The Big Chill

Jeremy gets as far as my office door, then turns back. “Wait, Mr Moire, that was only half my question. OK, I get that when you squeeze on a gas, the outermost molecules pick up kinetic energy from the wall moving in and that heats up the gas because temperature measures average kinetic energy. But what about expansion cooling? Those mist sprayers they set up at the park, they don’t have a moving outer wall but the air around them sure is nice and cool on a hot day.”

“Another classic Jeremy question, so many things packed together — Gas Law, molecular energetics, phase change. One at a time. Gas Law’s not much help, is it?”

“Mmm, guess not. Temperature measures average kinetic energy and the Gas Law equation P·V = n·R·T gives the total kinetic energy for the n amount of gas. Cooling the gas decreases T which should reduce P·V. You can lower the pressure but if the volume expands to compensate you don’t get anywhere. You’ve got to suck energy out of there somehow.”

“The Laws of Thermodynamics say you can’t ‘suck’ heat energy out of anything unless you’ve got a good place to put the heat. The rule is, heat energy travels voluntarily only from warm to cold.”

“But, but, refrigerators and air conditioners do their job! Are they cheating?”

“No, they’re the products of phase change and ingenuity. We need to get down to the molecular level for that. Think back to our helium-filled Mylar balloon, but this time we lower the outside pressure and the plastic moves outward at speed w. Helium atoms hit the membrane at speed v but they’re traveling at only (v-w) when they bounce back into the bulk gas. Each collision reduces the atom’s kinetic energy from ½m·v² down to ½m·(v-w)². Temperature goes down, right?”

“That’s just the backwards of compression heating. The compression energy came from outside, so I suppose the expansion energy goes to the outside?”

“Well done. So there has to be something outside that can accept that heat energy. By the rules of Thermodynamics, that something has to be colder than the balloon.”

“Seriously? Then how do they get those microdegree above absolute zero temperatures in the labs? Do they already have an absolute-zero thingy they can dump the heat to?”

“Nope, they get tricky. Suppose a gas in a researcher’s container has a certain temperature. You can work that back to average molecular speed. Would you expect all the molecules to travel at exactly that speed?”

“No, some of them will go faster and some will go slower.”

“Sure. Now suppose the researcher uses laser technology to remove all the fast-moving molecules but leave the slower ones behind. What happens to the average?”

“Goes down, of course. Oh, I see what they did there. Instead of the membrane transmitting the heat away, ejected molecules carry it away.”

“Yup, and that’s the key to many cooling techniques. Those cooling sprays, for instance, but a question first — which has more kinetic energy, a water droplet or the droplet’s molecules when they’re floating around separately as water vapor?”

“Lessee… the droplet has more mass, wait, the molecules total up to the same mass so that’s not the difference, so it’s droplet velocity squared versus lots of little velocity-squareds … I’ll bet on the droplet.”

“Sorry, trick question. I left out something important — the heat of vaporization. Water molecules hold pretty tight to each other, more tightly in fact than most other molecular substances. You have to give each molecule a kick to get it away from its buddies. That kick comes from other molecules’ kinetic energy, right? Oh, and one more thing — the smaller the droplet, the easier for a molecule to escape.”

“Ah, I see where this is going. The mist sprayer’s teeny droplets evaporate easy. The droplets are at air temperature, so when a molecule breaks free some neighbor’s kinetic energy becomes what you’d expect from air temperature, minus break-free energy. That lowers the average for the nearby air molecules. They slow their neighbors. Everything cools down. So that’s how sprays and refrigerators and such work?”

“That’s the basic principle.”

“Cool.”

~ Rich Olcott

Thanks to Mitch Slevc for the question that led to this post.

In A Pinch And Out Again

<Vinnie’s phone rings> “Yeah, Michael? That ain’t gonna work, Micheal.” <to me> “Michael wants to hoist us out through the elevator cab’s ceiling hatch.” <to phone> “No, it’s a great idea, Michael, it’d be no problem for Sy, he’s skinny, but no way am I gonna fit through that hatch. Yeah, keep looking for the special lever. Hey, call Eddie downstairs for some pizza you can send through the hatch. Yeah, you’re right, pizza grease and elevator grease don’t mix. Right, we’ll wait, like we got any choice. Bye.” <to me> “You heard.”

“Yeah, I got the drift. Plenty more time to talk about the improved portable kilogram standard.”

“I thought we were talking about lasers. No, wait, we got there by talking about the time standard.”

“We were and we did, but all the improved measurements are based on laser tech. Mode-locking, optical tweezers and laser cooling, for instance, are key to the optical clockwork you need for a really good time standard.”

“Optical tweezers?”

“Mm-hm, that’s yet another laser-related Nobel Prize topic. There’s been nearly a dozen so far. Optical tweezers use light beams to grab and manipulate small particles. Really small, like cells or molecules or even single atoms.”

“Grabbing something with light? How’s that work?”

“Particles smaller than a light beam get drawn in to where the beam’s electric field varies the most. With a tightly-focused laser beam that special place is just a little beyond its focus point. You can use multiple beams to trap particles even more tightly where the beams cross.”

“Is that how ‘laser cooling’ works? You hold an atom absolutely still and it’s at absolute zero?”

“Nice idea, Vinnie, but your atom couldn’t ever reach absolute zero because everything has a minimum amount of zero-point energy. But you’re close to how the most popular technique is set up. It’s elegant. You start with a thin gas of the atoms you want to work with. Their temperature depends on their average kinetic energy as they zip around, right?”

“Yeah, so you want to slow them down.”

“Now you shine in two laser beams, one pointing east and one pointing west, and their wavelengths are just a little to the red of what those atoms absorb. Imagine yourself sitting on one of those atoms coming toward the east-side laser.”

Blue shift! I’m coming toward the waves so I see them scrunched together at a wavelength where my atom can absorb a photon. But what about the other laser?”

“You’d see its wavelength red-shifted away from your atom’s sweet spot and the atom doesn’t absorb that photon. But we’re not done. Now your excited atom relaxes by emitting a photon in some random direction. Repeat often. The north-south momentum change after each cycle averages out to zero but east-west momentum always goes down. The gas temperature drops.”

“Cool.”

All this talk of particles balanced in force fields gives me an idea. “Vinnie, d’ya think we stopped closer to the fifth floor or the sixth?”

“I think we’re almost down to five.”

“Good, that gives us a better chance. Where were you standing when we stopped?”

“Right by the buttons, like always. Whaddaya got in mind?”

“Michael said that’s a new elevator door, right? No offense, you’re heavy and I’m no light-weight. Both of us were standing at the very front of the cab. I’m thinking maybe our unbalanced weight tilted the cab just enough to catch an edge on some part of the door mechanism they didn’t put in quite right. Let’s switch places and both jump up and while we’re in the air wallop the top of the cab’s back wall as hard as we can. OK, on three — one, two, three!” “

<B-BLAMkchitKKzzzzzrrrrrrr-T>

“Michael. It’s Vinnie. We’re out. Yeah, ‘s wunnerful, I’m glad you’re glad. Look, something was sorta outta place in the new door mechanism on five and now it’s way outta place and the cab’s probably here for the duration. Call your repair guys, but before you do that bring up some Caution tape and something that’ll block the door open. Quick-like, right? I’m holding this door but I ain’t gonna be a statue long ’cause I’m hungry.”

~~ Rich Olcott