Water, Water Everywhere — How Come?

Lunch time, so I elbow my way past Feder and head for the elevator.  He keeps peppering me with questions.

“Was Einstein ever wrong?”

“Sure. His equations pointed the way to black holes but he thought the Universe couldn’t pack that much mass into that small a space.  It could.  There are other cases.”

We’re on the elevator and I punch 2.  “Where you going?  I ain’t done yet.”

“Down to Eddie’s Pizza.  You’re buying.”

“Awright, long as I get my answers.  Next one — if the force pulling an electron toward a nucleus goes as 1/r², when it gets to where r=0 won’t it get stuck there by the infinite force?”

“No, because at very short distances you can’t use that simple force law.  The electron’s quantum wave properties dominate and the charge is a spread-out blur.”

The elevator stops at 7.  Cathleen and a couple of her Astronomy students get on, but Feder just peppers on.  “So I read that everywhere we look in the Solar System there’s water.  How come?”

I look over at Cathleen.  “This is Mr Richard Feder of Fort Lee, NJ.  He’s got questions.  Care to take this one?  He’s buying the pizza.”

“Well, in that case.  It all starts with alpha particles, Mr Feder.”

The elevator door opens on 2, we march into Eddie’s, order and find a table.  “What’s an alpha particle and what’s that got to do with water?”

Alpha particle

Two protons and two neutrons, assembled as an alpha particle

“An alpha particle’s a fragment of nuclear material that contains two protons and two neutrons.  99.999% of all helium atoms have an alpha particle for a nucleus, but alphas are so stable relative to other possible combinations that when heavy atoms get indigestion they usually burp alpha particles.”

“And the water part?”

“That goes back to where our atoms come from — all our atoms, but in particular our hydrogen and oxygen.  Hydrogen’s the simplest atom, just a proton in its nucleus.  That was virtually the only kind of nucleus right after the Big Bang, and it’s still the most common kind.  The first generation of stars got their energy by fusing hydrogen nuclei to make helium.  Even now, that’s true for stars about the size of the Sun or smaller.  More massive stars support hotter processes that can make heavier elements.  Umm, Maria, do you have your class notes from last Tuesday?”

“Yes, Professor.”

“Please show Mr Feder that chart of the most abundant elements in the Universe.  Do you see any patterns in the second and fourth columns, Mr Feder?”

Element Atomic number Mass % *103 Atomic weight Atom % *103
Hydrogen 1 73,900 1 92,351
Helium 2 24,000 4 7,500
Oxygen 8 1,040 16 81
Carbon 6 460 12 48
Neon 10 134 20 8
Iron 26 109 56 2
Nitrogen 7 96 14 <1
Silicon 14 65 32 <1

“Hmm…  I’m gonna skip hydrogen, OK?  All the rest except nitrogen have an even atomic number, and all of ’em except nitrogen the atomic weight is a multiple of four.”

“Bravo, Mr Feder.  You’ve distinguished between two of the primary reaction paths that larger stars use to generate energy.  The alpha ladder starts with carbon-12 and adds one alpha particle after another to go from oxygen-16 on up to iron-56.  The CNO cycle starts with carbon-12 and builds alphas from hydrogens but a slow step in the cycle creates nitrogen-14.”

“Where’s the carbon-12 come from?”

“That’s the third process, triple alpha.  If three alphas with enough kinetic energy meet up within a ridiculously short time interval, you get a carbon-12.  That mostly happens only while a star’s going nova, simultaneously collapsing its interior and spraying most of its hydrogen, helium, carbon and whatever out into space where it can be picked up by neighboring stars.”

“Where’s the water?”

“Part of the whatever is oxygen-16 atoms.  What would a lonely oxygen atom do, floating around out there?  Look at Maria’s table.  Odds are the first couple of atoms it runs across will be hydrogens to link up with.  Presto!  H2O, water in astronomical quantities.  The carbon atoms can make methane, CH4; the nitrogens can make ammonia, NH3; and then photons from Momma star or somewhere can help drive chemical reactions  between those molecules.”

“You’re saying that the water astronomers find on the planets and moons and comets comes from alpha particles inside stars?”

“We’re star dust, Mr Feder.”

~~ Rich Olcott

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Shopping The Old Curiosity

“Still got questions, Moire.”

“This’ll be your last shot this year, Mr Feder.  What’s the question?”

“They say a black hole absorbs all the light that falls on it. But the theory of blackbody radiation says a perfect absorber is also a perfect radiator. Emission should be an exact opposite flow to the incoming flow in every direction. Wouldn’t a black hole be shiny like a ball bearing?”Black hole as ball bearing 1
“A perfectly good question, but with crucial imperfections. Let’s start with the definition of a perfect absorber — it’s an object that doesn’t transmit or reflect any light. Super-black, in other words. So by definition it can’t be a mirror.”

“OK, maybe not a mirror, but the black hole has to send out some kind of exact opposite light to balance the arriving light.”

“Yes, but not in the way you think. Blackbody theory does include the assumption that the object is in equilibrium, your ‘exact opposite flow.’ The object must indeed send out as much energy as it receives, otherwise it’d heat up or cool down. But the outbound light doesn’t necessarily have to be at the same frequencies as the inbound light had. In fact, it almost never will.”

“How come not?”

“Because absorption and emission are two different processes and they play by different rules. If we’re including black holes in the discussion there are four different processes. No, five.  Maybe six.”

“I’m listening.”

“Good. Blackbody first. When a photon is absorbed by regular matter, it affects the behavior of some electron in there. Maybe it starts spending more time in a different part of the molecule, maybe it moves faster — one way or another, the electron configuration changes and that pulls the atomic nuclei away from where they were and the object’s atoms wobble differently. So the photon raises the object’s internal kinetic energy, which means raising its temperature, and we’ve got energy absorption, OK?”

“Yeah, and…?”

“At some later time, to keep things in equilibrium that additional energy has to be gotten rid of. But you can’t just paint one bit of energy red, say it’s special and follow it until it’s emitted. The whole molecule or crystal or whatever has excess energy as the result of all the incoming photons. When the total gets high enough, something has to give.  The object emits some photons to get rid of some of the excess. The only thing you can say about the outbound photons is that they generally have a lower energy than the incoming ones.”

“Why’s that?”

“Think of a bucket that’s brim-full and you’re dumping in cupfuls of water. Unless you’re pouring slowly and carefully, the dribbles escaping over the bucket’s rim will generally be many small amounts sloshing out more often than those cupfuls come in.  For light that’s fluorescence.”

“I suppose. What about the black hole?”

“The problem with a black hole is the mystery of what’s inside its event horizon. It probably doesn’t contain matter in the form of electrons and nuclei but we don’t know. There are fundamental reasons why information about what’s inside can’t leak out to us. All we can say is that when a light wave encounters a black hole, it’s trapped by the intense gravity field and its energy increments the black hole’s mass.  The mechanism … who knows?”

“Like I said, it gets absorbed. And gets emitted as Hawking radiation.”

“Sorry, that’s exactly what doesn’t happen. Hawking radiation arises from a different pair of processes. Process 1 generates pairs of virtual particles, which could be photons, electrons or something heavier. That happens at a chaotic but steady rate throughout the Universe.  Usually the particle pairs get back together and annihilate.  However, right next to the black hole’s event horizon there’s Process 2, in which one member of a virtual pair flies inward and the other member flies outward as a piece of Hawking radiation. Neither process even notices incoming photons. That’s not mirroring or even fluorescence.”

“Phooey, it was a neat idea.”

“That it was, but facts.”

~~ Rich Olcott

  • Thanks to lifeisthermal for inspiring this post.
  • Thus endeth a full year of Sy Moire stories.  I hope you enjoyed them.  Here’s to a new year and new ideas for all.

Curiosity in The Internet Market

“I got another question, Moire.”

“Of course you do, Mr Feder.  Let’s hear it.”

“I read on the Internet that there’s every kind of radioactivity coming out of lightning bolts.  So is that true, how’s it happen and how come we’re not all glowing in the dark?”

“Well, now, like much else you read on the Internet there’s a bit of truth in there, and a bit of not-truth, all wrapped up in hype.  The ‘every kind of radioactivity’ part, for instance, that’s false.”

“Oh yeah?  What’s false about that?”

“Kinds like heavy-atom fission and alpha-particle ejection.  Neither have been reported near lightning strikes and they’re not likely to be.  Lightning travels through air.  Air is 98% nitrogen and oxygen with a sprinkling of light atoms.  Atoms like that don’t do those kinds of radioactivity.”

“So what’s left?”

“There’s only two kinds worth worrying about — beta decay, where the nucleus spits out an electron or positron, and some processes that generate gamma-rays.  Gamma’s a high-energy photon, higher even than X-rays.  Gamma photons are strong enough to ionize atoms and molecules.”

“You said ‘worth worrying about.’  I like worrying.  What’s in the not-worth-it bucket?”

“Neutrinos.  They’re so light and interact so little with matter that many physicists think of them as just an accounting device.  Trillions go through you every second and you don’t notice and neither do they.  Really, don’t worry about them.”

“Easy for you to say.  Awright, so how does lightning make the … I guess the beta and gamma radioactivity?”

“We know the general outlines, although a lot of details have yet to be filled in.  What do you know about linear accelerators?”

“Not a clue.  What is one?”

Lighting and a diagram of a linac

Linac diagram adapted from
Sgbeer – Own work, CC BY-SA 3.0

“It’s a technology for making high-energy electrons and other charged particles.  Picture a straight evacuated pipe equipped with ring electrodes at various distances from the source end.  The source could be an electron gun or maybe a rig that spits out ions of some sort.  Voltages between adjacent electrodes downstream of a particle will give it a kick when it passes en route to the target end.  By using the right voltages at the right times you can boost an electron’s kinetic energy into the hundred-million-eV range.  That’s a lot of kinetic energy.  Got that picture?”

“Suppose that I do.  Then what?”

“Lightning is the same thing but without the pipe and it’s not straight.  The electrons have an evacuated path, because plasma formation drives most of the molecules out of there.  Activity inside the clouds gives them high voltages, up to a couple hundred megavolts.  But on top of that there’s bremsstrahlung.”

“Brem…?”

Bremsstrahlung — German for braking radiation.  You know how your car’s tires squeal when you make a turn at speed?”

“One of my favorite sounds, ‘specially when … never mind.  What about it?”

“That’s your tires converting your forward momentum into sound waves.  Electrons do that, too, but with electromagnetism.  The lightning path zigs and zags.  An electron’s path has to follow suit.  At each swerve, the electron throws off some of its kinetic energy as an electromagnetic wave, otherwise known as a photon.  Those can be very high-energy photons, X-rays or even gamma-rays.”

“So that’s where the gammas come from.”

“Yup.  But there’s more.  Remember those nitrogen atoms?  Ninety-nine-plus percent of them are nitrogen-14, a nice, stable isotope with seven protons and seven neutrons.  If a sufficiently energetic gamma strikes a nitrogen-14, the atom’s nucleus can kick out a neutron and turn into unstable nitrogen-13.  That nucleus emits a positron to become stable carbon-13.  So you’ve got free neutrons and positrons to add to the radiation list.”

“With all that going on, how come I’m not glowing in the dark?”

“‘Because the radiation goes away quickly and isn’t contagious.  Most of the neutrons are soaked up by  hydrogen atoms in passing water molecules (it’s raining, remember?).  Nitrogen-13 has a 10-minute half-life and it’s gone.  The remaining neutrons, positrons and gammas can ionize stuff, but that happens on the outsides of molecules, not in the nuclei.  Turning things radioactive is a lot harder to do.  Don’t worry about it.”

“Maybe I want to.”

“Your choice, Mr Feder.”

~~ Rich Olcott

At The Old Curiosity Shop

An imposing knock at the door, both impetuous and imperious.  I figured it for an Internet denizen.  “C’mon in, the door’s open.”

“You’re Moire?”

“I am.  And you are..?”

“The name’s Feder, Richard Feder, from Fort Lee, NJ.  I’m a stand-in for some of your commenters.”

“Ah, the post of business past.  You have a question?”

“Yeah.  How come hot water can freeze faster than cold water?”

“That’s really two questions. The first is, ‘Can hot water freeze faster than cold water?’ and the second is, ‘How come?‘  To the surprise of a lot of physicists, the experimental answer to the first question is, ‘Yes, sometimes.‘  But it’s only sometimes and even that depends on how you define freeze.”

“What’s to define?  Frozen is frozen.”

“Not so fast.  Are we talking surface ice formation, or complete solidification, or maybe just descent to freezing temperature?  Three very different processes.  There’s multiple reports of anomalous behavior for each one, but many of the reports have been contested by other researchers.  Lots of explanations, too.  The situation reminds me of Anne’s Elephant.”

“Why an elephant?  And who’s Anne?”

“Remember the old story about the blind men trying to figure out an elephant?  The guy touching its trunk said it’s a snake, the one at its side said it’s a wall, the dude at its leg said it’s a tree, and so on?  The descriptions differed because each observer had limited knowledge of something complicated.  This chilled-water issue is like that — irreproducible experiments because of uncontrolled unknown variables, mostly maybes on the theory side because we’re still far from a fundamental understanding.”

“Who’s Anne?”

“Anne is … an experience.  I showed her how the notion of Entropy depends on how you look at it.  Scientists have looked at this paradoxical cooling effect pretty much every way you can think of, trying to rule out various hypotheses.  Different teams have both found and not found the anomaly working with distilled water and with tap water, large amounts and small, in the open air and in sealed containers, in glass or metal containers, with and without stirring, with various pre-washing regimens or none, using a variety of initial and final temperatures.  They’ve clocked the first appearance of surface ice and complete opacity of the bulk.  They’ve tracked temperature’s trajectory in the middle of the container or near its wall… you name it.  My favorite observation was the 20th Century’s first-published one — in 1963 Erasto Mpemba noticed the effect while preparing ice cream.”

“What flavor?  Never mind.  Is there a verdict?”

“Vaguely.  Once you get approximately the right conditions, whether or not you see the effect seems to be a matter of chance.  The more sophisticated researchers have done trials in the hundreds and then reported percentages, rather than just ‘we see it’ or not.  Which in itself is interesting.”many elephants

“How’s that?”

“Well, to begin with, the percents aren’t zero.  That answers your first question — warm water sometimes does freeze faster than cold.  Better yet, the variability tells us that the answer to your second question is at the nanoscopic level.  Macroscopic processes, even chemical ones, have statistics that go the same way all the time.  Put a lit match to gasoline in air, you’ll always get a fire.  But if you set out 100 teaspoons of water under certain conditions and 37 of them freeze and the others don’t, something very unusual must be going on that starts with just a few molecules out of the 10²³ in those teaspoons.”

“Weird odds.”

This experiment’s even more interesting.  You’ve got two bottles of water.  You heat up bottle A and let it cool to room temperature.  B‘s been at room temperature all along.  You put ’em both in the fridge and track their temperatures.  A cools quicker.”

“That’s where I came in.”

“Both start at the same temperature, finish at the same temperature, and their Joules-per-second energy-shedding rates should be the same.  A cools in less time so A releases less heat.  Entropy change is released heat energy divided by temperature.  Somehow, bottle A went into the fridge with less entropy than B had.  Why?  We don’t really know.”

~~ Rich Olcott

  • – Thanks to Ilias Tirovolas, whose paper inspired this post.

Meanwhile, back at the office

Closing time.  Anne and I stroll from Al’s coffee shop back to the Acme Building.  It’s a clear night with at least 4,500 stars, but Anne’s looking at the velvet black between them.

“What you said, Sy, about the Universe not obeying Conservation of Energy — tell me more about that.”

“Aaa-hmmm … OK.  You’ve heard about the Universe expanding, right?”

“Ye-es, but I don’t know why that happens.”

“Neither do the scientists, but there’s pretty firm evidence that it’s happening, if only at the longest scales.  Stars within galaxies get closer together as they radiate away their gravitational energy.  But the galaxies themselves are getting further apart, as far out as we can measure.”

“What’s that got to do with Conservation of Energy?”

“Well, galaxies have mass so they should be drawn together by gravity the way that gravity pulls stars together inside galaxies.  But that’s not what’s happening.  Something’s actively pushing galaxies or galaxy clusters away from each other.  Giving the something a name like ‘dark energy‘ is just an accounting gimmick to pretend the First Law is still in effect at very large distances — we don’t know the energy source for the pushing, or even if there is one.  There’s a separate set of observations we attribute to a ‘dark energy‘ that may or may not have the same underlying cause.  That’s what I was talking about.”Fading white satin

We’re at the Acme Building.  I flash my badge to get us past Security and into the elevator.  As I reach out to press the ’12’ button she puts her hand on my arm.  “Sy, I want to see if I understand this entropy-elephant thing.  You said entropy started as an accounting gimmick, to help engineers keep track of fuel energy escaping into the surroundings.  Energy absorbed at one temperature they called the environment’s heat capacity.  Total energy absorbed over a range of temperatures, divided by the difference in temperature, they called change in entropy.”

The elevator lets us out on my floor and we walk to door 1217.  “You’ve got it right so far, Anne.  Then what?”

“Then the chemists realized that you can predict how lots of systems will work from only knowing a certain set of properties for the beginning and end states.  Pressure, volume, chemical composition, whatever, but also entropy.  But except for simple gases they couldn’t predict heat capacity or entropy, only measure it.”

My key lets us in.  She leans back against the door frame.  “That’s where your physicists come in, Sy.  They learned that heat in a substance is actually the kinetic energy of its molecules.  Gas molecules can move around, but that motion’s constrained in liquids and even more constrained in solids.  Going from solid to liquid and from liquid to gas absorbs heat energy in breaking those constraints.  That absorbed heat appears as increased entropy.”

She’s lounging against my filing cabinet.  “The other way that substances absorb heat is for parts of molecules to rotate and vibrate relative to other parts.  But there are levels.  Some vibrations excite easier than others, and many rotations are even easier.  In a cold material only some motions are active.  Rising temperature puts more kinds of motion into play.  Heat energy spreads across more and more sub-molecular absorbers.”

She’s perched on the edge of my desk.  “Here’s where entropy as possibility-counting shows up.  More heat, more possibilities, more entropy.  Now we can do arithmetic and prediction instead of measuring.  Anything you can count possibilities for you can think about defining an entropy for, like information bits or black holes or socks.  But it’ll be a different entropy, with its own rules and its own range of validity.  … And…”Riding the Elephant

She’s looming directly over me.  Her dark eyes are huge.

“And…?”

When we first met, Sy, you asked what you could do for me.  You’ve helped me see that when I travel across time and probability I’m riding the Entropy Elephant.  I’d like to show my appreciation.  Can you think of a possibility?”

A dark night, in a city that knows how to keep its secrets.  On the 12th floor of the Acme Building, one man still tries to answer the Universe’s persistent questions — Sy Moire, Physics Eye.

~~ Rich Olcott

Thoughts of Chair-man Moire

My apples and orange peels question, Sy,  isn’t that the same as Jeremy’s?  What’s the connection between heat capacity and counting?”

“You’re right, Anne.  Hmm.  Say, Al, all your coffee shop tables came with four chairs apiece, right?”

“Yup, four-tops every one, even in the back room.”

“You neaten them all up, four to a table, in the morning?”

“The night before.  There’s never time in the morning, customers demand coffee first thing.”

“But look, we’ve got six people seated at this table.  Where’d the extra chairs come from?”

“Other tables, of course.  Is this going somewhere?”

“Almost there.  So in fact the state of the room at any time will have some random distribution of chairs to tables.  You know on the average there’ll be four at a table, but you don’t know the actual distribution until you look, right?”

“Hey, we’re counting again.  You’re gonna say that’s about entropy ’cause the difference between four at a table and some other number is all random and there’s some formula to calculate entropy from that.”elephants and chairs

“True, Vinnie, but we’re about to take the next step.  How did these chairs wind up around this table?”

“We pulled them over, Mr. Moire.”

“My point is, Jeremy, we spent energy to get them here.  The more chairs that are out of position — ”

“The higher the entropy, but also the more energy went into the chairs.  It’s like that heat capacity thing we started with, the energy that got absorbed rather than driving the steam engine.”

“Awright, Anne!” from Jeremy <Jennie bristles a bit>, “and if all the chairs are in Al’s overnight position it’s like absolute zero.  Hey, temperature is average kinetic energy per particle so can we say that the more often a chair gets moved it’s like hotter?”

Jennie breaks in.  “Not a bit of it, Jeremy!  The whole metaphor’s daft.  We know temperature change times heat capacity equals the energy absorbed, right, and we’ve got a link between energy absorption and entropy, right, but what about if at the end of the day all the chairs accidentally wind up four at a table?  Entropy change is zero, right, but customers expended energy moving chairs about all day and Al’s got naught to set straight.”

“Science in action, I love it!  Anne and Jeremy, you two just bridged a gap it took Science a century to get across.  Carnot started us on entropy’s trail in 1824 but scientists in those days weren’t aware of matter’s atomic structure.  They knew that stuff can absorb heat but they had no inkling what did the absorbing or how that worked.  Thirty years later they understood simple gases better and figured out that average kinetic energy per particle bit.  But not until the 1920s did we have the quantum mechanics to show how parts of vibrating molecules can absorb heat energy stepwise like a table ‘absorbing’ chairs.  Only then could we do Vinnie’s state-counting to calculate entropies.”

“Yeah, more energy, spread across more steps, hiding more details we don’t know behind an average, more entropy.  But what about Jennie’s point?”

“Science is a stack of interconnected metaphors, Vinnie.  Some are better than others.  The trick is attending to the boundaries where they stop being valid.  Jennie’s absolutely correct that my four-chair argument is only a cartoon for illustrating stepwise energy accumulation.  If Al had a billion tables instead of a dozen or so, the odds on getting everything back to the zero state would disappear into rounding error.”

“How does black hole entropy play into this, Sy?”TSE classical vs BH

“Not very well, actually.  Oh, sure, the two systems have similar structures.  They’ve each got three inter-related central quantities constrained by three laws.  Here, I’ve charted them out on Old Reliable.”

“OK, their Second and Third Laws look pretty much the same, but their First Laws don’t match up.”

“Right, Al.  And even Bekenstein pointed out inconsistencies between classic thermodynamic temperature and what’s come to be called Hawking temperature.  Hawking didn’t agree.  The theoreticians are still arguing.  Here’s a funny one — if you dig deep enough, both versions of the First Law are the same, but the Universe doesn’t obey it.”

“That’s it, closing time.  Everybody out.”

~~ Rich Olcott

Taming The Elephant

Suddenly they were all on the attack.  Anne got in the first lick.  “C’mon, Sy, you’re comparing apples and orange peel.  Your hydrogen sphere would be on the inside of the black hole’s event horizon, and Jeremy’s virtual particles are on the outside.”

[If you’ve not read my prior post, do that now and this’ll make more sense.  Go ahead, I’ll wait here.]white satin and 5 elephantsJennie’s turn — “Didn’t the chemists define away a whole lot of entropy when they said that pure elements have zero entropy at absolute zero temperature?”

Then Vinnie took a shot.  “If you’re counting maybe-particles per square whatever for the surface, shouldn’t you oughta count maybe-atoms or something per cubic whatever for the sphere?”

Jeremy posed the deepest questions. “But Mr Moire, aren’t those two different definitions for entropy?  What does heat capacity have to do with counting, anyhow?”

Al brought over mugs of coffee and a plate of scones.  “This I gotta hear.”

“Whew, but this is good ’cause we’re getting down to the nub.  First to Jennie’s point — Under the covers, Hawking’s evaluation is just as arbitrary as the chemists’.  Vinnie’s ‘whatever’ is the Planck length, lP=1.616×10-35 meter.  It’s the square root of such a simple combination of fundamental constants that many physicists think that lP2=2.611×10-70 m², is the ‘quantum of area.’  But that’s just a convenient assumption with no supporting evidence behind it.”

“Ah, so Hawking’s ABH=4πrs2 and SBH=ABH/4 formulation with rs measured in Planck-lengths, just counts the number of area-quanta on the event horizon’s surface.”

“Exactly, Jennie.  If there really is a least possible area, which a lot of physicists doubt, and if its size doesn’t happen to equal lP2, then the black hole entropy gets recalculated to match.”

“So what’s wrong with cubic those-things?”

“Nothing, Vinnie, except that volumes measured in lP3 don’t apply to a black hole because the interior’s really four-dimensional with time scrambled into the distance formulas.  Besides, Hawking proved that the entropy varies with half-diameter squared, not half-diameter cubed.”

“But you could still measure your hydrogen sphere with them and that’d get rid of that 1033 discrepancy between the two entropies.”

“Not really, Vinnie.  Old Reliable calculated solid hydrogen’s entropy for a certain mass, not a volume.”

“Hawking can make his arbitrary choice, Sy, he’s Hawking, but that doesn’t let the chemists off the scaffold.  How did they get away with arbitrarily defining a zero for entropy?”

“Because it worked, Jennie.  They were only concerned with changes — the difference between a system’s state at the end of a process, versus its state at the beginning.  It was only the entropy difference that counted, not its absolute value.”

“Hey, like altitude differences in potential energy.”

“Absolutely, Vinnie, and that’ll be important when we get to Jeremy’s question.  So, Jennie, if you’re only interested in chemical reactions and if it’s still in the 19th Century and the world doesn’t know about isotopes yet, is there a problem with defining zero entropy to be at a convenient set of conditions?”

“Well, but Vinnie’s Second Law says you can never get down to absolute zero so that’s not convenient.”

“Good point, but the Ideal Gas Law and other tools let scientists extrapolate experimentally measured properties down to extremely low temperatures.  In fact, the very notion of absolute zero temperature came from experiments where the volume of a  hydrogen or helium gas sample appears to decrease linearly towards zero at that temperature, at least until the sample condenses to a liquid.  With properly calibrated thermometers, physical chemists knocked themselves out measuring heat capacities and entropies at different temperatures for every substance they could lay hands on.”

“What about isotopes, Mr Moire?  Isn’t chlorine’s atomic weight something-and-a-half so there’s gotta be several of kinds of chlorine atoms so any sample you’ve got is a mixture and that’s random and that has to have a non-zero entropy even at absolute zero.”

“It’s 35.4, two stable isotopes, Jeremy, but we know how to account for entropy of mixing and anyway, the isotope mix rarely changes in chemical processes.”

“But my apples and orange peels, Sy — what does the entropy elephant do about them?”

~~ Rich Olcott