Monday, February 08, 2016

Temperature Baths


The key to understanding the greenhouse effect is that it is a problem of energy flows, not of energy per se. a zeroth order thermodynamical model in which there are two large (in thermo speak infinite) heat baths, the sun @ 6000 K and space at 3 K. The earth, stuck between these monsters is too small to be a heat bath is better though of as a heat engine, but a very lazy one producing no work on the external surroundings and therefore having to reject an equal amount of heat to space as it absorbs from the sun.

If the heat engine slows down because some thermal radiation is blocked by greenhouse gases, other parts of the spectrum have to heat up to compensate.


25 comments:

CapitalistImperialistPig said...

I think that you might want to rethink this post.

CapitalistImperialistPig said...

To clarify the above, I don't think it's useful to think of the Earth as a heat engine here, for the reason you mention (it's not doing external work). Instead, it's better to think of it as a thermal resistor. What GHGs change is the thermal conductance. See, e.g., https://en.wikipedia.org/wiki/Thermal_resistance

The change in thermal conductance produces a change in temperature drop.

EliRabett said...

Don't think it makes much difference for the simile. The major point is that the Earth is an intermediary between two infinite heat baths, and that if you restrict the flow at one point, you have to open it wider at another to maintain balance.

Nick Stokes said...

"I don't think it's useful to think of the Earth as a heat engine here"
I do. All of weather, all of life, is part of the operation of that heat engine. And Eli puts his finger on what makes it run.

Entropy can be identified with the ability to do work. If a bunch of heat energy moves from hot to colder, entropy change dS means that TdS of work could have been done. And whether useful work was actually done, that amount of capacity is now lost. I wrote a post here tracking the growth and export of entropy from the Earth (it all has to go for steady state). There's followup here and here. Following entropy gives much more insight than just a resistance calc.

CapitalistImperialistPig said...

Nick,

The magic word here is external.. The internal work done on the planet tells us many things, but doesn't give a lot of insight into why GHGs warm the surface of the planet. If you still think it does, I would be interested in an explanation.

Eli - I don't think that's what really happening. The frequencies at which outgoing radiation originate have not changed that much - it's mostly the height of the atmosphere from which they are radiated that changes. On average, there won't be a change in the equilibrium radiating temperature of the Earth, but there will be a change in the effective radiating altitude consequent on the change in the atmosphere's effective thermal conductance.

Nick Stokes said...

"If you still think it does, I would be interested in an explanation."
There is a long version in the linked posts. But OK. GHGs do increase resistance. But a fixed (solar) flux must flow through (by various channels). Resistance increases entropy creation, because greater temperature differences are required. That entropy cannot be destroyed, but must be exported.

So what to do? The balance can be maintained in two ways:
1. Export more. That means the flux must radiate from a cooler surface. But S-B says a cooler surface can't radiate so much. The system can do something here by atmospheric circulation (heat engine). A more uniform TOA temperature exports more entropy for a given flux.
2. Create less. The big creation step is when sunlight is thermalised. As we know, sunlight can do a lot of work, and does do some, eg photosynthesis. But much free energy is lost. If the surface warms, less entropy is created.

That is why it provides insight. Instead of tracking and adding up a whole lot of flux/temp situations, you create a semi-invariant (entropy) which you can do accountancy with.

EliRabett said...

The problem is a to think of the greenhouse effect from a zillion miles. The Earth system is then a black box where you have no way of seeing what happens in the box, but simply have to follow the energy flows in and out of the box. You can take a look at the details of the radiative emission and absorption, but that is about it.

CapitalistImperialistPig said...

Eli - The major point is that the Earth is an intermediary between two infinite heat baths, and that if you restrict the flow at one point, you have to open it wider at another to maintain balance.

Sorry, but that's not what happening. When you put on an extra blanket on a cold night you aren't "opening some channel wider" you are just decreasing the thermal conductance between inside and out and thereby increasing the temperature difference. An exactly analogous increase in temperature difference between planetary surface and effective radiating surface occurs when you increase GHGs. Stuff about opening channels is just BS.

CapitalistImperialistPig said...

Nick - We can certainly agree that the entropy difference between low entropy photons coming in and high entropy photons leaving measures the Earth's entropy production. What I can't see is any simple relation between GHGs and that entropy production. Very similar entropy production would result even if the Earth were a simple gray (or black) body with no atmosphere.

Nick Stokes said...

CIP,
" Very similar entropy production would result even if the Earth were a simple gray (or black) body with no atmosphere."

Yes. And in that case, the entropy all has to be produced at the point of thermalisation, which means it has to be a lot colder there. Snowball Earth.

Fernando Leanme said...

This is just too nerdy for me. I see it as incoming canon balls, some of the canon balls bounce back, some are shatered and bounce back as baseballs. A tiny amount of baseballs falls back, and warms the ocean, the ocean water rises and drowns a few apes eating mangoes on the seashore.

Aaron said...

The original post is spot on. AGW warms the lower atmosphere and the oceans, but it cools the upper atmosphere. Then we have cold heavy air over warm moist air - that is super "atmospheric instability" that generates super weather. And, it is super weather that affects us.

You may not notice a fraction of a degree of warming, but you do notice the super hurricane, or super nor'easter, or super cloud burst, or super drought, that a fraction of a degree of global warming can produce.

Global warming affects all the weather, all the time. Weather attribution is silly. AGW has affected all the weather, everywhere, since 1880.

CapitalistImperialistPig said...

Nick - So far as I can tell we agree on the relevant facts: GHGs warm the planet, but don't make much difference net entropy production.

I think we can also agree that the planet has a lot of heat engines which do interesting things: grow plants, produce weather, etc. Many or most of them could not exist without an atmosphere that includes GHGs.

What I really objected to was Eli's picture of "new channels opening." I still don't much like it, but upon reflection, I can think of a possible example. A greater temperature difference across the troposphere ought to increase the amount of convection. If that really happens, then maybe Eli wins on points, but I still don't like the analogy.

andthentheresphysics said...

Isn't Eli's point relatively simple (or, maybe not :-) )? If you have no atmosphere, then as Nick says (and Nick's post were very useful here), all the entropy is produced on the surface, and it has to be cold. Observed from a distance, the planet would have a spectrum that would probably look like a pure blackbody (or close). As you add GHGs you start to generate entropy in the atmosphere and the temperature at which it is generated is now different. The spectrum, as observed from space, therefore changes, despite the same amount of energy being radiated into space as before. Therefore, a distant observer could distinguish between a planet with no atmosphere, and one with an atmosphere with GHGs and, potentially, could determine the energy flows within the system based on the outgoing spectrum.

Alternatively, I'm confused.

Fernando Leanme said...

Green House gases arent needed, incoming photons are bowling balls, quite a few outgoing photons are baseballs. Baseballs have more entropy.

Hank Roberts said...

... and then there's dribbling ...

-----see if this helps-----

"until a certain height, the atmosphere is opaque (you can't see through it) to IR radiation. Radiation can't make it out into space until it reaches a height where the atmosphere is transparent. As you go higher into the atmosphere, the temperature decreases at a rate of 9.8 ºC/km (this is called the atmospheric lapse rate), and the atmosphere becomes transparent at an altitude where the temperature is 255 K (the calculated temperature of the earth without greenhouse gases!). This is the region where the concentration gases thins out enough for IR radiation to pass into space.
...
... when you add additional greenhouse gases to the atmosphere. When there are more greenhouse gases, the thickness of the opaque layer increases (that is, IR radiation is emitted from high up in the atmosphere). Because the IR radiation is being emitted from a higher altitude, where it is colder, the equilibrium of the radiation system is off balance.

In order to restore equilibrium, the atmosphere must heat up, so that the emission to space is again equal to that of a 255 K blackbody. As the atmosphere heats up, so to does the earth's surface, resulting in global warming.

-----end quote-----
http://beacon.berkeley.edu/GHGs/TheGreenhouseEffect.aspx

andthentheresphysics said...


... and then there's dribbling ...

Huh?


-----see if this helps-----

Yes, if I wanted to explain it in a way completely unrelated to the point of this post, that's pretty much how I would have done it.

Am I missing some point you're trying to make?

Hank Roberts said...

> dribbling
Filling in the basketball part of his analogy, to end that thought.
--------

Then I quoted a clear explanation.

One thing they don't mention --

I understand the wavelength of the infrared photons emitted varies with the temperature of the CO2 molecules -- CO2 radiating infrared from a higher colder altitude is radiating slightly lower-energy longer-wavelength photons, right? Probably a trivial difference?

andthentheresphysics said...

Hank,
I'm not quite sure that I'm getting what your asking or suggesting. My own preference (unlike Nick's :-) ) is to think of energy rather than entropy. If there was no atmosphere, then radiation would escape directly from the surface, which would be cold and the outgoing spectrum would probably be close to a single temperature blackbody. As you add GHGs to the atmosphere, you will have some emission coming from the atmosphere and some from the surface. Given that these cannot have the same temperature, but you still need to emit the same amount of energy into space as before, the spectrum will be different. If you continue to add GHGs, the spectrum will continue to change. Hence, I think, you could argue that an outside observer could use features in the spectrum to analyse heat flows within the system - which I think is what Eli was suggesting.

Kevin O'Neill said...

Absorption spectra of Venus, Mars, Earth (credit Mark Elowitz via Postcards From Planet Earth).

This image, unfortunately, doesn't show intensity on the Y-axis, but that varies as well.

EliRabett said...

Eli agrees in essence with Dr. ATTP, and the image that Kevin O'Neill put up is spectacular (to an old spectroscopist).

Hank, it's not that the frequency shifts to lower values, but that the band narrows.

Brandon R. Gates said...

If the heat engine slows down because some thermal radiation is blocked by greenhouse gases, other parts of the spectrum have to heat up to compensate.

Progressively squeezing one's paw over the business end of garden hose comes to mind. Pressure inside and velocity out increase, flow rate stays the same.

I have a semi-related question for the bunnies. Suppose two equal volumes of gas -- call them a cubic meter each -- at STP, one 100% CO2 the other 100% N2. How does their radiative flux compare to the S-B prediction for a perfect black body?

Bonus question: place both containers of gas on separate 300 W hotplates at 400 K. What is their approximate equilibrium temperature assuming ambient conditions stay constant?

EliRabett said...

Effectively there is no IR radiation from N2. So if you assume that two contained "bubbles" of gas with a given temperature were placed in space the N2 would cool much more slowly.

However, the volumes of gas have to be contained, and assuming that the containers are identical and not IR transparent (e.g. glass) the radiation to the outside will be from the external surface of the container. Then, of course, you have the issues of conduction and convection which depend on details of the coupling to the hot plate and the surroundings.

Finally, heat content of the CO2 will be higher because of the higher specific heat at constant volume because there are 3 modes of vibrational motion rather than one (N2).

Brandon R. Gates said...

Eli,

Thanks for the response. I had considered that the properties of the containing vessel would need to be taken into account, as this was more of a thought experiment I was thinking of them as magically negligible, and radiatively transparent. Now, if the lab were in a vacuum ....

Anyway, I have encountered this question out in the wilds, and my response was that the CO2 container would have the lower equilibrium temperature, the N2 container the higher because the CO2 is a good LW emitter and the N2 is not, consistent with, "So if you assume that two contained "bubbles" of gas with a given temperature were placed in space the N2 would cool much more slowly."

"Aha," say the numpties, "you've just 'proven' the 'greehouse effect' is bunk."

"No," says me, "you just don't realize that all you've done is simulate the situation at TOA, not the surface, albeit at surface-level pressure."

"Well," comes the haughty reply, "everyone knows temperature increases with pressure, that's why it's warmer at the surface. CO2 is what keeps the N2-rich atmosphere from overheating."

That latter argument also explaining why the surface of Venus isn't solid dry ice. And of course totally ignoring that CO2 radiative cooling implies that emitted photons only move outbound and (possibly) are not reabsorbed and thermalized on the way out. Oh, and that perpetual heat engines violates the same 2nd law of thermodynamics they say slays the Sky Dragon.

I think the only thing they get right in this experiment is that the real atmosphere IS indeed getting much of its heat sensibly from the surface (but let's not forget latent heat). What they miss is that without the downward LW flux from those emitters, and that they absorb in the same band, the LW from the surface itself would have a straight shot into the void. All else being equal, surface temperature would be 254 K, not 288 K.

If any of the above is egregiously incorrect, please let me know.

I didn't take specific heat of the two gasses into account, thinking that the radiative effect would be dominant. Something else for me to knoodle.

Brandon R. Gates said...

PS: 100% CO2 at STP might throw a wrench in it ... extinction path at 15 microns would be pretty short, no?