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Utopia Talk / Politics / In which Sam learns of Entropy and work
Seb
Member
Sat Nov 11 04:54:49
A quick recap: all threads in order from latest to earliest.
http://www...hread=81418&time=1510366038823

http://www.utopiaforums.com/boardthread?id=politics&thread=81370&time=1509928219472

http://www.utopiaforums.com/boardthread?id=politics&thread=81315&time=1509928219472

http://www.utopiaforums.com/boardthread?id=politics&thread=81307&time=1509928219472

http://www.utopiaforums.com/boardthread?id=politics&thread=81256&time=1509928219472

http://www.utopiaforums.com/boardthread?id=politics&thread=81179&time=1509928219472

http://www.utopiaforums.com/boardthread?id=politics&thread=81150&time=1509928219472

http://www.utopiaforums.com/boardthread?id=politics&thread=81115&time=1509928219472

http://www.utopiaforums.com/boardthread?id=politics&thread=80996&time=1509928219472

__

Where we had got to in the last thread:

1. We both agree that the power spectrum of radiation radiated by the earth when in power balance will change as a result of increasing CO2.

2. We both agree that there is no difference in the power spectrum of the radiation incident on the earth (measured at the point it first starts interacting with the atmosphere) when in power balance before and after increasing CO2.

3. We both agree that in principle you can calculate the entropy change in the radiation field emitted and incident on the earth, and this entropy change will be different in power balance before and after increasing CO2.

Is that a fair summary so far Sam?



jergul
large member
Sat Nov 11 05:25:03
Seb
Emitted = incident when in equilibrium.
Seb
Member
Sat Nov 11 06:13:07
jergul:

1. The total power emitted is the same, that's not the same thing as the power spectrum. The power spectrum is different, and we can use statistical mechanics to calculate the entropy associated with a power spectrum. I'm not going to suggest we do that, just note that the entropy of the outgoing spectra when the earth system reaches power balance after we increase CO2 differs from before.

2. RE equilibrium, if you would indulge me, I would prefer to be more specific here - we are talking about a power balance rather than a thermal equilibrium. While both are types of equilibrium, I feel it's important to be very clear on the two and using a term other than equilibrium here helps make sure we keep that in mind. The Earth is not in thermal equilibrium with the sun, nor space - rather it is acting as a heat exchanger between the two. The Sun and space can be viewed as isotherms, and, for the purpose of simplicity, we are neglecting cosmic microwave background radiation as negligible, so lets treat space as a giant heat dump into which the radiation field of the radiated energy disappears, never to return.
jergul
large member
Sat Nov 11 09:32:58
Seb
I was just pre-empting sammy.

1. Yepp, the power balance will be different.

2. My problem with assuming equilibrium is that there is no problem if we assume equilibrium. Say we had equilibrium now. Yay global warming limited to about 1C. Paris accord overachieved! The system is not in equilibrium, nor is it projected to ever be in equilibrium. That is the whole problem and the reason why temperatures continue to increase.

The equilibrium is with itself. The heat exchanger is not getting warmer or colder to use your analogy (heat exchangers finding internal equilibrium is actually a real world issue. Start-up of NG cooling for LNG production on Melkøya is prohibitively energy costly. So unscheduled shut-downs are a lot worse than is commonly known).

In sum: I think you should break down your steps some more. Sammy is not going to accept number 3 unless you baby-step him through it.
Seb
Member
Sat Nov 11 09:52:51
I have no idea what you are trying to say jergul.

1. The energy incident on the planet should not change if the sun is constant. Let's assume that for now. In power balance, the earth should be emitting back out what is incident on it.

2. The system "now" is not in power balance - but if GHG gas concentrations were to magically stabilise, in about a century the planet would warm and power balance would then be re-established.

3. I thought he already agreed to point 3 in the last thread. Lets let Sam speak for himself.
jergul
large member
Sun Nov 12 03:31:24
Seb
Yah, I was not saying incident in was changing. The power form out is changing (different wavelengths of energy is leaving). A function of temperature (though a minute change).

Yah, the system is not in balance. Are you sure there is a century delay? The only heatsink of substance is the ocean.

Yah, well, he does not speak for himself that good.
Seb
Member
Sun Nov 12 04:53:03
Jergul:

To examine the principles of what's happening, is easier to zip forward to the future state where a hypothetical power balance has been established.

There are too many free parameters while the temperature itself is increasing.

Its on the order of a century IIRC - many decades at least*. The forcing is about 1.5w/m^2** so it takes a long time to warm up the surface to the point the system takes an "extra" 1.5w/m^2 back up to the top of the atmosphere.

*Obviously, temp rises faster at the beginning then the rate of increase tails off so at some point the tail of the transient response to a one off increase in GHG will be less than the impact of future variables that affect such things. I think centuries is based on looking at the transient response in isolation, and I can't remember how realistic the GHG input was (e.g. how quickly did it plateau). Let's say "many decades".

**I.e. CO2 increase results in about 1.5W/M^2 not leaving the surface that did before, until it's temp rises to the new value that leads to steady state.




jergul
large member
Sun Nov 12 05:57:55
Seb
I did a back of napkin calculation. It takes about 450 years for 1.6 W to heat 4 000 000 kg water and 10 000 kg atmosphere 1 degree.

The 0.9K increase currently measured simply shows that it will take a long time for increased heat to reach beyond the upper levels of the ocean. Though the clock did start ticking a while ago now (say 200 years ago).

So centuries is the correct measure. Particularly as emissions from system also increases as we assume we are trending towards some future equilibrium.

This actually means that global temperatures would fall by more than half a degree over time if we magically stabilized our human contribution today.

No worries though. We are not going to do that.

Interesting to quantify.
Sam Adams
Member
Sun Nov 12 14:03:45
"4 000 000 kg"

You forgot the ocean's communication with the surface stops at the thermocline. Its about 200 000 kg of water. 20 times less. Decades, not centuries.

"and this entropy change will be different in power balance before and after increasing CO2. "

Individual components may change a little. The planetary average will not.
jergul
large member
Sun Nov 12 14:25:55
Sammy
I did not forget (I also checked the 0.1 W from the ocean core). Commercial fishing depends on understanding it.

Your assumption is wrong is all. Because physics.

Seb
Toldya :).
Sam Adams
Member
Sun Nov 12 14:31:49
Obviously you did forget jergul, since you used the entire ocean mass instead of the above thermocline mass.

Your mind is weak.
Seb
Member
Sun Nov 12 14:45:26
Sam:

"Individual components may change a little. The planetary average will not."

I'm sorry, that doesn't make sense. Individual components of what?

The outgoing radiation has a power spectrum. That power spectrum constitutes a partition function (how much energy in each wave band). Changes in the occupancy of that partition function imply a change in entropy.

At this point, we don't care about the world at all. We are looking only at the inbound and outbound radiation field and observing the entropy change between inbound and outbound, and how that entropy change in the radiation field changes after an increase in CO2 when power balance has been restored.

I've helpfully couched this as a yes/no question to avoid confusion.

So, to repeat the question:

Do we agree that the entropy change between inbound and outbound radiation fields will be different in the case before, and after, global warming?
Sam Adams
Member
Sun Nov 12 15:03:19
Entropy could certainly refer to spectrally averaged entropy, in which case no, there is no change once the new equilibrium is reached. If you want to look at a spectral distribution of entropy, then yes there are changes.
jergul
large member
Sun Nov 12 15:08:33
Sammy
Your assumption is wrong. Because physics. It just takes time.

It is also true for CO2 sequestrion in ocean waters.
Sam Adams
Member
Sun Nov 12 15:15:03
Lol. A fisherman who doesnt understand the ocean.
jergul
large member
Sun Nov 12 15:45:11
Sammy
A process that takes centuries has no practical relevance to fishing.



Sam Adams
Member
Sun Nov 12 17:44:44
True, there is no reason why a peasant fisherman should learn things.

Nothing below the thermocline matters much.
obaminated
Member
Sun Nov 12 17:47:25
Its like you guys have nothing better to do.
Seb
Member
Sun Nov 12 17:50:07
Sam:

"there is no change once the new equilibrium is reached."

You are saying there is no difference between the entropy of the outbound radiation field in power balance after CO2 has increased compared to when CO2 concentrations were lower?

Why do you think that is the case? It would only be true if the power spectrum was identical, and you admit it is not. That is clearly wrong.
Seb
Member
Sun Nov 12 17:55:19
What is a "spectral distribution of entropy" - the term is meaningless to me.

I am talking about a bounded volume (integrate the total volume of space in which outbound radiation is travelling over 1 second to get a defined volume) and the frequency distribution of EM radiation therein.

That's a thermodynamic object, with a defined heat content and a defined partition function. That object has a calculable entropy, just as if it was a packet of gas.

We could even treat it as a photon gas actually - a collection of n collision-less particles with a distribution of energies expanding freely into space.

You seem to be trying to pretend this is a sort of "fake" entropy.
Seb
Member
Sun Nov 12 17:59:12
It's a simple yes or no question Sam.

Do we agree that the entropy change between inbound and outbound radiation fields will be different in the case before, and after, global warming?

It sounds to me like you are saying no: the entropy change between inbound and outbound will be identical even though they have different power spectra.

Which clearly isn't right.
Sam Adams
Member
Sun Nov 12 21:30:20
Entropy is not defined by power spectra. You can change power spectrum without changing entropy.

The inbound temperature(the sun) is the same. The outbound (the average radiating temp is the same). Thus entropy in the warmed world is the same.
Sam Adams
Member
Sun Nov 12 21:36:02
You do see how one part of the spectrum increasing would balance out another part that is decreasing. Indeed that is a requirement of equilibrium.
jergul
large member
Mon Nov 13 01:04:18
Sammy
And there comes the weasel words: "matters much".

It matters. It just takes centuries.

"The inbound temperature(the sun) is the same. The outbound (the average radiating temp is the same)."

Lol, you are hopelessly inaccurate sammy (what inbound temperature from the sun?).

The system's temperature is currently 0.9K higher due do greenhouse gases.
Seb
Member
Mon Nov 13 01:21:56
Sam:

So you were wrong when you said the power spectra differed?

Can you define physically what a temperature is please?
Seb
Member
Mon Nov 13 01:23:14
I've not asked about the entropy of the world. I asked about the entropy of the radiation field.

I couldn't have been more specific.
Seb
Member
Mon Nov 13 01:24:23
A helpful thought Sam, what are the requirements an ensemble of particles need to have in order to be said to have a temperature?
Seb
Member
Mon Nov 13 01:44:14
Also, entropy is defined as S=k ln (W) as any fule kno.

Boltzmann had it carved on his grave stone so prosperity would recognise him as being right (his colleagues disputed it, the existence of the atomic world remaining controversial).

As you clearly *didn't* get taught, W is the fraction of microstates corresponding to a macro state given by a partition function.

So we have a partition function, a thermodynamic system (the respective radiation fields). What's the problem?

This is a perfectly sensible way to proceed and how Max Planck calculated entropies of black bodies. So if it's good enough for Max plank it's good enough for you and me.

No, a shift in the spectrum would not balance the other in entropy terms. Consider a radiation field with a planckian power spectrum that in interacting with an object is emitted with a planckian power spectrum where the peak had shifted down, but the total power remained the same?

It's entropy would certainly have increased don't you agree?
jergul
large member
Mon Nov 13 01:47:15
The ensemble must be catholic. Because mass.
Seb
Member
Mon Nov 13 04:37:51
Jergul:

Actually they don't need mass. Just momentum, which photons have.

That means our radiation field has internal energy, an energy distribution, pressure and volume.

You absolutely can analyse it through classical thermodynamics.

jergul
large member
Mon Nov 13 04:58:54
Seb
You can absolutely analyse it through classical thermodynamics. But with respect to Q, not T.

Mass is a precondition for temperature. Space is full of radiation and energy. And very low on temperature.
Seb
Member
Mon Nov 13 08:11:58
That's not true actually, but I'd rather not interupt the flow.
jergul
large member
Mon Nov 13 08:38:26
Just use Q when you mean Q and not T seb.
Sam Adams
Member
Mon Nov 13 09:23:15
Seb, the entropy of the outgoing radiation is the integration of the entire spectrum agree?

You can change portions of the spectrum without changing its average.

Boiled down to the most basic expression of entropy, the outgoing and incoming temperatures are unchanged after the warming world has adjusted to its new equilibrium. Entropies of the whole systems are therefore unchanged.
Seb
Member
Mon Nov 13 09:46:58
Jergul:

Q and T are very different things. There's more Q in the coffee I spilled on my hand even though the spark from my sparkler that landed on it has a higher T, being a dust sized bit of molten iron. Which will give me the nastier burn?

We know the Q of the outgoing radiation. We are discussing S based on the change in power spectrum.

Sam:

The integral of the power spectrum would be the power. Power spectrum is power per fq.
Integrate over all frequency and you get power.

We don't need to know anything about the world. The radiation field is exactly specified by it's over all power and the power spectrum.

Why are you invoking the earth temperature to answer a very simple question?
Seb
Member
Mon Nov 13 10:08:31
So to recap:

1. We agree that in power ballance, the total power radiated and incident will all be the same.

2. The power spectrum of the emitted radiation will differ.

We do not yet agree:

3. therefore the entropy change of the radiation field incident and radiated will differ.

I'm not sure why you don't agree proposition 3, but it looks like because you've confused entropy and the integral of the power spectrum which is just total power, which we agree is the same.
Sam Adams
Member
Mon Nov 13 10:48:14
"Why are you invoking the earth temperature "

Change in entropy equals heat transfered divided by temperature.

If you have the same power AND the same radiating temperature, which we do overall, delta S is unchanged.

I agree that portions of the spectrum undergo changes, but the integrated value is the same.
Seb
Member
Mon Nov 13 13:08:07
Sam:

The integrated value is power, not entropy. We agree the integral should be the same

Do you agree that a change in the power spectrum means the entropy change between inbound and outbound must be different? remember this can be calculated directly from the power spectrum. You don't need to invoke the earth at all.
Sam Adams
Member
Mon Nov 13 14:05:55
"remember this can be calculated directly from the power spectrum."

Yes, by integrating across the power spectrum.

"Do you agree that a change in the power spectrum means the entropy change between inbound and outbound must be different?"

The entropy does not need to change. A change in one portion of the spectrum can (and in thus case is) balanced by other change in other portions of the spectrum.
jergul
large member
Tue Nov 14 02:35:58
"Sammy participates in class, but does not follow instructions well"
Seb
Member
Tue Nov 14 03:39:42
No Sam.

Integrating across the power spectrum gives you power.

A power spectrum is power p as a function of frequency f or wave number l. Integrating this function therefore gives you power.

The integral of the inbound power spectrum and outbound power spectrum are identical.

The only difference in those two radiation fields is the frequencies the power is distributed among.

So are you saying that there is no change in entropy between inbound and outbound radiation?

Sam Adams
Member
Tue Nov 14 09:49:12

"Integrating across the power spectrum gives you power"

Or entropy, when you include temperature as well.



"So are you saying that there is no change in entropy between inbound and outbound radiation? "

Nope its the same. Same average temperatures. Same power. =same entropy.
Seb
Member
Tue Nov 14 11:13:32
Sam:

How, exactly, do you include temperature here?

"Nope its the same"

You think the temperature of the incident radiation and the radiated radiation is the same? Are you sure about that?
Seb
Member
Tue Nov 14 11:16:09
Let's say you have two different power spectra

P1(f) and P2(f) such that Integral [P(f)] = U

How are you defining the temperature of the radiation?
Seb
Member
Tue Nov 14 13:34:04
Sam, another question.

Suppose you had a radiation field from an unknown body. How would you measure the temperature of the radiation field?
Sam Adams
Member
Tue Nov 14 13:40:57
"You think the temperature of the incident radiation and the radiated radiation is the same? Are you sure about that?"

Yup.
Seb
Member
Tue Nov 14 13:44:34
Sam, I'm really flabbergasted here. I'm not sure you've read that sentence properly.

You are saying that you think direct sunlight has the same temperature as radiated IR?

If so, I don't really know what to say other than "that is totally wrong".
Seb
Member
Tue Nov 14 13:51:34
I mean, previously you've been saying that the temperature of the radiated emissions from earth is the temperature of the upper radiating level.

In which case surely the temperature of the inbound radiation should be that of the surface of the sun?
Sam Adams
Member
Tue Nov 14 14:52:08

In which case surely the temperature of the inbound radiation should be that of the surface of the sun?

Indeed. I meant the same between the two states. Warmed planet and not.
Seb
Member
Tue Nov 14 15:12:51
Phew, that's a relief (aren't you glad I don't behave like you and start saying you think something bananas when you've obviously just misread).

Ok, so how do you measure the temperature of this radiation field then?

You are a martian, floating in space, and you detect this radiation field - how would you measure it's temperature?

Sam Adams
Member
Wed Nov 15 08:55:31
By the peak of its power spectrum.

Ok, now for you. Imagine 2 different power spectra. Spectrum 1 is simple. 100w coming from a radiating surface at 250k (which itself would be a spectrum but for now lets consider it a point source for simplicity). Spectrum 2 is only slightly less simple. 50w at 200k and 50w at 300k.

1 and 2 have...

Different spectrum. Same power. Same average radiating temp. Same entropy.
Seb
Member
Wed Nov 15 13:01:04
So a beam of laser light with all its power in say, 1050 nm and a gausian profile with a half width of say, 5nm has the same temperature as a planckian distribution peaking at 1500nm?

Is that what you are saying?
Seb
Member
Wed Nov 15 13:02:39
Because again, you are talking about the radiating surface, and you don't need to know anything at all about the radiating object here.

The thermodynamic properties of the radiation field are self contained.
Seb
Member
Wed Nov 15 13:04:54
I think what you appear to be saying is the entropy of a radiation field is determined by its power spectrum.

Temperature being a parameter that correlates to certain shapes of power spectra.
Sam Adams
Member
Wed Nov 15 14:25:52
I think you can figure out entropy from just power spectrum. I dont think you need to know emissivity, but i have not thought through that completely.

But a change to the power spectrum does not need to change entropy... that i am 100% on.
Seb
Member
Thu Nov 16 01:51:54
So, for example, a Gaussian power distribution with the same peak frequency would have the same entropy as planck distribution of the same area and peak?

Are you sure about that?

If you took a gas, and plotted the energy distribution of the atoms in a similar way, changes to that would definitely require entropy to change. Let's imagine a gas where half is thermalized, but there's a strong current of circulating current of fast moving air so there's a fat upper tail. That clearly has a different entropy content.

Sam Adams
Member
Thu Nov 16 09:04:41
"So, for example, a Gaussian power distribution with the same peak frequency would have the same entropy as planck distribution of the same area and peak? "

Not necessarily, no. You can certainly change the power spectrum such that entropy changes do occur. You can also change it in a way that entropy does not occur, such as our atmospheric case.
Sam Adams
Member
Thu Nov 16 09:05:20
That entropy *change* does not occur.
Seb
Member
Thu Nov 16 09:21:33
Could you give a worked example of that being the case?

The formal definition of entropy suggests that actually that's not possible. It would physically mean that for a given macro state, non thermal power spectra with the same total power could have the same liklihood. I.e. that would imply that for any arbitrary power spectrum is likely that there's a corresponding black body that would emit that power spectrum rather than its corresponding planck distribution.

Not much evidence of that.
Sam Adams
Member
Thu Nov 16 09:41:13
Ahh, but the atmosphere is not a blackbody. We have different compounds at different concentrations at different altitudes and temperatures. Theres a wide variety of jacked up looking spectrums we can create with that.
Seb
Member
Thu Nov 16 13:21:33
Sam:

Again, the atmosphere at this point is completely irrelevant.

There's nothing magical about the atmosphere.

Your argument hinges so far on a fundamental point of physics.

The question here is: can two power spectra have the same entropy for a given heat content.

This is analogous to saying two different ensembles of ideal gas particles with the same total internal energy but different distribution functions for momentum can have the same entropy content.

I think that is wrong, and I've explained why I think it is wrong: it would mean a hypothetical black body could emit multiple different spectra rather than a single plank distribution.

This is a bold assertion on your part, and before we can move on to talking more about the interaction between the earth and the radiation field it emits, this is a point we really need to lock down.

Can you give a worked example - i.e. a formal mathematical treatment - of two radiation fields with differing power spectrum but same overall energy content and show they have the same entropy?
Sam Adams
Member
Thu Nov 16 13:48:17
"it would mean a hypothetical black body could emit multiple different spectra"

I do not see how this is implied at all, considering i am talking about something that is very not a blackbody.

See my post of yesterday at 0855 for a very simplified example.
Seb
Member
Thu Nov 16 13:57:17
Sam:

It would, because the reason a black body emits that particular spectrum is made on entropy grounds. c.f. Wein and Planck.

Now if there are two corresponding spectra that have the same power, same entropy content, but different power spectra, then we need a new reason it emits a Planck distribution rather than this hypothetical other spectrum of the same power, same entropy but different distribution among frequency components.
Seb
Member
Thu Nov 16 14:17:25
Regarding your example, there is a difference.

S=4/3 U/T

So for 100W at 250k:

S= 0.53

Whereas in case two overlapping spectra, it would be S=0.89.

Sam Adams
Member
Thu Nov 16 14:28:34
From causius...

S=heat/temp

No?
Sam Adams
Member
Thu Nov 16 14:29:42
Heat transfer, that is.
Sam Adams
Member
Thu Nov 16 14:38:18
In which case 100/250 almost exactly matches 50/200 + 50/300. .4 to .415. I could definetly jigger with more to make it even closer.
Seb
Member
Thu Nov 16 16:16:05
It's a little more complex for radiation, it's an irreversible reaction.

But the form is similar:

Let's say Q/T

So in case one you have 100/250=0.4 , in case 2 you have 50/200 + 50/300 = 0.25 + 0.17= 0.42
Seb
Member
Thu Nov 16 16:20:53
What do you mean you could "easily jigger with it"

You want to get a/b = x/y + w/z
Such that a = x+w and b = (y+z)/2

Being close doesn't cut it
Seb
Member
Thu Nov 16 16:25:33
I'm shatterd and drunk right now but I'll think you'll find that's a mathematical impossibility
Sam Adams
Member
Thu Nov 16 16:41:35
Ok, it cant go to 0. A power spectrum change does create non zero entropy change. I will concede that. But it can be very near 0.
Seb
Member
Fri Nov 17 10:36:33
That's a heck of a concession Sam.

The obvious implication of the same heat flow resulting in a larger increase in entropy is that as I said earlier, changing the emmissivity (even at only a few wavelengths) does mean the same inbound radiation field can result in result in more or less work being done on the system (this isn't surprising, we are after all changing a key property relating temperature and heat flow).

You described this a "magical choice" and that it was a violation of thermodynamics, an argument from fundamental principle.

Now you accept that it is entirely reasonable consequence of physics.

You also argued any change of work would be limited to the transient response period, but again, we can see that by physical necessity it must continue in steady state.

Granted, we are a way off showing that this effect would drive temperature gradients change, but your argument that it doesn't because it violates the law of physics is clearly not sustainable.

I'm driving to France now. We'll start to get into this radiating surface next.
Sam Adams
Member
Fri Nov 17 11:40:29
I will concede that i should have said ~0 instead of exactly 0. This is a very minor effect though, on the order of <0.1% in global warming scales, which for practical weather, is 0.
Seb
Member
Fri Nov 17 11:57:19
Sam:

Your argument wasn't about scale, it was about it being fundamentally impossible due to thermodynamics.

Before you were saying "this is a fundamental violation of thermodynamics, it is impossible for it to happen." and indeed claiming it meant I had "forgotten" thermodynamics.

Now you are saying "ok, it's not a violation of thermodynamics, but I think it is too small to be relevant".

That is a categorical difference in position and it seems, in the end, I understand thermo better than you do - and also that my thread titles are more accurate!

We'll move to the next point tomorrow.
Sam Adams
Member
Fri Nov 17 12:06:48
It was certainly impossible to do what you were asking of it... noticeable changes to the outgoing energy balance. To the first few orders, you were wrong. I'll be perfectly happy to concede meaningless low order effects so long as you learn the overriding pattern.
Seb
Member
Fri Nov 17 14:17:27
Sam:

One is an argument of scale. Another is an argument of the laws of physics.

Perpetual motion machines are impossible. Not even a little bit.

It's a bit disturbing you don't see the difference.

You were 100% wrong in arguing that it was physically impossible.

We'll move on to scale tomorrow - but first lets have a brief chat about the upper radiating surface you keep referring to.

Can you state to me the physical definition of the upper radiating surface and how you determine what altitude it sits at?
Sam Adams
Member
Fri Nov 17 15:15:51
No seb, the impossibility of your extra work does not change. That very minor spectral entropy distribution difference would instead cause the most minor of radiating level temperature changes such that outbound entropy would be the same as before.

The effective radiating level is merely the median of the outbound power spectrum... and the temperature/altitude to which that corresponds.
Seb
Member
Fri Nov 17 15:25:02
Sam:

"the impossibility of your extra work does not change."

You've just accepted that:

1. The difference between the inbound and outbound power spectrum changes.

2. That change requires an increased entropy change

3. Thermodynamicaly, a simply analysis treating the radiation as heat demonstrates that more work must being done.

Not only is increased work possible, it's actually impossible for it not to be the case.

The only remaining question is what it's scale is.

Something being small is not the same as something being impossible.

But so far you've not quantified any of this, and shown no basis for what constitutes small. So we can leave that to be for now.

On to the radiating surface.

"The effective radiating level is merely the median of the outbound power spectrum... and the temperature/altitude to which that corresponds."

Explain specifically how you make the correspondence.





Sam Adams
Member
Fri Nov 17 15:38:23
"That change requires an increased entropy change"

Or a temperature change.
Seb
Member
Fri Nov 17 15:44:54
Sam, think about it.

We were talking about the power spectra after power balance has been achieved.

The earths temperature and atmospheric temperature profile is stable at that point.

Yet we can see that because the entropy change between the inbound and outbound radiation is higher than previous, more work must be being done than previously. Even after power balance.

And because we are in power balance, we know it's not raising temperature.

Now that doesn't prove it's going into weather, nor does it quantify how high it is.

But earlier, you were arguing that it was aerodynamically forbidden and arguing it could was tantamount to magic.

And now you have come to realise that actually it is a physical necessity, but assert without evidence that it's too small to care about.

Anyway, moving on - because this is over now - radiating level.

Explain how you make the correspondence.
Sam Adams
Member
Fri Nov 17 15:50:25

"Yet we can see that because the entropy change between the inbound and outbound radiation is higher than previous"

No. That is still impossible. The entropy/work cannot change, as that is the definition of equilibrium. The radiating temp would have to change slightly.
Seb
Member
Fri Nov 17 17:37:52
Sam:

"The entropy/work cannot change, as that is the definition of equilibrium."

1. You say that, but you've agreed to every point raised so far on multiple occasions. You have incident radiation, outbound radiation, and the earth. There's nothing else in the system. And we can see from the inbound and outbound radiation that there is now a greater increase in entropy than before.

What you mean is "I don't want this to be true because it ruins my argument."

2. The mistake in your thinking is that you believe that the Earth is in thermal equilibrium. You are wrong. It is in power balance, which is different.

Earlier, you tried to argue the earth was in thermal equilibrium with itself. That's why I've insisted in the above discussion we treat the earth as a single object and look only at the inbound and outbound radiation that bounds the system.

The earth can be modeled to a very high degree of accuracy* as a heat exchanger between two isotherms: the sun at 6k, and space at about 3k. Energy is constantly flowing from the Sun, through the earth, and out into space.

And we can see precisely because there is a power flow from the sun through the earth and out into space that the system is definitely not in thermal equilibrium. And because the inbound and outbound radiation represent the boundary conditions for the earth as a system in itself, we can see that additional work is being done on it on a continuous basis in stead state after CO2 has been increased.

The fact in power balance the temperature of the earth is constant doesn't mean that work isn't being done here. Your assumption of thermal equilibrium is flawed.

And this ought to be obvious: as you yourself have pointed out, organised structures like hurricanes represent energy from the sun doing work - but that energy ends up as heat which is then also radiated such that the same total power is radiated "at a lower temperature" than previously.

Consider this: if there were no greenhouse effect at all - say the atmosphere was pure argon - there would still be an "upper radiating level" at the same temperature as before. There would still be the same power output as before. But the world would be a lot colder, and there would be a lot fewer hurricanes. And the outbound power spectrum while having the same overall power would have a smaller difference in entropy from the incident radiation.

Now here's the important thing: all temperature is is a measure of how energy is distributed within an ensemble of particles. It's only accurate when we are talking about maxwellian distributions of particle velocities or a planckian power spectrum for radiation. At it's most fundamental level, temperature is an emergent quantity and is a parameter defining a particular distribution of energy that systems relax into due to equipartition.

So when we talk about a shift in the power spectrum, we are absolutely talking about something very similar to a change in temperature. In fact, temperature is a special case of distribution of energy in system, and a change in temperature is a special case of a change in distribution. Your mistake is to view it as fundamental, and the frequency shift due to emissivity as a minor weird complication. This is because you are working from an incomplete understanding of classical thermodynamics downwards, rather than statistical mechanics upwards.

Anyway, it's pointless having this argument now - you've agreed to every proposition and the logical conclusion, whether you want to accept what you have agreed to is nor really important.

If you really want to, you need to explain why, if the earth is in thermal equilibrium, that the inbound and outbound power spectra differ at all. They wouldn't if the earth was in thermal equilibrium with its environment.

Lets move on to the radiating surface. How, exactly, does it's temperature correspond to the outbound radiation spectrum and power?

*we haven't modeled CMBR, starlight etc.
Seb
Member
Sun Nov 19 10:43:11
Ttt
Sam Adams
Member
Mon Nov 20 10:44:18
"there is now a greater increase in entropy than before."

No. I agreed entropy must change if the spectrum is different, and power and temperature are equal.

For our planet, radiating temp will change slightly in the new equilibrium, such that entropy does not change. Emphasis on slightly.
Seb
Member
Mon Nov 20 17:34:13
Sam:

Two major mistakes here.

Firstly, Temperature and spectrum are the same thing - not independent things. There is therefore no way you can keep the temperature but change the spectrum.

Secondly, if U - the energy content in the power spectrum - is constant, and T/spectrum is changing, then by definition: S=Q/T.

As the IR emitted by the earth is the dissipated heat then you have S=4/3 * U/T where U is the internal energy of the radiation field (i.e. the power it contains) and T the temperature of the field.

Given that S_incident = 4/3 U/T where U is the incident power (which we are assuming is constant) and T is it's temperature (that of the sun, also assumed constant) - then the only way your Delta S = (S_incident - S_emitted) = const can be achieved is if U_emitted dropped in correspondence with T_emitted. However as the condition for power balance here is U_emitted = U_incident. Anything else and then the Earth would no longer be in power balance and there would definitely be free energy at the earths surface.

So, to go back to the first point:

The Temperature is just denoting a particular power spectrum. Because the segments of the power spectrum that change in the case of global warming are not well characterised by a Planckian distribution (i.e. black body) - any attempt to understand the impact of GHG and radiative forcing by using radiating temperature will necessarily fail because it ignores the fundamental physical mechanism by which it works.

As I pointed out, because the radiating temperature is defined by taking the total power emitted by the earth, and then saying "ok, what temperature would a black body need to be to emit this power" - the radiating temperature is absolutely constant if the earth is in power balance and the incident power on the earth is constant.

If you removed the green house effect entirely (i.e. even the natural GHG that keeps the earth from being the iceball it would otherwise be) by replacing the atmosphere with a suitable gas, then the radiating temperature would be precisely what it is now. The only thing that would change would be it's height, and that only because the temperature profile in the atmosphere is determined by radiative transport.

The earth isn't a black body - the critical bits of the spectrum are very very far from a black body spectrum.

The radiating temperature and level are convenient approximations that work well for modelling weather, but are not good enough and do not include the necessary physics to understand the impacts of climate change.

Finally, there is simply no physical reason why the system should adjust itself so as to give no change in work.

Asserting it must do so is simply arguing your pride is somehow a driving law of physics.

At this point, having been confronted with the mathematical impossibility and physical absurdities, you are starting to look like the drunk driver that is searching for his keys down the street, away from his car and under the lampost because that's where the light is.


Seb
Member
Mon Nov 20 17:47:30
* point of clarification - in the above I've used S=4/3 U/T which is what you use if you have a black body spectrum.

If you don't have a black body spectrum, to put it bluntly, you can't use S=4/3 U/T because the U/T term in the formal derivation no longer emerges.

You would get some horrible summation/integration over frequencies instead.

But basically this idea you can alter the power spectrum but keep using the temperature of the black body that best fits the peak of the distribution is physically inconsistent and gives a very wrong answer.

Sam Adams
Member
Tue Nov 21 16:20:52
Seb, i think you need to learn that equilibrium means the various layers of the atmosphere settle into a temperature such that there is no change in entropy. This is the definition of equilibrium.

I agree that the radiating temperature is no longer equal to what it was due to the changing power spectrum, but thats a very minor deviation you are whining about, like a 4th order error in my assumptions, and is utterly irrelevent to the values that it does change. It does not affect what you want it to at all.
Seb
Member
Wed Nov 22 01:55:18
Sam:

No. That's not the definition of equilibrium, nor is it the kind of equilibrium the earth is in. "The atmosphere is in hydrostatic equilibrium" isn't the same as "the earth is in thermal equilibrium with the sun and space". The above analysis doesn't even care about the distribution of power in the atmosphere. By simple thermodynamic analysis of the earth's boundary conditions we can see that more work is being done - as you define it.

We're your statement re equilibrium true, there would be no heat flow in the atmosphere and no ability to drive weather which you have characterised as being driven by work extracted from gradients.

If there is no entropy change, there can be no work done unless hurricanes are reversible processes.

At least,in so far as you have previously related work, entropy, weather and temp gradients.

Indeed you entire argument has been driven by the idea that temp gradients can't increase because it would increase work done (which implies an entropy increase is occurring while the current baseline of work is being done).

"Very minor"
1. Is not the same as "fundamentally impossible" - which you previously argued.

"It's nearly impossible, I meant nearly impossible!!". Are you the supporting comic act in a family movie?

2. Prove it. Doubling hurricane frequency is less than a rounding error on solar flux. I suspect you are using the wrong baseline.
Sam Adams
Member
Wed Nov 22 11:03:41
Seb think about the blatant thermo violation you are trying to do. You are asking for more work to be done on the atmosphere/earth without any change in temperature.
Sam Adams
Member
Wed Nov 22 11:07:08
"Prove it. "

Ok. Look at the hurricane graph. No change.

"Doubling hurricane frequency is less than a rounding error on solar flux"

Utterly false.
Seb
Member
Wed Nov 22 13:09:50
Sam:

No, we've just been through this.

We can see that the entropy content of the outbound radiation is greater than before thanks to the frequency shifts. Insofar as the outbound radiation has a temperature (it's non B&B spectrum so using a temperature to characterise the energy distribution of the radiation field is just wrong really), it's changed.

Not only is this consistent with more work being done. It's actually a thermodynamic requirement that more work be done.

Thermodynamics says the opposite of what you've been arguing.

Looking at the hurricane graph now proves nothing. We are at the very beginning of the transient response and most additional work at this point is being done on sinks. Surface warning, ice melting etc.

How much energy in a hurricane Sam?
werewolf dictator
Member
Fri Nov 24 19:12:10
you two are on like your tenth thread.. after a big hurricane season that killed like a measly 250 americans.. like it matters whether there is no change in hurricane graph or whether you can squint hard enough and believe global warming killed an extra 10 people or something..

meanwhile in stuff that actually matters..

http://www...eases/2015/05/150520193831.htm

“Cold weather kills 20 times as many people as hot weather, according to an international study analyzing over 74 million deaths in 384 locations across 13 countries. The findings, published in The Lancet.. The study analysed over 74 million (74,225,200) deaths between 1985 and 2012 in 13 countries with a wide range of climates, from cold to subtropical.. Around 7.71% of all deaths were caused by non-optimal temperatures, with substantial differences between countries, ranging from around 3% in Thailand, Brazil, and Sweden to about 11% in China, Italy, and Japan. Cold was responsible for the majority of these deaths (7.29% of all deaths), while just 0.42% of all deaths were attributable to heat.“

_____

being on earth with you two is like being locked in a freezing house with people having fingers and toes amputated from frostbite.. and having to listen to two people endlessly argue whether you should turn heat on because you might have a heart attack on the way to the thermostat
Sam Adams
Member
Sat Nov 25 10:25:21

"We can see that the entropy content of the outbound radiation is greater than before thanks to the frequency shifts. "

That would be the case only if the temperature does not shift as well.

I agree with you that a spectrum change while holding temperature and power constant would change entropy. But temperature changes in the case of our atmosphere.
Sam Adams
Member
Sat Nov 25 10:29:53
If the planetary temperature is stable, then the work done on the earth by the sun is equal to the work done on our surroundings by the earth.

You cannot violate the fundamental thermo laws.
Seb
Member
Sun Nov 26 04:04:45
Sam:

Nonsense. All temperature means for radiation physically is "distribution of energy of em radiation amongst frequencies". Ditto for particles - it refers to the distribution of energy between kinetic modes in an ensemble of particles. Where that distribution is non planckian for radiation, or non Maxwellian for massive particles, temperature has a poorly defined meaning.

It's scientifically illiterate to say that the power spectrum changes but is offset by the temperature. The power spectrum *is* the thing that matters, temperature only matters in so far as it characterises that power spectrum.

In the case of global warming, we've established it doesn't represent the power spectrum.

The fact you treat them as distinct parameters shows you just don't understand what temperature is, how thermodynamics is a bulk expression of statistical mechanics.


"then the work done on the earth by the sun is equal to the work done on our surroundings by the earth."

Firstly, this is not the same thing as you said in your previous comment. Secondly, it is not correct, and claiming it is consistent with thermodynamics is simply wrong.

Second, it's not true. For example, a direct equivalent "when the temperature in a steam turbine is steady, the work done by the steam in the expansion chamber is equal to the work done by the exhaust on the surroundings".

(Both systems are directly equivalent - can be modelled as a flow of heat through a heat exchanger).

Back that statement up with a full set of equations showing that to be the case, and we can talk. But as it stands it is nonsense.
Sam Adams
Member
Sun Nov 26 14:17:16
Power spectrum can change, while entropy and total power remains constant. If the average radiating temp changes.

Unfortunatly for you, this is something like a 4th order effect and is utterly undetectable in the weather record. The primordial core heat of the planet matters mote.
Seb
Member
Sun Nov 26 18:07:15
Sam:
Nonsense Sam, for a number of reasons.

1. The power spectrum of emitted radiation is exactly and entirely specified by it's power spectrum. It's spectrum is non planckian. Therefore, it's temperature is ill-defined. Power distributions that are non-planckian cannot be defined by a "temperature" as a temperature is just a parameter specifying a planck distribution. Temperature is an emergent quantity, not a fundamental property. Equipartition of energy among modes is the fundamental principle that leads to temperature existing. When that principle is violated, temperature loses a lot of it's meaning. It is very clear you do not understand the basis of thermodynamics at all.

Any "change" in the temperature of the radiation is already factored in by a comparison of the two power spectra.

2. The average radiating temperature is just a mathematical model - it's the temperature at which a black body (which the atmosphere is not) would emmit the same power as the earth does.
This means:

a. The average radiating temperature cannot change. It is exactly defined by the total power radiated, and as you have repeatedly pointed out, is invariant at 255 K. It cannot change, unless the total power flux out of the planet changes. In which case there must be a coresponding net sink of energy. If the planet is in power balancce with the sun, it absolutely has to be 255k.

b. Because the average radiating temperature is backward defined by the total power, it doesn't represent the actual "temperature" of the radiation. As noted, because the atmosphere isn't a black body and because radiation isn't black-body radiation conforming to a planckian power spectrum - the radiation don't actually have temperature in a meaningful sense. The parts changing are far, very far, from black body curve of 255k. Which is the reason that the surface isn't 255k, which is the temperature it would be if the greenhouse effect did not exist.

c. Further, a cursory glance at coefficients of absorption and partial pressures of CO2, and the height of the "upper radiating surface" - which is just the point where the atmosphere first drops to the semi-arbitrarily defined temperature- which shows that the radiation from that part of the spectrum isn't even comming from that surface.

Basiacally, the upper radiating surface is lies to children: like saying electrons orbit atoms nucelii. It's a reasonably simplistic model that lets you do some stuff, but breaks down when you want to do other stuff. Just as when you want to understand chemistry you need to give up on simplistic electron "orbits" and understand the wave nature of electrons, so with radiative transport you need to give up on simplistic models that ignore the physics of radiatve transfer.

3. What is the underlying physical cause of this supposed shift in the temperature of the upper radiating surface? Asside from being a physically illiterate - as in not even wrong - hand waving exercise to try and preserve your rapidly evaporating pride. Do illuminate us.

Unfortunately for you though you are talking complete nonsense.

But it's very easy for you to refute me.

Explain to me how you would calculate the entropy of a power spectrum that is both characterised by a temperature but also arbitrary.

This should be simple enough, you just need to provide the formula you are using for the power spectrum.

Finally,you say it is a fourth order effect. Fourth order has a very specific mathematical meaning. So if you are convinced it is fourth order, show your working and demonstrate it is a fourth order effect.

I must say though, it is remarkable that you have moved to quantifying an effect you didn't even accept existed a few posts ago - when you mistakenly thought entropy content of two bodies of differnet temperature was the same as one of the average temperature and combined heat content.

Lets start like this:

How much energy in an average hurricane Sam?
Sam Adams
Member
Sun Nov 26 19:18:27
"Power distributions that are non-planckian cannot be defined by a "temperature""


I can define any power spectrum by its average. Plankian or non plankian. Furthermore, i can assign a theoretical plank temp to that average, for the sake of easier discussion. Obviously the planet is not radiating uniformly at its ave radiating temp.

"What is the underlying physical cause of this supposed shift in the temperature of the upper radiating surface?"

If the planet radiates too little the atmosphere warms. If it radiates too much it cools. Thus arriving at its equilbrium temperature such that outgoing energy matches incoming energy. It cannot be otherwise. Every atmosphere does this.

The exact mechanism that initially perturbs the system is of course, in this case, the increased optical depth in the longwave spectrum by co2. The atmosphere then expands a little and increases its water vapor optical depth as well, increasing the average radiating height slightly, and the changing average radiating temperature just enough to match your spectral shift, which is very near 0 though i shall concede nonzero.
Seb
Member
Mon Nov 27 03:34:08
Sam:

"I can define any power spectrum by its average."

You disproved this earlier when you noted that the sum of two power fluxes of different temperatures cannot have the same entropy content if it has the average temperature.

The natural corollary:

Take a spectrum that is the superposition of two planckian distributions

50w of BB radiation with T = 200k plus 50w of BB radiation with T = 300

Now take 50w of BB radiation with T = 100 plus 50W of BB radiation with T = 400

And finally 100w at T=250.

All have different entropies.

You cannot characterise by average.

We already went over this.
Nimatzo
iChihuaha
Mon Nov 27 04:23:50
"That's a heck of a concession Sam."

I have to agree with seb, on this specific point.

Not agreeing about the fundamentals of thermodynamics, is not a trivial thing. Thermo dynamics which Einstein famously said, was the one thing about the universe he was sure would not be overthrown. You can't spend 3-4 threads questioning and debating it and then with a sleight of hand make it all go away.

To be continues..
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