Month: January 2025

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