Old Sol And The Pasta Pot

<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.”

“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

“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.”

“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.”

“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

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

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?”

“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