# 2. Wiens vs. Planck - The History of Spectrums - Curves of Confusion

21/01/2020

Physicists are a strange breed (they are going to cringe at this post). They are brilliant no doubt, but when it comes to explaining things to the rest of us who are not brilliant they really do a lousy job. A prime example is spectrum charts. The majority of spectrum charts show a y axis with some kind of intensity / energy reading and an X axis that correlates that energy value to a wavelength (or its inverse frequency) of electromagnetic information. Pretty straightforward. When you do the math and plot the numbers you get an exponential line starting high and dropping down in classic fashion to a low base as we progress from (hot) short wavelengths to (long) wavelengths.

This early version of this plotted line is labelled as the Rayleigh Jeans (RJ) line.  It's easy to create using the Wiens formula. It's easy to read. Useful too. You can find a wavelength such as the C02 sensitive UV 15 um and assign an single intensity number to it from the line without bothering to actually calculate it directly from the tools given to do so. This is the easy to use calculator.

But there's a problem. The RJ line cannot rise to infinity in the short wavelength range as the simple Wiens formula would force it to do. It's impossible. We'd fry from short wave hot UV extremes.  Adjustment to this conundrum came from Planck in his interpretation and mathematical correction of the original line.  The Planck formula does two things; 1. splits the real curve slightly away from the theoretical RJ line and rises parallel to it rather than on it and 2. peaks at some point then falls off rapidly to nothing.

Planck fixed the RJ problem with a mathematical correction factor but couldn't explain why it worked.  Einstein said that the black body generating the curve had limited total energy (quanta) inside itself and the peak is the point where it runs out of supply. This brought on the new quantum physics discipline which stated that energy could exist in solid form or wave form (but never both at the same time).

So now we have to imaging that these waves are generated by hollow objects that are treated as being black bodies (generate a range of wavelengths) that will follow a simple line upwards until they run out of solid energy (quanta) to supply the demand. The "tap" so to speak is wide open and you can't get anymore out of it.  They then fall off rapidly to zero. The resultant "bell type curves" can be calculated from Planck's equation.

Using this calculator we can produce complete spectral curves by choosing the desired temperature ( I chose 192 K,  255K and 300 K) and the range of wavelengths you want the image plotted over ( I chose 2 to 20 um).

It can be seen that you don't get a one wavelength / temperature line as the classical calculator implies, but rather you get a RANGE of wavelengths emitted from the blackbody with the curve peaks shifting right or left depending on the designated temperature of that black body.

Einstein's description of "running out of supply" is obviously too simplistic according to these curves. They show emissions occurring at all wavelengths in the range, with peaks occurring that are different according to how "hot" the black body is. They don't give a one wavelength / one temperature line as classical theory implies - they give a RANGE which shifts along the scale and attains different heights along the Y axis.

Also seen in the image below, where we see several black body curves stacked on top of one another with separate peaks each labelled with a temperature value and with peaks occupying positions higher up the invisible RJ line as the labelled temperatures increase.

It makes sense that the higher the temperature of the black body generating the emissions the greater the volume of energy that can be delivered before it maximizes and runs out of gas. This means their curve peaks are also higher on the energy scale as the black body temperature generating the waves increases.

It can also be seen that the entire curve not just the peak is higher on the scale compared to lower temperature curves positioned below the on the scale. Also, it takes real serious heat to create a definitive curve. The lower heat ranges tend to flatten out and don't form strong peaks or deliver significant energy values to the Y scale. Part of this is the scale of the graph, which can be corrected by adjusting the Y axis as a log scale to incorporate all the range of energies. Thus:

Those are very nice charts. You get clean rise on all curves and formation of crisp, round spectra at each black body temperature, even though the range between them is extremely large. This is definitely an improvement on the classical linear Y scale presented above that where lower black body curves kind of disappear into the X axis.

We give you another chart like the one above.  Note that the red line is NOT the Rayleigh-Jeans line which is not drawn in. This line is drawn to connect the peaks in order to show a shift to the left occurring as each new curve is drawn. It is sometimes called the Wiens line.

NOW THIS IS BETTER.

So these are the types of charts being used to describe the thermodynamic properties of objects such as black paint or the Earth. We get a number of clearly defined bell curve like spectrums that shift left or right and rise up the energy scale as their temperature increases. Very nice, but remember a couple of things:

1. Planck is in conflict with Wiens - Planck says that ALL wavelengths are produced by a black body no matter what their temperature. There is no restriction such as saying 15 um IR can ONLY be produced if the black body is -80 C like the Wiens formula states. It says 15 um wavelengths can be produced at ANY temperature the black body is assigned.

2. If the peak of a black body indicates the "emptying out" of energy that the body holds as Einstein stated, then why does the curve show a fall off line after the peak has been attained and exhausted. Did it run out of energy or not? Was this just a "dribble" of energy spilling out after the main volume of energy had been excreted? Does one level of y axis energy have two values of X that are equivalent, even though they are dramatically different wavelengths?

3. A black body is not a real thing. It is a theoretical object. Perhaps a lot of its properties are theoretical as well. Most of the beautiful spectral curves you see are Modelled Curves, not actual experimental results found by analyzing real black bodies. Remember, a model can be changed just by altering a variable. So beware.

The best Description of a Black Body I can Think of - A Spectral Adjustment Tool

A black body is a theoretical object which has gained an enormous amount of attention in the physics world and has been applied to the concept of global warming in a massive way.

It defies the very basic laws of quantum physics in a number of ways, the most important being that it appears to be able to create and emit "cold" IR waves out from a "hot" body (and vice versa). Basic quantum physics laws state that the wavelength of a beam is dependent on the temperature of the body creating the beam. This means one temperature - one wavelength, not a range of wavelengths.

But look at spectrums for black bodies and there's a whole range of wavelengths being sent out from a single source at a single temperature - creating unique spectrums that are profiled according to the assigned temperature of the body. How can this be?

Best I've got is:

"Think of a black body as being a big black hollow ball, with a tiny hole punched in it.

The black ball is heated, whether through receiving all and any wavelengths of electromagnetic radiation that bounce on to its outside surface from outside, or convection heating from the air surrounding it, or conducted heat into its receptive surface. No matter what the method, the net effect of "continuing input heat" is to create a "black hollow ball" with a specific overall unchanging temperature.

Now, the heat that is accepted on the outside of the black ball is conducted inside and stored and retained as electromagnetic photons waves that "bounce around" inside the cavity of the ball, bouncing off the walls and intermingling as they cannot escape from the interior "en masse". The only place that gives them an exit is the tiny hole in the black ball and it only allows so much energy out at a time, so it spreads out the time that energy dissipates in a way that the exit rate equals the rate at which heat is being added from the outside surface. ie. temperature of the ball remains constant.

Why a mixture of wavelengths inside the ball? The interior cavity "optimizes" the mixture of waves inside itself so as to provide the absolute "best fit" for the various wavelengths of energy held versus the space and dimensions allowed to hold it. More importantly, the concentration of energy held and also the distribution of wavelengths it holds changes with temperature of the ball. This gives the classic multiple spectrums we see as the temperature of the ball is increased.

Now, of most importance, the black ball dispels its electromagnetic blend of energy through the tiny hole as a heterogenous mixture of energies and wavelengths at the same time. Thus, we get a range of energies being delivered out from the interior space to the outside space where we are able to detect and characterize them. This blended range makes up the spectrum for that particular "black body" and explains why a body that classically should deliver only one wavelength of energy (because it is only one temperature) actually delivers a multiple mix of wavelengths at the same time in spite of coming from an object with only one temperature."

Is it for real? Damned if I know. Physicists seem to love the thing but really, we've never seen or even created one in real life. It's great for global warmists because they can declare the Earth a "black body" and explain why 15 um waves will radiate upward at night from a source that is 255 K instead of one that should be 195 K to create that particular wavelength. Why would they do that? Well, we can't have absorption and retention if we don't have any compatible wavelengths to absorb in the first place, do we?

CLIFF'S BLACKBODY THEORY - WHY WE GET A RANGE OF WAVELENGTHS AT "ONE" BB TEMPERATURE.

Suppose we first accept the theory that the blackbody has an internal cavity with a wide variety of wavelengths bouncing around it.  The "mix" sets the Black Body temperature. Then we have to accept that the first wavelengths to "escape" the blackbody are the short wavelength high energy ones. (In other words, read the Planck curve from the left to the right). As high energy photons escape first, the temperature of the black body falls. This drop in temperature either generates longer wavelengths or just releases the pre-exiting lower energy photons and wavelengths, particularly the IR 15um wavelength that we are concerned about.

This process continues until the black body drops to absolute zero. Then it "replenishes" to the original temperature with new input of outside energy. This happens instantly, not slowly over a period of time and so cannot be measured with our crude instrumentation.

It also reconciles the disparity between Wiens Law that relates wavelength to temperature and Planck that delivers a range of wavelengths out of a BB with only "one" temperature.

So, the black body really becomes a spectral adjustment tool - a filter if you will that takes in energy and gives out a unique spectral range of energies. It bypasses classical emw formation laws and dispenses of the need to be at specific temperatures for each wavelength that comprises its blend of outgoing radiation. Is it real? ...?

HERE'S A FEW QUORA REPLIES TO MY RATHER NAIVE (AND SOMEWHAT INSULTING) QUESTIONS TO THE PROS:

Ann Dieh: Is a blackbody actually a giant sponge that sucks up incoming radiation of all wavelengths, adjusts it to a particular profile dependent on temperature and then spits it out according to its own personal profile?

A blackbody is a theoretical piece of matter which does not reflect any incoming radiation (light, UV, IR, microwave and other) So in a way, you could describe it a a sponge for radiation, though I personally wouldn't use this term.

The energy transfered to it due to the incomming radiation is completely converted into heat (not adjusted), for which the blackbody has no other ways to get rid of as radiating it away by itselve.

It's emission is dependent on the temperature alone according to Planck's [math]T^4[/math]law (not personal profile), so its emission spectrum can be used to determine the temperature of the blackbody.

Joshua Engel: "Is a blackbody actually a giant sponge that sucks up incoming radiation of all wavelengths, adjusts it to a particular profile dependent on temperature and then spits it out according to its own personal profile?"

You have to be careful about "simplifying" physics concepts because they're already as simple as people could think to make them. Any questions you ask about your further simplification are by definition going to be answered by people explaining why your simplification is wrong.

A blackbody doesn't emit just one wavelength. It emits every wavelength. It peaks (emits the most energy) at one specific wavelength, which may be what you interpreted as "one wavelength per temperature".

It may help to separate the fact that a black body absorbs energy from the fact that it emits them. In one step, it absorbs energy, and gets hotter. As a completely independent fact, it also emits energy, depending on its temperature. Because it's completely independent, it doesn't matter what wavelengths fell on it, or even if it's completely in the dark. You could just whack it with a stick, and that will make it hotter. Regardless of how it became hot, it emits the same spectrum of frequencies.

Joshua Engel: Is a blackbody actually a giant sponge that sucks up incoming radiation of all wavelengths, adjusts it to a particular profile dependent on temperature and then spits it out according to its own personal profile?

It's not a "personal profile". There is exactly one blackbody "profile", Planck's law. It gives you the amount of radiation you get for a particular wavelength at a particular overall blackbody temperature. Those are all the variables you get in the equation.

Planck's law described an idealized blackbody. No real object is ideal. To the degree that it's different from idea, it's not a blackbody.

Planck's law is a consequence of quantum mechanics: energy comes in at a variety of wavelengths, and the body heats up. The body then emits energy at all wavelengths, with the total energy for each wavelength being the same - except that energy is quantized so you can't emit a very-high energy photon very often. The rest of the profile can be derived from there.

So yeah, it absorbs energy and re-radiates it. Describing it as a "sponge" doesn't really add anything, and the whole idea of a blackbody is to abstract away the particulars.

David Rosen, PhD Physics & Solid State, City University of New York Graduate Center (1985): When we say a black body is 250 K do we consider this to be "pure" temperature or is it a "net" temperature caused by mixing photons of various energies together?

All 'pure' temperatures are net 'temperatures' in your jargon. Blackbody radiation has not fundamental temperature. All temperatures are 'net' temperatures.

Maybe you are talking about the diffrence between the spectral temperature and the density temperature. The radiation inside a black body has a specific spectrum and a specific energy density determined by the equilibrium temperature.

That was equiibrium thermodynamics. Now a peek at nonequilibrium thermodynamics.

If you poke a hole in the black body, some light will escape. The spectrum won't change since the photons conserve energy. However, the energy density of the radiation will change. So there is one temperature associated with the spectrum and a smaller temperature associated with the density.

This isn't a thermal equilibrium, however. The spectrum and the density each has a different quasiequilbrium.

You can decide which is the pure temperature and which is the net temeprature. To me, no temperature is pure unless the system is in thermal equilibrium!

How do Modelled Spectrums compare to actual Earth Measurements of outgoing IR?

In order to show the "usefulness" or "validity" of Modelled Spectrums they are commonly placed over charts that have been produced from "actual" measurements of IR radiation being recorded by Satellites orbiting over the Earth. Whether this is oversimplification of real life remains to be seen. It does have an effect of giving modelled spectrums more weight than they should probably have and could lead to misinterpretation of how the system really works.

Satellite Measuring Earth and Sky IR

NOTE: I think we need to remember that these values were obtained above the Earth's atmosphere. As such they contain ALL the IR radiated from Earth's surface ALONG WITH the IR given off by the atmosphere itself in its process of dumping heat to outer space (it can only be by irradiance). This means that the 667 cm-1 "dip" shown above (and attributed to C02 absorption) might just be a smaller emittance of 15 micron IR from a sky cooled to -80 C, and not from the Earth where C02 can get in between and "trap"

Earth Spectrums - below is a neat little (modelled) spectrum of IR waves that represent how the Earth receives and then dispenses with Sun added heat during the cool night time hours. It covers a range of 2 to 20 microns. It also has a temperature assigned to it on most charts (not this one), generally 255 K , so the implication is that our Earth sitting at 255 K after a day of heating emits a whole range of IR waves of different wavelengths ranging from hot waves at 2 microns to cold waves at the 25 micron mark. We discussed this in the following blog:

The downfall of this image is that it treats the earth as if it is a single homogenous body as such that it can be considered as a pure "black body". In real life this is just not true. Earth is a "gray body" composed of an infinite carpet of miniature (rocks, trees, sticks, blacktop, streetlights, etc.) black bodies, each following the basic rules for emitting energy waves according to their own personal temperatures. More below.

Carbon Dioxide - Now we might not normally care about a generalized representation of radiation except for carbon dioxide.  Under the umbrella of this (calculated) spectrum there are 3  wavelengths that are labelled as being C02 absorption zones. These three spots apparently catch these waves, hold them and then prevent them from getting to outer space by sending them back to Earth. This back radiation violates the Second Law of Thermodynamics but apparently there is "maybe law" that substitutes for it when we need to justify our theories of back warming.

This is apparently a satellite measurement of the Earth emission spectrum, taken over Africa on a clear night (ie. low humidity, no cloud cover, C02 still present in gas mixture). Reading wavelengths on the X axis line we see:

Note: because this is a SATELLITE image we would expect that it is measuring the IR that left the ground and made it to the top of the atmosphere as well as any IR that would be generated by gases in the atmosphere that pointed upwards and headed towards outer space. It assumes low water vapor effect but this might not be so. It also shows C02 having an effect by reducing the transmission of 15 um IR that reaches the satellite.

THIS OPENS MORE QUESTIONS THAN ANSWERS:

WHERE IS THE 15 UM IR BEING CREATED? IT REQUIRES AN EMISSION BODY THAT IS  -80 C IN ORDER TO CREATE A WAVELENGTH OF THIS VALUE, SO WHERE IS THAT EMISSION BODY?

ALSO, HOW DO WE GET TRANSMISSIONS OF IR THAT ARE EVEN COLDER THAT 15 UM IN WARM AREAS (EVEN AT NIGHT) SUCH AS THE AFRICAN DESERT. WHAT'S GENERATING THOSE WAVELENGTHS?

Well, if the Earth acts as black body the answer is simple - because it makes 15 um radiation no matter what the temperature of the ground is. Simple.

COLD SIDE                                                                                         HOT SIDE

a. African Desert b. Mediterranean c. Antarctica

In the Satellite image above - Antartica is showing 15 um transmission as expected (667 c-1). As temperature rises the hot side (right side) wavelengths increase as expected (until they are way too hot for Earth to manufacture) while 15 um appears to be the same level of emission. An anomaly is that as temperature rises on the right side the left side rises as well (but that's colder, so why?) - can only assume it's measuring IR from clouds and water vapor that weren't there in the cold Antarctica scan.

Note how beautifully those overlaid modelled black body spectrums correlate to the "actual" spectrum produced by measurements of IR reaching outer space and being detected by the Satellite. Amazing how well they fit, isn't it?

Most importantly - did C02 filter out IR at the 667 mark in the warm scans or was there simply not enough IR to reach the golden heights demonstrated by the hot side and the cloud side (?) of the scan? Depends on which school you want to belong to, I guess.

Also, does the increased height of the left side (clouds?) make it APPEAR that C02 has absorbed IR in the 667 range. If there was absolutely no water vapour in a. and b. graphs perhaps the graph would just fall at 667 and stay low, indicating no transmissions in any of the wavelengths to the left of 667. This would make sense. Really need to know where the 667 to 400 wavelengths are being generated - is it really coming from the ground or are these atmospheric radiations and reflections from atmospheric gases.

Really need to measure actual IR given off by Earth surfaces without these interferences.  Frankly the Antarctica one is the best of bunch - free of water vapour and showing the emissions following the temperature lines, almost linearly as expected by the Wiens line. This is significant because the atmosphere above Antarctica is almost clear of interfering gases such as water and perhaps even C02. The other charts are most certainly "contaminated" by C02 and H20 as nothing can get vapor levels down as low as good strong low temperatures as found in the Antarctica.

Let's consider the "big picture" - Well, for a start the "window" in which the Earth transmits out IR is shown in perspective below as the yellow peak. rather insignificant considering the entire range we are exposed to and send out as higher wavelengths. Alarmists absolutely fixate on this window, giving it credit for almost all of Earth's cooling when really it is only around 20% of the balance. Absorption loses are predominantly due to water, not due to Co2 as seen in their windows above.

SO WHY DO WE KEEP FOOLING AROUND WITH BLACK BODY EMISSION / ABSORPTION SPECTRUM CURVES ???

Black Body - IPCC says the Sun and more importantly the Earth have to be considered as being "black bodies" and that the rules of thermodynamics regarding black bodies apply to them. A black body is actually theoretical but basically it is an object that is capable of absorbing electromagnetic energy at all wavelengths and also of emitting electromagnetic energy at all wavelengths. It does not exclude anything. This definition may be so but it (falsely) gives the impression that it can emit electromagnetic radiation of different wavelengths at the same time, while also stating that the wavelengths of it emissions are dependent on its black body temperature. Like having your cake and eating it too...

Enter Wiens Law - physics has objectified the situation with numbers and formulas. It has done this when the Wiens Law / formula was proposed, proved and established as being absolute. Wiens Law says that the wavelength of emission from a black body is directly related to its temperature. By filling in the dots on the provided calculator  below you can define the wavelength of energy that a black body will emit at any temperature you want to investigate. Very cool.

Does Earth violate Wiens Law? - so how can Earth be a black body at 255 K and pass out a range of IR radiation covering very hot wavelengths at 2 microns to quite cold waves at 25 microns? Shouldn't it pass one, and only one wavelength that relates to the 255 K mark, and not a range? Is Wiens Law valid or not? Is Earth a black body or not?

Earth can't be a black body, and it can't be just 255 K (this is some kind of massive average designed to parallel the performance of a theoretical black body) - we may have to think of Earth as a Planet that is covered completely over its surface with an infinite number of individual black bodies, all of whom are at different temperatures and all of whom follow Wiens Law when radiating out IR to space.

It is the only logical explanation on how we can create a bell (oops, sorry Planck) curve covering the whole range and besides, it's true - just step off the lawn on to a blacktop road and you can feel the difference in temperatures in these two "black bodies".

My Rendition - Earth Composed of Black Bodies

So what really is the Temperature - well, as you can see in the above representation Earth is actually made of an infinite number of black bodies (grass, roads, lights, sidewalks, buildings, oceans, ice, volcanoes, smokestacks, nuclear cooling towers, heaters, air conditioners, car exhausts, hot rocks, sand, lava, etc. etc.) each radiating at different "black body"temperatures and all sending out different unique wavelengths of IR electromagnetic energy. I guess the so called "temperature" is some kind of half assed averaging of them all but for the life of me I don't know how you could determine that. I guess we stick with the method used in one of my other blogs.

That's O.K. for general discussions, but we have given superpowers to one molecule - Carbon Dioxide - as to its ability to catch IR at three wavelengths 2.3, 4.5, and 15 microns. These waves HAD to have come from one of those mini black bodies mixed among the others as shown in our depiction of Earth as cardboard box above. It doesn't change its wavelength spontaneously by some kind of invisible thermal friction force or whatever. It keeps going as its original wavelength until it encounters a gas molecule that absorbs it - completely.

S0 to review our "new" theory - the infrared exhaust portion of the earth's collection of daytime heat comes in the form of an amorphous mixture of photon based electromagnetic radiation composed of many frequencies and wavelengths formed according to the principles of Wiens Law from another amorphous mixture of blackbodies residing down at the Earth's surface. Gases such as C02 respond to the 15 micron wavelengths in the mixture that are coming at it from the objects that generated them at -80 C.

You have to ask though, just how many of those waves are there in the total blend? Doesn't seem like it could be much considering how cold the objects have to be in order to create them and the general lack of these objects in our common spaces.

How do you determine what the temperatures of the mini black boxes are? - well, Wiens Formula of course!

Now it really gets interesting. Time to read the following blog: