Category: Uncategorized

Five More Alternate Universes?

On By rolcottIn Cosmology, Crazy Theories, UncategorizedLeave a comment

I unlock my office door and there’s Vinnie inside, looking out the window. “Your 12th‑floor view’s pretty nice, Sy. From above the tree tops you can see leaf buds just starting to show their early green colors.”

“What are you doing here, Vinnie? I thought you were charter‑flying to Vancouver.”

“The guy canceled. Said with all the on‑again, off‑again tariffs there’s no sense traveling to make a deal when he doesn’t know what he’s dealing with. So I got some time to think.”

“And you came here so it’s something physics‑technical.”

“Yeah, some. I notice colors a lot when I’m flying. Some of those trees down there this time of year are exactly the same bright yellow‑green as some of the rice paddies I’ve flown over. But all the trees get the same hard dark green by August before they go every different color when the chlorophyll fades away.”

“I’ve noticed that. So you came here to talk about spectra?”

“Some other time. This time I want to talk about dark matter.”

“But we call it dark matter precisely because it doesn’t do light. All our normal matter is made of atoms and the atoms are made of electrons and nuclei and each nucleus is made of protons and neutrons and protons and neutrons are made of quarks. Electrons and quarks carry electrical charge. Anything with electrical charge is subject to electromagnetism, one way or another. Dark matter doesn’t notice electromagnetism. If dark matter had even the slightest interaction with light’s electromagnetic field, we wouldn’t be able to see galaxies billions of lightyears away.”

“Calm down, Sy, breath a couple times. Stay with me here. From your stuff and what else I’ve read, all we know about dark matter is a lot of things it isn’t or doesn’t do. The only force we know it respects is gravity so it attracts itself and also normal matter and they all clump up to make galaxies and such, right?”

<a bit reluctantly and on a rising note> “Mm‑hnn…?”

“I read your three‑part series about the Bullet Cluster, where we think two galaxy clusters went though each other and their gas clouds gave off a lot of X‑rays that didn’t match where the stars were or where the gravity was so the astronomers blame dark matter for the gravity, right?”

“That’s pretty much it. So?”

“So the other thing I got from that series was maybe there’s friction between dark matter and other dark matter, like it doesn’t just slide past itself. If dark matter is particles, maybe they’re sorta sticky and don’t bounce off each other like billiard balls. That doesn’t make sense if all they do is gravity.”

“I see where you’re going. You’re thinking that maybe dark matter feels some kind of force that’s not gravity or electromagnetism.”

“That’s it! We’ve got light photons carrying electromagnetic forces to hold our molecules and rocks together. Could there be dark photons carrying some dark‑sticky force to connect up dark molecules and dark rocks and stuff?”

“That’s an interesting—”

“I ain’t done yet, Sy. It gets better. I’ve read a bunch of articles saying there’s about five times as much dark matter in the Universe as normal matter. You physicists love symmetry, suppose it’s exactly five times as much. There’d be six kinds of force, one called electromagnetism and a different snooty force each for five kinds of dark matter and that’ll add up to the 25% we can’t see. Like, a purple dark force for purple dark rocks, naturally they’re not really purple, and a yellow dark force and so on.”

“You’re proposing that each kind of dark matter responds only to its own special force, so no cross‑communication?”

“Yup, gravity’s the only thing they’d all agree on. That bein’ the case, the galaxies would hold six times as many stars as we think, except 5/6 of them are invisible to our 1/6. Five alternate universes sharing space with ours. Cozy, huh?”

“Clever, Vinnie, except for the evidence that most galaxies are embedded in huge nearly‑spherical halos of dark matter. The halos would have collapsed long ago if only gravity and stickiness were in play.”

“Dang.”

~ Rich Olcott

Old Sol And The Pasta Pot

On By rolcottIn Astronomy: Stellar Science, UncategorizedLeave a comment

<chirp, chirp> “Excuse me, folks, it’s my niece. Hello, Teena.”

“Hi, Uncle Sy. What’s a kme?”

“Sorry, I don’t know that word. Spell it.”

“I’ve never seen it written down. Brian says the Sun’s specially active and gonna spit out a kme that’ll bang into Earth and knock us out of our orbit.”

“Ah, that’s a C‑M‑E, three separate letters. It stands for Coronal Mass Ejection. As usual, Brian’s got some of it right and much of it wrong. The right part is that the Sun’s at the peak of its 11‑year activity cycle so there’s lots of sunspots and flares—”

“He said flares, too. They’re super bright and could cook an Astronaut and it’d happen so fast we won’t have any warning.”

“Once again, partially right but mostly wrong. Here, let me give you to Cathleen who can set you straight. Cathleen, did you catch the conversation’s drift?”

<phone‑pass pause> “Hello, Teena. I gather you’re upset about solar activity?”

“Hi, Dr O’Meara. Yes, my sorta‑friend Brian likes to scare me with what he brings back from going down YouTube rabbit holes. I don’t really believe him but. You know?”

“I understand. Rabbit holes do tend to collect rubbish. Here, let me send you a diagram I use in my classes.” <another pause> “Did you get that?”

“Mm‑hm. Brian showed me a picture like that without the cut‑out part because he was all about the bright flashes.”

“Of course he was. I’ll skip the details, but the idea is that the Sun generates its heat and light energy deep in the reaction zone. Various processes carry that energy up through other zones until it hits the Sun’s atmosphere. You’ve watched water boil on the stove, surely.”

“Oh, yes. Mom put me in charge of doing the pasta last year. I don’t care what they say, a watched pot does eventually boil if there’s enough heat underneath it. I experimented.”

“Wonderful. That process, heat rising into a fluid layer, works the same way on the Sun as it does in your pasta pot. Heat ascends through the fluid but it doesn’t do that uniformly. No, the continuous fluid separates into distinct cells, they’re called Bénard cells, where hot fluid comes up the center, spreads out and cools across the top and then flows down the cell’s outer boundary.”

“That’s what I see happen in the pot with low water and low heat just before the bubbling starts.”

High-res image of the Sun’s surface by DKIST.
Credit: NSO/AURA/NSF, under CC A4.0 Intl license.

“Right, bubbling will disturb what had been a stable pattern. The cells in the Sun’s surface, they’re called granules, continually rise up to the surface and crowd out neighbors that have cooled off enough to sink or disappear.”

“Funny to say something on the Sun is cool.”

“Relatively cool, only 4000K compared to 6000K. But the Sun has bubbles, too. The granules run about 1500 kilometers wide and last only a quarter‑hour. There’s evidence they’re in top of a supporting layer of supergranules 20 times wider. Or maybe the plasma’s magnetic field is patchy. Anyhow, the surface motion is chaotic. Occasionally, especially concentrated heat or magnetic structure punches out between the granules. There’s a sudden huge release of superhot plasma, a blast of electromagnetic energy radiating out at all frequencies — that’s one of Brian’s flares. Lasts about as long as the granules.”

“That’s what could cook an astronaut?”

“Not really, The radiation’s pretty spread out by the time it’s travelled 150 million kilometers to us. The real danger is from high‑energy particle storms that travel along the Sun’s magnetic field lines. Space crews need to take shelter from them but particle masses travel slower than light so there’s several hours notice.”

“So what about the CMEs?”

“They’re big bubbles of plasma mass that the Sun throws off a few times a year on average. Maybe they come from ultra‑flares but we just don’t know. Their charged particles and magnetic fields can mess up our electronic stuff, but don’t worry about their mass. If a CME’s entire mass hit us straight on, it’d be only a millionth of a millionth of Earth’s mass. We’d roll on just fine.”

~ Rich Olcott

Rows, Columns And Freedom

On By rolcottIn Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

“Geez, Sy. You know I hate equations. I was fine with the Phase Rule as an arithmetic thing but you’ve thrown so much algebra at me I’m flummoxed. How about something I can visualize?”

“Sorry, Vinnie, the algebra was just to show where the Rule came from. Application’s not in my bailiwick. Susan, it’s your turn.”

“Sure, Sy, this is Chemistry. Okay, Vinnie, what’s the Rule about?”

“Degrees of freedom, but I’m still not sure what that means. ‘Independent intensive variables’ doesn’t say much to me.”

“Understandable, seeing as you don’t like equations. Visualize a spreadsheet. There’s an ‘Energy’ header over columns A and B. The second row reads ‘Name’ and ‘Value’ in those two columns. Then one row each for Temperature and Pressure.”

“This is more like it. Any numbers in the value column?”

“Not yet. They’ll be degrees of freedom, maybe. Next, ‘Components‘ in cell C1, ‘Name’ in C2 and then C rows, one for each component.”

“Do we care how much of each component?”

“Not yet.* Next visualize a multi‑column ‘Phases‘ header over one column for each phase. The second row names the phase. Below that there’s a row for each component. The whole array is for figuring how each component spreads across the phases assuming there’s enough of everything to reach equilibrium. With me?”

“A little ahead, I think. Take one of Kareem’s lava pools on Io, for instance. It’s got two components, iron and sulfur, and two molten phases, iron‑light 5:95 floating on top of iron‑heavy 60:40. Phase Rule says the freedom degrees is C–P+2=2–2+2, comes to 2 but that disagrees with the 6 open boxes I see.”

“But the boxes aren’t independent. Think of the interface between the two phases. One by one, atoms in each phase wander across to the other side. At equilibrium the wandering happens about as often in both directions.”

Adapted from Walder and Pelton
Click image to expand

“That’s your reversibility equilibrium.”

“Right, thermodynamics’ classic competition between energy and entropy — electronic energy holding things together against entropy flinging atoms everywhere. Pure iron’s a metallic electron soup that can accept a lot of sulfur without much disturbance to its energy configuration. That means sulfur’s enthalpy doesn’t differ much between the two environments and that allows easy sulfur traffic between the two phases. On the other hand, pure sulfur will accept only a little iron because iron disrupts sulfur‑sulfur moleular bonding. Steep energy barrier against iron atoms drifting into the 95:5 phase; low barrier to spitting them out. Kareem’s phase diagram for atmospheric pressure shows how things settle out for each temperature. There’s a neat equation for calculating the concentration ratios from the enthalpy differences, but you don’t like equations.”

“You’re right about that, Susan, but I smell weaseling in your temperature‑pressure dodge.”

Water’s phase diagram

“Not really. You’ve read Sy’s posts about enthalpy’s internal energy, thermal and PV‑work components. Heat boosts entropy’s dominance and tinkers with the enthalpies.”

Meanwhile, I’ve been tapping Old Reliable’s screen. “I’m playing water games over here. Maybe this will help clarify the freedom. Water can be ice, liquid or vapor. At high temperature and pressure, the liquid and gas phases become a single phase we call supercritical. Here’s a sketch of water’s phase diagram. Only one component so C=1 … and a spreadsheet summarizing seven conditions.

“The first four are all at atmospheric pressure, starting at position 1 — just water vapor in a single phase so P=1, DF=2. We can change temperature and pressure independently within the phase boundaries. If we chill to point 2 liquid water condenses. If we stop there, on the boundary, we’re at equilibrium. We could change temperature and still be at equilibrium, but only if we change pressure just right so we stay on that dotted line. The temperature‑pressure linkage constraint leaves us only one degree of freedom — along the line.”

“Ah, 3 and 5 work the same way as 1 but for liquid and solid, and 4‘s like 2. The Fixed ones—?”

“One unique temperature‑pressure combination for each equilibrium. No freedoms left.”

  • * Given specific quantities of iron and sulfur, chemists can calculate equilibrium quantities for each phase. Susan assigned that as a homework problem once.

~ Rich Olcott

The Quest for Independents

On By rolcottIn Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

The thing about Vinnie is, he’s always looking for the edges and loopholes. He’d make a good scientist or lawyer but he’s happy flying airplanes. “Guys, I heard a lot of dodging when you started talking about that Gibbs Rule. You said it only works when things are in equilibrium. That’s what Susan was talking about when she said Loki Lake on Io ain’t an equilibrium ’cause there’s stuff getting pumped in and going away so the equations don’t balance. I got that. But then you threw in some other excepts, like no biology or other kinds of work. What’s all that got to do with the phases and chemistry?”

“They’re different processes that drive a system away from equilibrium. Biology, for example. Every kind of life taps energy sources to maintain unstable structures. Proteins, for instance — chemically they’re totally unstable. Oxidation, random acid‑base reactions, lots of ways to degrade a protein molecule’s structure until its atoms wind up in carbon dioxide and nitrogen gas. Your cells, though, they continually burn your food for energy to protect old protein molecules or build new ones and DNA and bones and everything. I visualize someone riding a bicycle up a hillside of falling bowling balls, desperately fighting entropy just to keep upright.”

“Fearsome image, Susan, but it fits. From a Physics perspective, dumping in or extracting any kind of work disrupts any system that’s at equilibrium. The Phase Rule accounts for pressure-volume energy because that’s already part of enthalpy—”

“Wait, Sy, I don’t see pressure‑volume or even ‘PV‘ in
  ’degrees of freedom=components–phases+2‘.”

“That’s what the ‘2′ is about, Vinnie. If it weren’t for pressure‑volume energy, that two would be a one.”

“C’mon.”

“No, really. ‘Degrees of freedom’ counts the number of intensive properties that are independent of each other. Neither temperature nor pressure care about how much of something you’ve got, so they’re both intensive properties. Temperature’s always there so that’s one degree of freedom. If PV energy’s part of whatever process you’re looking at, then pressure comes into the Rule by way of the enthalpies we use to calculate equilibrium situations. I guess you could write the Rule as
  DF=C–P+1T+1PV.“

“That’s not the way we learned that in school, Sy. It was
  DF=C–P+1+N,
with ‘N’ counting the number of work modes — PV, gravitational, electrical, whatever fits the problem.”

“How would you do gravitational work on an ice cube, Kareem?”

“Wouldn’t be a cube, Vinnie, it’d be a parcel of Jupiter’s atmosphere caught in a kilometers‑high vertical windstream. Water ice, ammonia ice, ammonium polysulfide solids, all in a hydrogen‑helium medium. A complicated problem; whoever picks it up will have to account for gravity and pressure effects.”

“Come to think of it, the electric option is getting popular and Kareem’s iron‑sulfur system may be a big player. My Chemistry journals have carried a sudden flurry of papers about iron‑sulfur batteries as cheap, safe alternatives to lithium‑based designs for industry‑sized storage where low weight isn’t a consideration. Battery voltage is intensive, doesn’t care about size. Volt’s extensive ‘how much’ buddy is amps. Electrical work is volts times amps so it fits right in with the Rule if I write
  DF=C–P+1T+1PV+1VA
A voltage box with sulfur electrodes on one side and iron electrodes on the other would be way out of equilibrium.”

“But why components minus phases? Why not times? What if it comes out negative? What’d that even mean?”

Water’s phase diagram

“Fair questions, Vinnie. Degrees of freedom counts independent properties, right? You’d think the phases‑components contribution to DF would be P*C but no. The component percentages in C must total 100%. If you know all but one percentage, the last percentage isn’t independent. Same logic applies to the P phases. That leaves (C–1) and (P–1) independent variables. For the P phases P*C drops to P*(C–1) variables. But you also know that each component is in equilibrium across all phases. Each equilibrium reduces the count by one, for C*(P–1) reductions. Do the subtraction
  P*(C–1)–C*(P–1)=C–P
You’re left with only C–P quantities that can change without affecting other things. If the result’s negative it’ll constrain exactly that many other intensive variables, like with water’s triple point.”

~ Rich Olcott

Water Rites

On By rolcottIn Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

Vinnie pulls a chair over to our table, grabs some paper napkins for scribbling. “You guys know I hate equations, but this Phase Rule one is simple enough even I can play. It says ‘degrees of freedom’ equals ‘components’ minus ‘phases’ plus 2, right? Kareem’s phase diagram has a blue piece with a slush of iron crystals floating in an iron‑sulfur melt. There’s two components, iron and sulfur, two phases, crystals and melt, so the degrees come to 2–2+2=2 and that means we get to choose any two, you said intensive properties, to change. Do I got all that straight, tell me more about degrees and what’s intensive?”

Phase diagram for the iron:sulfur system
Adapted from Walder and Pelton
Click image to expand

“Good job, Vinnie, and good questions. Extensive properties are about how much. In Kareem’s experiment, he’s free to add iron or sulfur in whatever quantities he wants. By contrast, intensive properties don’t care about how much is there. The equilibrium melt’s iron:sulfur ratio stays between zero and one whatever the size of Kareem’s experiment. The ratio’s an intensive property. So are temperature and pressure. If he kept his experimental pressure constant but raised the temperature, I expect some of the crystals would dissolve. That’d lift the iron:sulfur ratio.”

“How about raising the pressure, Kareem?”

“I suspect that’d squeeze iron back into the crystalline mass, but I’ve not tried that so I don’t know. Different materials behave different ways. Raising the pressure on normal water ice melts it, which is why ice skates work.”

Susan suddenly pulls her tablet from her purse and starts fiddling with it.

“Fair enough. Okay, in your diagram’s top yellow piece where it’s all molten, there’s still 2 components but one phase so the Rule goes 2–1+2=3. You’re saying 3 degrees means you can choose whatever temperature, pressure and mix ratio you want and it’d still be molten.”

“You’ve got the idea, Vinnie. What I’m really interested in, though, is what happens when I add more components. To model Io’s lava pools I need to roll in oxygen and silicon from the surrounding rocks. I’m looking at a 4‑component situation which could have multiple phases and things are complicated”

Vinnie’s got that ‘gotcha’ glint in his eye. “Understood. But how about going in the other direction? If you’ve got only one component then you could have either 1–2+2=1 or 1–3+2=0. How do either of those make sense?”

Susan shows a display on her tablet. “As soon as Kareem mentioned ice I figured this phase diagram would come in handy. It’s for water — single component so there’s no variation along a component axis, just pressure and temperature.”

“Kareem had to read his chart to us. Now it’s your turn.”

“Of course. By convention, pressure’s on the y‑axis, temperature’s along the x‑axis. The pressure range is so wide that this chart uses a logarithmic scale which is why the distances look weird. Over there on the cold side, there’s two kinds of ice. Ice Ic has a cubic crystal structure. Warm it up past 240K and it converts to a hexagonal form, Ice Ih. That’s the usual variety that makes snowflakes.”

“TP!” <snirk, snirk>

“Cal, please. That’s water’s Triple Point, Vinnie’s 1–3+2=0 situation where all three phases are in equilibrium with each other so there’s no degrees of freedom. The solid‑liquid and liquid‑vapor boundaries are examples of Vinnie’s 1–2+2=1 condition — only one degree of freedom, which means that equilibrium temperature and pressure are tightly linked together. Squeeze on ice, its melting point drops, so we ice skate on a thin film of liquid water. Normal Boiling Point holds at standard atmospheric pressure but if you heat water while up on a balloon ride it may not get hot enough to hard‑boil those eggs you brought for the picnic.”

“What’s going on in the gray northeast corner?”

“CP‘s the Critical Point at the end of the 1–2+2=1 line. The liquid-vapor surface disappears. No gas or liquid in the container, just opalescent supercritical fog. There’s only one phase; temperature and pressure are independent. Beyond CP you’re in 1–1+2=2 territory.”

~ Rich Olcott

The Hacker’s Rap

On By rolcottIn General: Fun Stuff, Uncategorized2 Comments
  • And now for something completely different…

 <click>  <click>  <click>  <click>
So your Mac’s gone splat?
 Well how ’bout that?
Now baby, don’t you panic.
By the light of my screen
You’ll be in a different scene
When I’ve made ME your data mechanic.

 <click>

You think you got secrets?
 You ain’t met me yet.
I’m on a roll,
 you’ve lost control
An’ there ain’t no RESET.
Ethics ain’t my style.
Nasty makes me smile:
You’re in a jam
 ’cause I’ve got a plan
For your personal keyset.
Might as well resign, dear,
Your system’s mine, that’s clear,
Yeah, my attack
 does not hold back
  It’ll feel like a cardiac
    hack,
      Jack,
‘Cause I’m a HACKER!
Ain’t no mush-head slacker.
I can mess your metal mind an’ that’s a fact, son!
Check this action:
 If I feel a dejection
  Because of a rejection,
 I can make a selection
 From my collection,
 Set up a connection
 And you’ll get a digital infection
  That defies detection
  Or correction.
 Virus inspection
  Ain’t no protection
 And your objection
 Confirms my direction
 And amplifies my —
        satisfection.

‘Cause I’m a HACKER!
I got tons of tricks in my pack here.
Ain’t no food in the freezer?
No problem, man – I can download pizza.
 Can’t touch this, eithah
  cause it’s a virtual pizza!

You run Windows?
 You’ll hear the wind blow.
You run iOS?
 Say “Bye-bye,” oh yes.
You run Chrome?
 Won’t be no-one home.
You run Android?
 I’ll hit you like an asteroid.
You run Linux?
 You’ll feel the force of my
   mimic gimmicks.
Go on, run to a mainframe —
 You’ll still be in my pain game.
You feel safe in the cloud somewhere?
 You’re right in front of my easy chair.

‘Cause I’m a HACKER!
I POP <click> I FIZZ
 when I find what ROOT’s password is.
I SMILE <click> I GRIN <click>
 I sack the system that lets me in.
Things SPIN <click> Things SPARK <click>
 And suddenly your screen goes dark —
A sadder but wiser LAN you’ll be
‘Cause I am
 TROUBLE
 with a capital T
 and that rhymes with C
 and that stands for
  <click>  <click>  <click>  <click>
   CLICK

~ Rich Olcott


Surf Lake Loki? No, Thanks.

On By rolcottIn Astronomy: Planetary Science, Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

Vinnie’s been eavesdropping (he’s good at that). “You guys said that these researcher teams looked at how iron and sulfur play together at a bunch of different temperature, pressures and blend ratios. That’s a pretty nice chart, the one that shows mix and temperature. Got one for pressure, like the near‑vacuum over Loki’s lava lake on Io?”

“Not to my knowledge, Vinnie. Of course I’m a lab chemist, not a theoretical astrogeochemist. Kareem’s phase diagram is for normal atmospheric pressure. I’d bet virtually all related lab work extends from there to the higher pressures down toward Earth’s center. Million‑atmosphere experiments are difficult — even just trying to figure out whether a microgram sample’s phase in a diamond anvil cell is solid or liquid. Right, Kareem?”

“Mm‑hm, but the computer work’s hard, too, Susan. We’ve got several suites of software packages for modeling whatever set of pressure-temperature-composition parameters you like. The problem is that the software needs relevant thermodynamic data from the pressure and temperature extremes like from those tough‑to‑do experiments. There’s been surprises when a material exhibited new phases no‑one had ever seen or measured before. Water’s common, right, but just within the past decade we may have discovered five new high‑pressure forms of ice.”

“May have?”

Artist’s concept of Loki Patera,
a lava lake on Jupiter’s moon Io
Credit: NASA/JPL-Caltech/SwRI/MSSS

“The academics are still arguing about each of them. Setting aside that problem, modeling Io’s low‑pressure environment is a challenge because it’s not a lab situation. Consider Cal’s pretty picture there. See those glowing patches all around the lava lake’s shore? They’re real. Juno‘s JIRAM instrument detected hot rings around Loki and nearly a dozen of its cousins. Such continual heat release tells us the lakes are being stirred or pumped somehow. Whatever delivers heat to the shore also must deliver some kind of hot iron‑sulfur phase to the cooler surface. That’ll separate out like slag in a steel furnace.”

“It’s worse than that, Kareem. Sulfur’s just under oxygen in the periodic table, so like oxygen it’s willing to be gaseous S2. Churned‑up hot lava can’t help but give off sulfur vapor that the models will have to account for.”

I cut in. “It’s worse than that, Susan. I’ve written about Jupiter’s crazy magnetic field, off‑center and the strongest of any planet. Io’s the closest large moon to Jupiter, deep in that field. Sulfur molecules run away from a magnetic field; free sulfur atoms dive into one. Either way, if you’re some sulfur species floating above a lava lake when Jupiter’s field sweeps past, you won’t be hanging around that lake for long. Most likely, you’ll join the parade across the Io‑to‑Jupiter flux tube bridge.”

Susan chortles. “Obviously not an equilibrium. It’s a steady state!”

“Huh?” from everyone. Cal gives her, “Steady state?”

“Chemical equilibrium is when a reaction and its reverse go at equal rates, right, so the overall composition doesn’t change. That’s the opposite of situations where there’s a forward reaction but for some reason the products don’t get a chance to back‑react. Classic case is precipitation, say when you bubble smelly H2S gas through a solution that may contain lead ions. If there’s lead in there you get a black lead sulfide sediment that’s so insoluble there’s no re‑dissolve. Picture an industrial vat with lead‑contaminated waste water coming in one pipe and H2S gas bubbling in from another. If you adjust the flow rates right, all the lead’s stripped out, there’s no residual stink in the effluent water and the net content of the vat doesn’t change. That’s a steady state.”

“What’s that got to do with Loki’s lake?”

“Sulfur vapors come off it and those glowing rings tell us it’s giving off heat. It’s just sitting there not getting hotter and probably not changing much in composition. There’s got to be sulfur and heat inflow to make up for the outflow. The lake’s in a steady state, not an equilibrium. Thermodynamic calculations like Gibbs’ phase rule can’t tell you anything about the lake’s composition because that depends on the kinetics — how fast magma comes in, how fast heat and sulfur go out. Kareem’s phase diagram just doesn’t apply.”

~ Rich Olcott

Phases And Changes

On By rolcottIn Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

“Okay, so the yellow part of your graph is molten iron and sulfur, Kareem. What’s with all the complicated stuff going on in the bottom half?”

“It’s not a graph, Cal, it’s a phase diagram. Mmm… what do you think a phase is?”

“What we learned in school — solid, liquid, gas.”

“Sorry, no. Those are states of matter. Water can be in the solid state, that’s ice, or in the liquid state like in my coffee cup here, or in the gaseous state, that’d be water vapor. Phase is a tighter notion. By definition, it’s an instance of matter in a particular state where the same chemical and physical properties hold at every point. Diamond and graphite, for example, are two different phases of solid carbon.”

“Like when Superman squeezes a lump of coal into a diamond?”

“Mm-hm. Come to think of it, Cal, have you ever wondered why the diamonds come out as faceted gems instead of a mold of the inside of his fist? But you’ve got the idea — same material, both in the solid state but in different phases. Anyway, in this diagram each bordered region represents a phase.”

Phase diagram for the iron:sulfur system
Adapted from Walder and Pelton

“It’s more complicated that that, Kareem. If you look close, each region is actually a mixture of phases. The blue region, for instance, has parts labeled ‘bcc+Liquid’ and ‘fcc+Liquid’. Both ‘bcc’ and ‘fcc’ are crystalline forms of pure iron. Each blue region is really a slush of iron crystals floating in a melt with just enough sulfur to make up the indicated sulfur:iron composition. That line at 1380°C separates conditions where you have one 2‑phase mix or the other.”

“Point taken, Susan. Face it, if region’s not just a straight vertical line then it must enclose a range of compositions. If it’s not strictly molten it must be some mix of at least two separate more‑or‑less pure components. That cool‑temperature mess around 50:50 composition is a jumble when you look at micro sections of a sample that didn’t cool perfectly and they never can. The diagram’s a high‑level look at equilibrium behaviors.”

“Equilibrium?”

“‘Equi–librium’ came from the Latin ‘equal weight’ for a two-pan balance when the beam was perfectly level. The chemists abstracted the idea to refer to a reaction going both ways at the same rate.”

“Can it do that, Susan?”

“Many can, Cal. Say you’ve got a beaker holding some dilute acetic acid and you bubble in some ammonia gas. The two react to produce ammonium ions and acetate ions. But the reaction doesn’t go all the way. Sometimes an ammonium ion and an acetate ion react to produce ammonia and acetic acid. We write the equation with a double arrow to show both directions. Sooner or later you get equally many molecules reacting in each direction and that’s a chemical equilibrium. It looks like nothing’s changing in there but actually a lot’s going on at the molecular level. Given the reactant and product enthalpies Sy’s been banging on about, we can predict how much of each substance will be in the reaction vessel when things settle down.”

“Banging on, indeed. You’re disrespecting a major triumph of 19th‑Century science. Before Gibbs and Helmholtz, industrial chemists had to depend on rules of thumb to figure reaction yields. Now they just look up the enthalpies and they’ can make good estimates. Gibbs even came up with his famous phase rule.”

“You’re gonna tell us, right?”

“Try to stop him.”

“The Gibbs Rule applies to systems in equilibrium where there’s nothing going on that’s biological or involves electromagnetic or gravitational work. Under those restrictions, there’s a limit to how things can vary. According to the rule, a system’s degrees of freedom equals the number of chemical components, minus the number of phases, plus 2. In each blue range, for instance, iron and sulfur make 2 components, minus 2 phases, plus 2, that’s 2 degrees of freedom.”

“So?”

“Composition, temperature and pressure are three intensive variables that you might vary in an experiment. Pick any two, the third is locked in by thermodynamics. Set temperature and pressure, thermodynamics sets the composition.”

~ Rich Olcott

A Lazy Summer Day at 1400°C

On By rolcottIn Astronomy: Planetary Science, Chemistry, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

Susan Kim and Kareem are supervising while Cal mounts a new poster in the place of honor behind his cash register. “A little higher on the left, Cal.”

“How’s this, Susan? Hey, Sy, get over here and see this. Ain’t it a beaut?”

“Nice, Cal. What’s it supposed to be? Is that Jupiter in the background?”

“Yeah, Jupiter all right. Foreground is supposed to be a particular spot on its moon Io. They think it’s a lake of molten sulfur!”

“No way, from that picture at least! I’ve seen molten sulfur. It goes from pale yellow to dark red as you heat it up, but never black like that.”

“It’s not going to be lab-pure sulfur, Susan. This is out there in the wild so it’s going to be loaded with other stuff, especially iron. But the molten sulfur I’ve seen in volcanoes is usually burning with a blue flame. I guess the artist left that out.”

“No oxygen to burn it with, Kareem. Why did you mention iron in particular?”

“Yeah, this article I took the image from says that lake’s at 1400°C. I thought blast furnaces ran hotter than that.”

I’ve been looking things up on Old Reliable. “They do, Cal, typically peaking near 2000°C.”

“So if this lake has iron in it, why isn’t the iron solid?”

“Same answer as I gave to Susan, Cal. The iron’s not pure, either. Mixtures generally melt or freeze at lower temperatures than their pure components. Sy would probably start an entropy lecture—”

“I would.”

“But I’m a geologist. Earth is about ⅓ iron. That’s mixed in with about 10% as much sulfur, mostly in the core where pressures and temperatures are immense. We want to understand conditions down there so we’ve spent tons of lab time and computer time to determine how various iron‑sulfur mixtures behave at different temperatures and pressures. It’s complicated.” <brings up an image on his phone> “Here’s what we call the system’s phase diagram.”

“You’re going to have to read that to us.”

Adapted from Walder and Pelton
Click image to expand

“I expected to. Temperature increases along the y‑axis. Loki’s temp is at the dotted red line. Left‑to‑right we’ve got increasing sulfur:iron ratios — pure iron on the left, pure sulfur on the right. The idea is, pick a temperature and a mix ratio. The phase diagram tells you what form or forms dominate. The yellow area, for instance, is liquid — molten stuff with each kind of atom moving around randomly.”

“What’s the ‘bcc’ and ‘fcc’ about?”

“I was going to get to that. They’re abbreviations for ‘body‑centered cubic’ and ‘face‑centered cubic’, two different crystalline forms of iron. The fcc form dominates below that horizontal line at about 1380°C, converts to bcc above that temperature. Pure bcc freezes at about 1540°C, but add some sulfur to the molten material and you drive that freezing temperature down along the blue‑yellow boundary.”

“And the gray area?”

“Always a fun thing to explain. It’s basically a no‑go zone. Take the point at 1400°C and 80:20 sulfur:iron, for instance. The line running through the gray zone along those red dots, we call it a tie line, skips from 60:40 to 95:5, right? That tells you the 60:40 mix doesn’t accept additional sulfur. The extra part of the 80:20 total squeezes out as a separate 95:5 phase. Sulfur’s less dense than iron so the molten 95:5 will be floating on top of the 60:40. Two liquids but they’re like oil and water. If you want a uniform 80:20 liquid you have to shorten the tie line by raising the temp above 2000°C.”

“All that’s theory. Is there evidence to back it up?”

“Indeed, Sy, now that Juno‘s up there taking pictures. When the spacecraft rounded Io last February JunoCam caught several specular reflections of sunlight just like it had bounced off mirrors. At first the researchers suspected volcanic glass but the locations matched Loki and other hot volcanic calderas. The popular science press can say ‘sulfur lakes’ but NASA’s being cagey, saying ‘lava‘ — composition’s probably somewhere between 10:90 and 60:40 but we don’t know.”

Artist’s concept of Loki Patera,
a lava lake on Jupiter’s moon Io
Credit: NASA/JPL-Caltech/SwRI/MSSS

~ Rich Olcott

A Sublime Moment

On By rolcottIn Chemistry, Physics: Entropy and Thermodynamics, Uncategorized1 Comment

It’s either late Winter or early Spring, trying to make up its mind. Either way, today’s lakeside walk is calm until I get to the parking lot and there he is, all bundled up and glaring at a huge pile of snow. “Morning, Mr Feder. You look even more out of sorts than usual. Why so irate?”

“The city’s dump truck buried my car in that stuff.”

“Your car’s under that? But there’s a sign saying not to park in that spot when there’s a snow event.”

“Yeah, yeah. Back on Fort Lee we figure the city just puts up signs like that to remind us we pay taxes. I’ll park where I want to. Freedom!”

“I’m beginning to understand you better, Mr Feder. Got a spare shovel? I can help you dig out.”

“My car shovel’s in the car, of course. I got another one at home for the sidewalk.”

I notice something, move over for a better view. “Step over here and look close just above the top of the pile where the sunlight’s hitting it.”

“Smoke! My car’s burning up under there!”

“No, no, something much more interesting. You’re looking at something that I’ve seen only a couple of times so you’re a lucky man. That’s steam, or it would be steam at a slightly higher temperature. What you’re looking at is distilled snow. See the sparkles from ice crystals in that cloud? Beautiful. Takes a very special set of circumstances to make that happen.”

“I’d rather be lucky in the casino. What’s so special?”

“The air has to be still, absolutely no breeze to sweep floating water molecules away from the pile. Temperature below freezing but not too much. Humidity at the saturation point for that temperature. Bright sun shining on snow that’s a bit dirty.”

“Dirty’s good?”

“In this case. Here’s the sequence. Snow is water molecules locked into a crystalline structure, right? Most of them are bonded to neighbors top, bottom and every direction. The molecules on the surface don’t have as many neighbors, right, so they’re not bonded as tightly. So along comes sunlight, not only visible light but also infrared radiation—”

“Infrared’s light, too?”

“Mm-hm, just colors we can’t see. Turns out because of quantum, infrared light photons are even more effective than visible light photons when it comes to breaking water molecules away from their neighbors. So a top molecule, I’ll call it Topper, escapes its snow crystal to float around in the air. Going from solid directly to free-floating gas molecules, we call that sublimation. Going the other way is deposition. Humidity’s at saturation, right, so pretty soon Topper runs into another water molecule and they bond together.”

<sarcasm, laid on heavily> “And they make a cute little snow crystal.”

“Not so fast. With only two molecules in the structure, you can’t call it either solid or liquid but it does grow by adding on more molecules. Thing is, every molecule they encounter gives up some heat energy as it ties down. If the weather’s colder than it is here, that’s not enough to overcome the surrounding chill. The blob winds up solid, falls back down onto the pile. If it’s just a tad warmer you get a liquid blob that warms the sphere of air around it just enough to float gently upwards—”

“Like a balloon, I got the picture.”

“Floats up briefly. It doesn’t get up far before the surrounding chill draws out that heat and wins again. Not so brief when there’s a little dirt in there.”

“The dirt floats?”

“Of course not. The dirt’s down in the snow pile, but it’s dark and absorbs more sunlight energy than snow crystals do. What the dirt does is, it tilts the playing field. Heat coming from the dirt particles increases the molecular break‑free rate and there’s more blobs. It also warms the air around the blobs and floats them high enough to form this sparkling cloud we can see and enjoy.”

“You can enjoy it. I’m seeing my car all covered over and that’s not improving my mood.”

“Better head home for that shovel, Mr Feder. The snow dumper’s coming back with another load.”

~ Rich Olcott