from the atmosphere is not merely possible but commonplace and so their required conditions are not met.

The one minute response should be sufficient but, if not, read on for the verbose version.

Let’s look at the absolutist position.

Implied from their contention GE is in violation the 2nd Law is that Earth’s atmosphere constitutes a separate body, which I would suggest is untrue from a radiative perspective but we won’t deal with that extensively here. Sol is the hotter body and is transferring energy via Earth to space, entropy increases and all is well in the universe. Earth’s atmosphere simply constitutes the non-uniform surface of an imperfect black body (gray body) Earth. This, however, will be a most unsatisfactory description for the absolutist. For the absolutist Sol radiates to cooler body Earth, Earth heats cooler body atmosphere and atmosphere radiates heat only to cold of space.

Certainly it is possible to view the atmosphere as a cooler heat reservoir than Earth (or Earth’s non gas surface, since there is no bright line boundary for emissivity) but is it reasonable to conclude there may be no heat transfer from the discrete entity “atmosphere” to the discrete entity “Earth”? Therefore let us briefly explore the concept of separate entities where every and all energy transfer must be from Earth to atmosphere and no transfer is possible from atmosphere to Earth since this would allegedly violate the 2nd Law.

Does Earth ever falsify this scenario?

The answer, of course, is “constantly”.

Now, before keyboards are pounded in anger and beverages are spilled let me lay out a simple and presumably non contentious scenario where at least some portion of energy exported from Earth’s non gaseous surface to the atmosphere is returned to surface and thus invalidates the rigid concept of discrete bodies with unidirectional energy flow:

Some of Earth’s accumulated energy is exported via evapotranspiration (latent and sensible heat loss to atmosphere), clouds form from condensing water vapor, some precipitation occurs and (to make it really obvious) some rain falls on glaciers (snow, ice fields…). The liquid water precipitating out of (falling from) the atmosphere is warmer than our glacier (or snow or ice fields) and by melting same it is undeniably returning some of Earth’s previously exported energy back to Earth – this is a feedback. Does precipitation then falsify the 2nd Law? It doesn’t, of course, since Earth is exporting more heat than it is receiving via feedback and heat flow is still from warmer to cooler but undeniably the atmosphere is returning some energy to Earth and thus keeping it from cooling as rapidly as it otherwise would.

Here’s another one that should not be difficult to envisage: warm air flow over glaciers, snow or ice fields warming and melting their surface. Is this not Earth receiving energy from the atmosphere despite Earth, in toto, being a greater heat reservoir than the atmosphere? I’m sure readers can recall plenty of circumstances like hot air off a desert region heating downwind regions, the heat plume from urban areas etcetera as localized examples of Earth to atmosphere to Earth heat transfer and who has not experienced humid nights reducing rate of heat loss?

In fact Earth transfers a great deal of heat from the tropics towards the poles via the atmosphere all the time. I would suggest this should cause a considerable conflict for those holding the dogmatic stance that there may be no energy transfer from the discrete body “atmosphere” to the discrete body “Earth”.

These everyday occurrences are not contrived and nor do they violate the 2nd Law for the simple reason the 2nd Law does not preclude feedback – read Clausius again:

No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.

On the whole Earth loses more energy to (and through) the atmosphere than it receives from the atmosphere, so heat flow is from the warmer to the cooler reservoir. There should be nothing contentious in any of the above. The key point however is that feedback very obviously exists and that returning some portion of exported heat inevitably results in a reduced rate of cooling and that this reduced rate of cooling results in the exporting body being warmer than it would otherwise have been. You could say this heats the Earth although technically it “less-cools” the Earth.

What the Second Law of Thermodynamics does not say:

In fact there is no mention of feedback nor rate of heating or cooling at all. This is important since the temperature of an object is a function of both energy gain and energy loss.

So what about the greenhouse effect (GE) specifically, surely this would breach the 2nd Law as a “transfer of heat from a body of lower temperature to a body of higher temperature“? Again, this would only be true if GE had the sole result of transferring heat from a cooler to a warmer body but that too would be an incomplete and incorrect understanding of GE.

All matter with a temperature above absolute zero emits electromagnetic radiation due to the conversion of a body’s thermal energy into electromagnetic energy (that’s why it’s called thermal radiation). It is a spontaneous process of radiative distribution of entropy. Overall entropy is increasing as Sol distributes energy to space, Earth is in the emission path of some of this energy and is warmed (you can play with calculators here to derive expected equilibrium temperature under various conditions) and in turn emits to space at a lesser intensity than the sun by virtue of its having a cooler temperature.

Gaia fantasies notwithstanding, Earth does not “choose” to radiate selectively in particular directions any more than the sun or any other object does, they simply radiate in all directions. At the same time as the sun is irradiating Earth, Earth is irradiating the sun, albeit at a much lower intensity. Technically Earth is keeping the sun slightly warmer than it would otherwise be by returning a tiny portion of the energy the sun radiates. This is possible under the 2nd Law because the sole result of the continuous exchange of energy at disparate intensity is the transfer of heat from the body of higher temperature to the body of lower temperature.

Similarly, even though the Earth’s atmosphere is not really a separate body we can view it as a separate heat reservoir and follow the multiple exchanges. The atmosphere is mainly heated by the Earth (although it does absorb a small portion of the sun’s inbound radiation in the least energetic infrared part of the spectrum) and, having a non-zero temperature, also emits thermal radiation in all directions. Since Earth occupies roughly half of all possible emission directions from the atmosphere it necessarily receives roughly half the emissions from the atmosphere. Earth’s non-gaseous surface, being warmer than the atmosphere, emits at greater intensity and maintains the transfer of heat from the body of higher temperature to the body of lower temperature.

Now we come to the part that 2nd Law absolutists really object to.

Greenhouse effect (GE) maintains Earth at a higher temperature than would otherwise be the case but this does not mean the sole result is the transfer of heat from a body of lower temperature to a body of higher temperature. So how can this be?

Recall that the entities involved are actually Sol, Earth and the universe. Entropy is increasing as Sol radiates energy, some of which is absorbed by Earth and radiated at a reduced intensity. No violation of the 2nd Law there.

Recall also that the atmosphere can and does redistribute energy around the Earth all the time and without being accused of violating the 2nd Law in doing so.

So how can the atmosphere increase Earth’s temperature without transferring heat from a cooler to a warmer reservoir?

Let’s see if I can show you. A graphic artist I am not and my graphics generally look like they fell from the top of the ugly tree and hit every branch on the way down, so let’s try with some round numbers.

Assume, for a moment, the sun exports 1,000 units of energy. Earth without an atmosphere absorbs 100 of these (no, it’s not even close to scale). Earth then promptly exports 100 units to space, one unit of which is straight back at the sun. Entropy has increased with Sol’s energy being distributed to the universe with a net loss to the sun of 999 units (1,000 out less one back from Earth), the sun has cooled a little and Earth remains unchanged with however many units it had before.

Does the atmosphere add any heat?

Now let’s add an atmosphere and greenhouse effect: Earth again receives 100 units from Sol and exports exports them, 50 units directly to space (one straight back at the sun) and 50 units to its atmosphere. The atmosphere exports 25 units to space and 25 units to Earth. The sun is still down 999 units (1,000 less 1 back from Earth), Earth still exported the 100 units from the sun, but this time half was to the atmosphere and received a quarter in return. While heat transfer was still from the hot sun to the cooler Earth and from the cool Earth to the cooler atmosphere and cold space 25 units are now returned and temporarily retained by Earth, raising its temperature. No energy was created and none came from the atmosphere – it is all sun sourced. Earth’s temperature has increased and its export rate (emission intensity) will rise according to its temperature until such time as it is again in equilibrium, exporting as much energy as it receives both from the sun and returned from the atmosphere as feedback.

Although the actual mechanism is different the effect is the same as you wrapping yourself in a blanket – the blanket is not a source of warmth and provides no energy but your temperature increases because your rate of heat loss to the universe is slowed. Shrug off your blanket and your rate of cooling increases, lowering your temperature. Likewise Earth’s temperature rises and falls according to changes in the balance and rate of heating and cooling.

Those still unconvinced should think about hikers trapped in a blizzard surviving by digging a snow cave and sheltering therein – the surrounding snow is not a source of heat in any meaningful way but by slowing heat loss it allows the hiker to raise their body temperature to survivable levels. The immediate source of heat is that generated by the occupant of the snow cave from food consumed and their body temperature is determined by the net result of the rate at which they can generate heat and the rate at which they are losing it. The snow keeps the occupant warmer than they would otherwise be despite the obvious fact heat flow is still from the warmer occupant’s body to the cooler snow surrounding. Thus our 2nd Law is still intact even though our snow cave occupant’s body is warmer than when it was not surrounded by snow. Just as our snow cave occupant had a finite energy source (food consumed) but managed to adjust their temperature by altering the energy loss side of the equation Earth, too, has a finite energy source – the sun – but can have its temperature adjusted by altering the rate of energy loss.

Earth’s temperature relationship with its star is slightly more complex than the above description since we have to take into account albedo (the amount of incoming radiation reflected rather than absorbed) but it does roughly approximate black body law. An Earth without an atmosphere would likely be similar to our moon so assuming a similar albedo (the moon reflects about 12% of incoming solar radiation) and adjusting black body calculations accordingly shows us that it would achieve an equilibrium temperature of about 270 K (just below the freezing point of water). Having an atmosphere facilitates bright clouds and snow fields which increase Earth’s albedo to about 30% and using this number without adding greenhouse feedback is how people come up with approximate black body estimates of about 255 K for Earth without an atmosphere (we think using albedo figures including bright clouds somewhat incongruous since clouds require an atmosphere but that it not really important here).

To return to the original question of whether there is a conflict between greenhouse effect and the Second Law of Thermodynamics the answer is no, none whatsoever.

Finally, do claims of no GE fit measured temperatures?

Bluntly, no. Even if the sun had an effective emission temperature of about 6300 K (which would mean our satellites are somehow missing about 15% of incoming solar radiation) Earth could not be as warm as it is without GE unless its albedo was much lower than it is (about 20% lower, which means our satellites are measuring far too much reflected shortwave radiation). For both of these ongoing measures to be so far astray would require not merely NASA but the Japanese, European, Russian and Chinese space agencies to all be either wildly wrong or all colluding in some massive greenhouse conspiracy. I’m afraid I haven’t that much faith in international cooperation ;-)

Disclaimer: No little bunnies were harmed and no energy or matter was created or destroyed in this description of Earth’s altered temperature.