Category: Physics

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

Xanax For Molecules

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

Vinnie plops down by our table at Cal’s Coffee. “Hi, guys. Glad you’re both here. Susan, Sy here says you’re an RDX expert so I got a question.”

“Not an expert, Vinnie, it’s just one of a series of compounds in one of my projects. What’s your question?”

“How come the stuff is so touchy but it’s not touchy? You can shoot a bullet into a lump of it, nothing happens, but set off a detonator next to it and WHAMO! Why do we need a detonator, and what’s in one anyway?”

“Sy, what sets off an H‑bomb?”

“An A‑bomb. You need a lot of energy in a confined region to crowd those protons enough that they fuse.”

“And what sets off an A‑bomb?”

“Hey I know that one, Susan, I saw the Oppenheimer movie. You need some kind of explosives going off just right to cram two chunks of plutonium together real fast so they do the BANG! thing instead of just melting. Wait! I see where you’re going — little explosions trigger big explosions, right?”

“Bravo! You’ve got the idea behind activation energy.”

“Geez, another kind of energy?”

“Yes and no, Vinnie. Enthalpy and its cousins are about the net change when something happens. We can use them to predict how a complex reaction will settle down, but they don’t tell us much about the kinetics, how fast things will happen. Think for a minute about those H‑bomb hydrogen atoms. What prevents them from fusing?”

“I guess under normal conditions they’re too far apart and even when they get close their electron clouds push against each other.”

<Sketching on a paper napkin> “Fair enough. Okay, here’s what the potential energy curve looks like, sorta. There’s hydrogen atom A over there at the right-hand end of the curve. B‘s a second hydrogen on the left and heading inwards. With me?”

“So far.”

“Right. Now, B comes roaring in with some amount of kinetic energy and hits the potential energy bump where those electron clouds overlap. If it has enough kinetic energy to overcome that barrier, it keeps on going. Otherwise it bounces back with the kinetic energy it had maybe minus some that A picked up in the recoil.”

“So the first barrier is the electron‑electron repulsion, but the potential dips in the middle where the clouds merge and that’s where molecules happen.”

“Right, Sy. But then there’s the second barrier as B‘s positive charge encounters A‘s. Inverse‑square law and all that, it’s an enormous hurdle. Visualize lots of Bs with different kinetic energies running up against that wall again and again until finally, if the pressure’s high enough, one gets past and the fusion releases more energy than the winning B had originally. The higher the wall, the fewer Bs hit As per unit time and the slower the reaction.”

“Looking at the before‑and‑afters, the reaction only happens if energy’s released, but how fast it goes is that barrier’s fault.”

“Perfect, Vinnie. Take RDX, for example. You’re right, it’s touchy. If you’ve got the pure stuff, never look at it cross‑eyed unless you’re behind a blast shield. Lots of energy released, very low energy of activation.”

“But like I said, you can shoot a gun at it, no effect.”

“That wasn’t pure RDX, it was probably some version of C‑4.”

“Yeah, C‑4, don’t know any of the details.”

“C‑4’s explosive is RDX, but it’s also got some plasticizer for that putty consistency, and a phlegmatizer. I love that word.”

“Phlegmatizer? That’s a new one for me.”

“It’s an additive to keep the explosive calm — phlegmatic, get it? — until it gets excited on purpose, which is the detonator’s job.” <scribbling on a stack of paper napkins> “Okay, here’s that same activation energy curve, an RDX particle on the right, and an incoming shock wave. The gray region is the phlegmatizer, usually paraffin or a heavy oil. Think of it as a shock absorber, absorbing or deflecting the shockwave before it can activate the explosive. A detonator’s designed to activate and erupt so quickly that its shock peak arrives before the phlegmatizer can spread it out.”

“Like they say, timing is everything.”

~ Rich Olcott

Tightening Up Fast And Loose

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

Cal brings out a fresh batch of scones. He’s tonging them onto the racks when I suddenly get a whiff of mocha latte. I glance back and there’s Susan Kim, grinning at me. “Hi, Sy. Grab your scone and a table. I have a bone to pick with you.”

A few moments later we’re seated. Cal’s coffee’s especially smooth today. “Okay, what’s the bone?”

“You’re playing fast and loose with your enthalpy definition. Yes, there’s change in temperature times entropy, enthalpy’s thermal component, and an expansion‑contraction component you called pressure‑volume. But it’s just sloppy to call what’s left ‘the chemical portion.’ What it is, really, is the combination of every other kind of energy something has that some process could extract. Chemical reactions are just one piece.”

“Strong words, coming from a chemist. What else should be packed in there?”

“Radioactivity, for one. It’s a heat source that doesn’t depend on chemical reactions. Atom for atom, a nuclear disintegration can yield millions of times more energy than a chemical reaction does. Trouble is, radioactive atoms only break down when they feel like it so the energy’s all random heat. I’m sure there’s a bunch of other non‑chemical ways to increase something’s apparent enthalpy.”

“Hmm. Challenge accepted. … It’s all about which process will extract some kind of energy from your something. How about the something’s a tightly‑wound spring? No, wait, that’s chemical, because the energy’s stored in stretched metal‑metal bonds.”

“No, I’ll accept spring tension because there’s no change in chemical composition during the unwind process. What’s another one?”

“Ah. Easy. Kinetic energy if the something’s flying through the air to hit something else.”

“Now you’re cooking. Gravitational potential energy if it’s falling down. Oh, suppose it’s magnetized and goes through a conductive loop on the way down?”

“Nope, doesn’t count. The object’s kinetic energy would produce a jolt of electrical potential in the loop, but it’s own magnetization wouldn’t change. Nice, that distinction sharpens the point — what you count as enthalpy’s third component depends on which change process you’re talking about. If there’s no chemical change, then the chemical part of the internal component of the enthalpy change is zero. In the early days of thermodynamics, for instance, everyone was working on steam. Water may corrode your equipment over the long term, but otherwise it’s just hot water molecules becoming not‑as‑hot water molecules and there’s no change in internal energy. The only energy terms you have to think about are pressure‑volume and temperature‑entropy. That’s why they defined it that way.”

“Which one wins?”

“Hmm?”

“You’ve pared enthalpy changes down to just two kinds of energy. I’ve got to wonder, which one has the bigger contribution?”

<pulls up a display on Old Reliable> “This is just for the water‑steam system, mind you. Vinnie was surprised. It’s all based on specific heat measurements so visualize one kilogram of liquid water.”

“A liter, right.”

“The line labeled ‘Mechanical’ is the amount of energy you’d get by expanding that kilogram from 0°C up to the temperatures laid out on the x‑axis. No significant expansion up near boiling temperature, then it follows the Ideal Gas Law, PV=nRT. At atmospheric pressure and in this temperature range the expansion relative to 0°C runs about 200 kilojoules per kilogram.”

“And the ‘Thermal’ line?”

“That’s lab‑measured heat capacity values I pulled from the CRC Handbook, each multiplied by the corresponding temperature in kelvins. That’s the amount of energy our kilogram of water molecules holds just by being at the temperature it’s at. The gas makes a nice straight line, at least in the range before heat shatters the molecules.”

“That’s what, fifteen or sixteen times more energy than the mechanical part? Wow! You know, back in Physical Chemistry class they just threw around lots of confusing thermodynamics formulas but never put numbers to them. I had no idea the entropy effect could just swamp whatever else.”

“Numbers do make a difference.”

“This clarifies something I didn’t understand back then. Entropy’s about randomness, right, and a gas molecule can be in more locations in a large volume than in a small one. V=nRT/P says volume rises linearly with temperature and that’s the linear rise in your chart.”

~ Rich Olcott

The Little Engine That Cooled

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

“Chemical potential energy is something else, Sy. You’ve got like this lump of putty just sitting there and suddenly WHAMO! Kinetic energy all over the place.”

“Sounds like you’ve been playing with explosives, Vinnie.”

“Sorta. Some of the Specials down at the base let me watch a couple of their C-4 practice shots. You know anything about C-4?”

“A little, like what it’s made of. Susan Kim’s interested in the main ingredient for some chemical reason. She calls it RDX, drew me a picture of it once. Nice symmetrical molecule loaded with nitrogen and carbon atoms just itching to fly away as a dozen separate gas molecules. Funny, how such violent stuff can be so relaxed until just the right thing sets it off. Like some people I know.”

Combustion of an RDX molecule

“Ouch. Yeah, it happens, but I’m mellowing, okay? A dozen fragments per molecule, got it. Hey, what chemical is ‘NOx‘?”

“Could be nitrous oxide N2O, or nitric oxide NO, or some combination depending, which is why there’s no number in the equation in front of oxygen’s O2. Combustion is messy.”

“Yeah, enthalpy all over the place! Those separate gas molecules spread out to a way bigger volume than the solid molecule used up. Lotsa pressure‑volume work there, right?”

“True, but gas expansion’s only one factor in an RDX discharge. Did the guys at the base mention that if you detonate that putty when it’s spread thin it can burn through an I‑beam?”

“So there’s heat, too. Can’t be much stacked up against the expansion.”

“Don’t be so sure. I’m not up on RDX thermochemistry. I never asked Susan and I don’t know whether she or anyone knows the breakout. It’s hard to do a precision measurement on an explosion, even if you do it in milligram quantities. I’ve got a good substitute for that, though. Water’s way simpler and much more thoroughly studied.”

“How is water a substitute? It doesn’t explode.”

“True, but it boils. No changes in molecular bonding, so enthalpy’s chemical part isn’t a factor. Carnot taught us to figure the pressure‑volume and thermal parts separately. Suppose you load a liter of water into a cylinder‑piston arrangement that stays at one atmosphere pressure. Get it up to boiling temperature then measure the energy input while the water boils away. The water absorbs energy while it turns to steam, right, even though there’s no change in temperature.”

“It stays at 212°?”

“212°F is 100°C or 373 K, stays steady provided the pressure stays at one atmosphere, 14.7 psi or 101325 pascals, whichever units you want to use. Pressure and temperature work together when it comes to phase changes. Anyway, the only way your rig can maintain that exact pressure is to do some kind of work, lifting a weight or something, until the cylinder’s final volume above the piston is 1705 liters. That’ll be 172 kilojoules of useful work.”

“Big cylinder.”

“Granted, but we supposed a liter of water. Scale the equipment to handle just a milliliter of water and the swept volume’s down to 1.7 liters. Neat how the metric system works. But now you’ve got a design decision to make. You can release the steam with a loud CHUFF that carries away 92% of the energy you put into it—”

“That’s no good.”

“— or you can run it through a condenser that preheats the feed water for the next cycle. Saves a lot of fuel that way.”

“That’d be my choice.”

“Mm-hm. That was Watt’s crucial improvement on Newcomen’s design. Funny thing, though. Both guys are credited with ‘inventing the steam engine’ but neither one built a device like the engines we’re used to, ones that develop power by pushing on a piston. The big demand in their day was pumping water out of mine shafts. Newcomen and Watt built vacuum gadgets.”

Watt’s steam pumping engine

“I had a well once. You can’t pull water up more than about 35 feet.”

“Right. Vacuum pumping is limited. Unfortunately, so was manufacturing technology in Watt’s time. Making a piston and cylinder that would fit together efficiently over a wide temperature range was a big challenge.”

“Their engines sucked, huh?”

~ Rich Olcott

Deep Dive

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

“Sy, I’m trying to get my head wrapped around how the potential‑kinetic energy thing connects with your enthalpy thing.”

“Alright, Vinnie, what’s your cut so far?”

“It has to do with scale. Big things, like us and planets, we can see things moving and so we know they got kinetic energy. If they’re not moving steady in a straight line we know they’re swapping kinetic energy, give and take, with some kind of potential energy, probably gravity or electromagnetic. Gravity pulls things into a circle unless angular momentum gets in the way. How’m I doing so far?”

“I’d tweak that a little, but nothing to argue with. Keep at it.”

“Yeah, I know the moving is relative to whether we’re in the same reference frame and all that. Beside the point, gimme a break. So anyway, down to the quantum level. Here you say heat makes the molecules waggle so that’s kinetic energy. What’s potential energy like down there?”

<grabs another paper napkin> “Here’s a quick sketch of the major patterns.”

“Hmm. You give up potential energy when you fall and gravity’s graph goes down from zero to more negative forever, I guess, so gravity’s always attracting.”

“Pretty much, but at this level we don’t have to bother with gravity at all. It’s about a factor of 1038 weaker than electric interactions. Molecular motions are dominated by electromagnetic fields. Some are from a molecule’s other internal components, some from whatever’s around that brandishes a charge. We’ve got two basic patterns. One of them, I’m labeling it ‘Waggle,’ works like a pendulum, sweeping up and down that U‑shape around some minimum position, high kinetic energy where the potential energy’s lowest and vice‑versa. You know how water’s H‑O‑H molecules have that the V‑shape?”

“Yeah, me you and Eddie talked about that once.”

“Mm‑hm. Well, the V‑shape gives that molecule three different ways to waggle. One’s like breathing, both sides out then both sides in. If the hydrogens move too far from the oxygen, that stretches their chemical bonds and increases their potential energy so they turn around and go back. If they get too close, same thing. Bond strength is about the depth of the U. The poor hydrogens just stretch in and out eternally, swinging up and down that symmetric curve.”

“Awww.”

“That’s a chemist’s picture. The physics picture is cloudier. In the quantum version, over here’s a trio of fuzzy quarks whirling around each other to make a proton. Over there’s a slightly different fuzzy trio pirouetting as a neutron. Sixteen of those roiling about make up the oxygen nucleus plus two more for the hydrogens plus all their electrons — imagine a swarm of gnats. On the average the oxygen cloud and the two hydrogen clouds configure near the minimum of that U‑shaped potential curve but there’s a lot of drifting that looks like symmetrical breathing.”

“What about the other two waggles?”

“I knew you’d ask. One’s like the two sides of a teeterboard, oscillating in and out asymmetrically. The other’s a twist, one side coming toward you and then the other side. Each waggle has its own distinct set of resistance forces that define its own version of waggle curve. Each kind interacts with different wavelengths of infrared light which is how we even know about them. Waggle’s official name is ‘harmonic oscillator.’ More complicated molecules have lots of them.”

“What’s that ‘bounce’ curve about?”

“Officially that’s a Lennard-Jones potential, the simplest version of a whole family of curves for modeling how molecules bounce off each other. Little or no interaction at large distances, serious repulson if two clouds get too close, and a little stickiness at some sweet-spot distance. If it weren’t for the stickiness, the Ideal Gas Law would work even better than it does. So has your head wrapped better?”

“Sorta. From what I’ve seen, enthalpy’s PV part doesn’t apply in quantum. The heat capacity part comes from your waggles which is kinetic energy even if it’s clouds moving. Coming the other way, quantum potential energy becomes enthalpy’s chemical part with breaking and making chemical bonds. Did I bridge the gap?”

“Mostly, if you insist on avoiding equations.”

~ Rich Olcott

Up, Down And Between

On By rolcottIn Physics: Entropy and Thermodynamics, Uncategorized1 Comment

Vinnie finishes his double‑pepperoni pizza. “Sy, these enthalpies got a pressure‑volume part and a temperature‑heat capacity part, but seems to me the most important part is the chemical energy.”

I’m still working on my slice (cheese and sausage). “That’s certainly true from a fuel engineering perspective, Vinnie. Here’s a clue. Check the values in this table for 0°C, also known as 273K.”

Link to Larger image

“Waitaminute! That line says the enthalpy’s exactly zero under the book‘s conditions. We talked about zeros a long time ago. All measurements have error. Nothing’s exactly zero unless it’s defined that way or it’s Absolute Zero temperature and we’ll never get there. Is this another definition thing?”

“More of a convenience thing. The altimeters in those planes you fly, do they display the distance to Earth’s center?”

“Nope, altitude above sea level, if they’re calibrated right.”

“But the other would work, too, say as a percentage of the average radius?”

“Not really. Earth’s fatter at the Equator than it is at the poles. You’d always have to correct for latitude. And the numbers would be clumsy, always some fraction of a percent of whatever the average is—”

“6371 kilometers.”

“Yeah, that. Try working with fractions of a part per thousand when you’re coming in through a thunderstorm. Give me kilometers or feet above sea level and I’m a lot happier.”

“But say you’re landing in Denver, 1.6 kilometers above sea level.”

“It’s a lot easier to subtract 1.6 from baseline altitude in kilometers than 0.00025 from 1.00something and getting the decimals right. Sea‑level calibrations are a lot easier to work with.”

“So now you know why the book shows zero enthalpy for water at 273K.”

“You’re saying there’s not really zero chemical energy in there, it’s just a convenient place to start counting?”

“That’s exactly what I’m saying. Chemical energy is just another form of potential energy. Zeroes on a potential scale are arbitrary. What’s important is the difference between initial and final states. Altitude’s about gravitational potential relative to the ground; chemists care about chemical potential relative to a specific reaction’s final products. Both concerns are about where you started and where you stop.”

“Gimme a chemical f’rinstance.”

<reading off of Old Reliable> “Reacting 1 gram of oxygen gas and 0.14 gram of hydrogen gas slowly in a catalytic fuel cell at 298K and atmospheric pressure produces one gram of liquid water and releases 18.1 kilojoules of energy. Exploding the same gas mix at the same pressure in a piston also yields 18.1 kilojoules once you cool everything back down to 298K. Different routes, same results.”

Meanwhile, Jeremy’s wandered over from his gelato stand. “Excuse me, Mr Moire. I read your Crazy Theory about how mammals like to keep their body temperature in the range near water’s minimum Specific Heat, um Heat Capacity, but now I’m confused.”

“What’s the confusion, Jeremy?”

“Well, what you told me before made sense, about increased temperature activates higher‑energy kinds of molecular waggling to absorb the heat. But that means that Heat Capacity always ought to increase with increasing temperature, right?”

“Good thinking. So your problem is…?

“Your graph shows that if water’s cold, warming it decreases its Heat Capacity. Do hotter water molecules waggle less?”

“No, it’s a context thing. Gas and liquid are different contexts. Each molecule in a gas is all by itself, most of the time, so its waggling is determined only by its internal bonding and mass configuration. Put that molecule into a liquid or solid, it’s subject to what its neighbors are doing. Water’s particularly good at intermolecular interactions. You know about the hexagonal structure locked into ice and snowflakes. When water ice melts but it’s still at low temperature, much of the hexagonal structure hangs around in a mushy state. A loose structure’s whole‑body quivering can absorb heat energy without exciting waggles in its constituent molecules. Raising the temperature disrupts that floppy structure. That’s most of the fall on the Heat Capacity curve.”

“Ah, then the Sensitivity decrease on the high‑temperature side has to do with blurry structure bits breaking down to tinier pieces that warm up more from less energy. Thanks, Mr Moire.”

“Don’t mention it.”

~~ Rich Olcott

Early Days in The Sunshine

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

“Wait, Sy. From what you just said about rocket fuel, its enthalpic energy content changes if I move it. On the ground it’s ‘chemical energy plus thermal plus Pressure times Volume.’ Up in space, though, the pressure part’s zero. So how come the CRC Handbook people decided it’s worthwhile to publish pages and pages of specific heat and enthalpy tables if it’s all ‘it depends’?”

“We know the dependencies, Vinnie. The numbers cover a wide temperature range but they’re all at atmospheric pressure. ‘Pressure times Volume‘ makes it easy to adjust for pressure change — just do that multiplication and add the result to the other terms. It’s trickier when the pressure varies between here and there but we’ve got math to handle that. The ‘thermal‘ part’s also not a big problem because if you something’s specific heat you know how its energy content changes with temperature change and vice‑versa.”

<checking a chart on his phone> “This says water’s specific heat number changes with temperature. They’re all about 1.0 but some are a little higher and some a little lower. Graph ’em out, looks like there’s a pattern there.”

<tapping on Old Reliable’s screen> “Good eye. High at the extreme temperatures, lower near — that’s interesting.”

Data from CRC handbook, 39th Ed, pp 2081-2082

“What’s that?”

“The range where the curve is flattest, 35 to 40°C. Sound familiar?”

“Yeah, my usual body temperature’s in there, toward the high side if I’ve got a fever. What’s that mean?”

“That’s so far out of my field all I’ve got is guesses. Hold on … there, I’ve added a line for 1/SH.”

“What’s that get you?”

“A different perspective. Specific Heat is the energy change when one gram of something changes temperature by one degree. This new line, I’ve called it Sensitivity, is how many degrees one unit of heat energy will warm the gram. Interesting that both curves flatten out in exactly the temperature range that mammals like us try to maintain. The question is, why do mammals prefer that range?”

“And your answer is?”

“A guess. Remember, I’m not a biologist or a biochemist and I haven’t studied how biomolecules interact with water.”

“I get that we should file this under Crazy Theories. Out with it.”

“Okay. Suppose it’s early days in mammalian evolution. You’re one of those early beasties. You’re not cold-blooded like a reptile, you’re equipped with a thermostat for your warm blood. Maybe you shiver if you’re cold, pant if you’re hot, doesn’t matter. What does matter is, your thermostat has a target temperature. Suppose your target’s on the graph’s coolish left side where water’s sensitivity rises rapidly. You’re sunning yourself on a flat rock, all parts of you getting the same calories per hour.”

“That’s on the sunward side. Shady side not so much.”

“Good point. I’ll get to that. On the sunward side you’re absorbing energy and getting warm, but the warmer you get the more your heat sensitivity rises. Near your target point your tissues warm up say 0.4 degree per unit of sunlight, but after some warming those tissues are heating by 0.6 degrees for the same energy input.”

“I recognize positive feedback when I see it, Sy. Every minute on that rock drives me further away from my target temperature. Whoa! But on the shady side I don’t have that problem.”

“That’s even messier. You’ve got a temperature disparity between the two sides and it’s increasing. Can your primitive circulatory system handle that? Suppose you’re smart enough to scurry out of the sunlight. You’ve still got a problem. There’s more to you than your skin. You’ve got muscles and those muscles have cells and those cells do biochemistry. Every chemical reaction inside you gives off at least a little heat for more positive feedback.”

“What if my thermostat’s set over there on the hot side?”

“You’d be happy in the daytime but you’d have a problem at night. For every degree you chill below comfortable, you need to generate a greater amount of energy to get back up to your target setting.”

“Smart of evolution to set my thermostat where water’s specific heat changes least with temperature.”

“That’s my guess.”

~~ Rich Olcott

Hiding Under Many Guises

On By rolcottIn Physics: Entropy and Thermodynamics, Uncategorized3 Comments

Vinnie lifts his pizza slice and pauses. “I dunno, Sy, this Pressure‑Volume part of enthalpy, how is it energy so you can just add or subtract it from the thermal and chemical kinds?”

“Fair question, Vinnie. It stumped scientists through the end of Napoleon’s day until Sadi Carnot bridged the gap by inventing thermodynamics.”

“Sounds like a big deal from the way you said that.”

“Oh, it was. But first let’s clear the ‘is it energy?’ question. How would Newton have calculated the work you did lifting that slice?”

“How much force I used times the distance it moved.”

“Putting units to that, it’d be force in newtons times distance in meters. A newton is one kilogram accelerated by one meter per second each second so your force‑distance work there is measured in kilograms times meters‑squared divided by seconds‑squared. With me?”

“Hold on — ‘per second each second’ turned into ‘per second‑squared.” <pause> “Okay, go on.”

“What’s Einstein’s famous equation?”

“Easy, E=mc².”

“Mm-hm. Putting units to that, c is in meters per second, so energy is kilograms times meters‑squared divided by seconds‑squared. Sound familiar?”

“Any time I’ve got that combination I’ve got energy?”

“Mostly. Here’s another example — a piston under pressure. Pressure is force per unit area. The piston’s area is in square meters so the force it feels is newtons per meter‑squared, times square meters, or just newtons. The piston travels some distance so you’ve got newtons times meters.”

“That’s force‑distance work units so it’s energy, too.”

“Right. Now break it down another way. When the piston travels that distance, the piston’s area sweeps through a volume measured in meters‑cubed, right?”

“You’re gonna say pressure times volume gives me the same units as energy?”

“Work it out. Here’s a paper napkin.”

“Dang, I hate equations … Hey, sure enough, it boils down to kilograms times meters‑squared divided by seconds‑squared again!”

“There you go. One more. The Ideal Gas Law is real simple equation —”

“Gaah, equations!”

“Bear with me, it’s just PV=nRT.”

“Is that the same PV so it’s energy again?”

“Sure is. The n measures the amount of some gas, could be in grams or whatever. The R, called the Gas Constant, is there to make the units come out right. T‘s the absolute temperature. Point is, this equation gives us the basis for enthalpy’s chemical+PV+thermal arithmetic.”

“And that’s where this Carnot guy comes in.”

“Carnot and a host of other physicists. Boyle, Gay‑Lussac, Avagadro and others contributed to Clapeyron’s gas law. Carnot’s 1824 book tied the gas narrative to the energetics narrative that Descartes, Leibniz, Newton and such had been working on. Carnot did it with an Einstein‑style thought experiment — an imaginary perfect engine.”

“Anything perfect is imaginary, I know that much. How’s it supposed to work?”

<sketching on another paper napkin> “Here’s the general idea. There’s a sealed cylinder in the middle containing a piston that can move vertically. Above the piston there’s what Carnot called ‘a working body,’ which could be anything that expands and contracts with temperature.”

“Steam, huh?”

“Could be, or alcohol vapor or a big lump of iron, whatever. Carnot’s argument was so general that the composition doesn’t matter. Below the piston there’s a mechanism to transfer power from or to the piston. Then we’ve got a heat source and a heat sink, each of which can be connected to the cylinder or not.”

“Looks straight‑forward.”

“These days, sure. Not in 1824. Carnot’s gadget operates in four phases. In generator mode the working body starts in a contracted state connected to the hot Th source. The body expands, yielding PV energy. In phase 2, the body continues to expand while it while it stays at Th. Phase 3, switch to the cold Tc heat sink. That cools the body so it contracts and absorbs PV energy. Phase 4 compresses the body to heat it back to Th, completing the cycle.”

“How did he keep the phases separate?”

“Only conceptually. In real life Phases 1 and 2 would occur simultaneously. Carnot’s crucial contribution was to treat them separately and yet demonstrate how they’re related. Unfortunately, he died of scarlet fever before Clapeyron and Clausius publicized and completed his work.”

~ Rich Olcott