Tag: Enthalpy

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

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

Energy Is A Shape-shifter

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

Another dinner, another pizza at Eddie’s place. Vinnie wanders over to my table. “Hi, Sy, got a minute?”

“Not doing anything other than eating, Vinnie. What’s on your mind other than the sound of my chewing?”

“At least you keep your mouth closed. No, it’s about this energy thing you’ve gotten back into. I read that enthalpy piece and it’s bothering me.”

“In what way?”

“Well, you said that something’s enthalpy is the energy total of ‘thermal plus Pressure‑Volume plus chemical energy,’ right? I’m trying to fit that together with the potential energy and kinetic energy we talked about a while ago. It’s not working.”

“Deep question for dinner time but worth the effort. Would it help if I told you that the ‘actual versus potential’ notion goes back to Aristotle, the ‘kinetic’ idea came from Newton’s enemy Leibniz, but ‘enthalpy’ wasn’t a word until the 20th century?”

“Not a bit.”

“Didn’t think it would. Here’s another way to look at it. The thinkers prior to the mid‑1700s all looked at lumpy matter — pendulums, rolling balls on a ramp, planets, missiles — either alone or floating in space or colliding with each other. You could in principle calculate kinetic and potential energy for each lump, but that wasn’t enough when the Industrial Revolution came along.”

“What more did they want?”

“Fuel was suddenly for more than cooking and heating the house. Before then, all you needed to know was whether the log pile was stocked better than it was last year. If not, you might have a few chilly early Spring days but you could get past that. Then the Revolution came along. Miners loved Watt’s coal‑fired water‑pump except if you bought one and ran out of coal then the mine flooded. The miners learned that some kinds of coal burned hotter than others. You didn’t need as much of the good kind for a day’s pumping. The demand for a coal‑rating system got the scientists interested, but those lumps of coal weren’t falling or colliding, they just sat there with their heat locked inside. The classical energy quantities didn’t seem to apply so it was time to invent a new kind of energy.”

“That’s how Conservation of Energy works? You just spread the definition out a little?”

“That’s the current status of dark energy, for instance. We know the galaxies are moving apart against gravity so dark energy’s in there to balance the books. We have no good idea why it exists or where it comes from, but we can calculate it. ‘Internal energy’ put the Victorian‑era physicists in the same pickle — ‘atom’ and ‘molecule’ were notions from Greek and Roman times but none of the Victorians seriously believed in them. The notion of chemical bond energy didn’t crop up until the twentieth century. Lacking a good theory, all the Victorians could do was measure and tabulate heat output from different chemical reactions, the data that went into handbooks like the CRC. Naturally they had to invent thermodynamics for doing the energy accountancy.”

“But if it’s just book-balancing, how do you know the energy is real?”

“Because all the different forms of energy convert to each other. Think of a rocket going up to meet the ISS. Some of the rocket fuel’s chemical energy goes into giving the craft gravitational potential energy just getting it up there. At the same time, most of the chemical energy becomes kinetic energy as the craft reaches the 27600 km/h speed it needs to orbit at that altitude.”

<grin> “All?”

“Okay, we haven’t figured out how to harness dark energy. Yet.”

“HAW! Wait, how does enthalpy’s ‘chemical+PV+thermal’ work when the pressure’s zero, like out in space?”

“Then no work was done against an atmosphere up there to make way for the volume. Suppose you suddenly transported a jug of fuel from Earth up to just outside of the ISS. Same amount of fuel, so same amount of chemical energy, right? Same temperature so same thermal component?”

“I suppose.”

“The volume that the jug had occupied on Earth, what happened to it?”

“Suddenly closed in, probably with a little thud.”

“The thud sound’s where the Earth‑side PV energy went. It all balances out.”

~ Rich Olcott