Demonstration I1-11: Thermal Expansion is perennially one of mour most popular thermodynamics demonstrations. This simple setup has two primary pieces: a solid metal sphere, and a metal plate with a hole in it, each mounted on insulated handles. Under normal circumstances (i.e. at room temperature), the hole is just slightly too small for the ball to fit through it. See what happens in this video.

 All that changes, though, when the plate is heated.

A Puzzling Prediction

 Most students have learned already that metals tend to expand when heated. If using this in class, this demonstration is often best introduced after showing off one or two others that illustrate this (consider I1-15: Pin Breaker and I1-13: Bimetallic Strip for examples). But in this case, though, we have a puzzle: The metal plate has a hole in it. We expect the plate to expand outwards… but what happens to the hole? Does it get bigger, or smaller?

This is a good question to pose to your students before carrying out the demonstration. And don’t just ask the question – encourage them to discuss it amongst themselves, and to lay out not just what they predict will happen, but why. This is a good opportunity to encourage logical reasoning and communication skills, as well as an understanding of the physics involved.

The Hole Story

 Once the plate is heated, the ball moves freely through the hole, as seen in this video. As the plate expanded, the hole in it expanded as well!

What’s happening? The thermal expansion of the plate is linear – the distance between any two points on the plate expands by the same ratio. One way to approach understanding this: Imagine a plate with no hole in it, but with just a circle drawn on the plate. We’d of course expect the circle to expand as the plate does. The distance between the points along the circle expands at the same ratio as the distance between the outer edges of the plate. If we then cut a hole in the expanded plate, this distance wouldn’t change.* The same principle applies if the hole is there all along. The distance between any two points along the edge of the hole – essentially the “inner edge” of the plate – must expand at the same ratio as the rest of the plate. So the hole grows larger, and the plate cannot grow backwards into the hole. This constant ration is called the coefficient of expansion.

*OK, a technicality here: The distance wouldn’t change so long as our cutting tool didn’t bend the plate or make it hotter from friction as it cut!

This demonstration has been very popular in classes like PHYS121, PHYS171, and PHYS260 - anywhere that faculty want to introduce the idea of linear thermal expansion and the coefficient of expansion in an interesting way. It's also a fun and engaging way to drive students to think hard about a physical problem, and to practice discussing their reasoning and understanding the reasoning of others. This is perhaps the most valuable lesson of all.

 Today we’re taking a look at some models of diffusion: Demonstrations I6-21 and I6-25. These both use the behaviour of ping-pong balls to model the behaviour of molecules in a gas.

Each of these models uses ping-pong balls of different colors to represent different molecules in a gas. In I6-21, we have a mechanically shaken chamber divided by a plastic barrier. We can put balls of one color on one side and balls of another color on the other side. When the chamber vibrates, the balls bounce around like the molecules in a gas. When the barrier is removed, the balls begin to drift onto each other’s sides, and soon there is no distinction between the two.

This is also a good example of the principle of entropy – while it is very easy and probable to disorder this system, as the two sets of balls mix together, it is highly improbable (though not impossible, given a small enough number of balls) that all of the balls of each color will suddenly sort themselves out again! Thus, the system tends towards the more disordered state.

In I6-25, we start with columns of balls at the top of an array of pegs. The balls are held in place by a small plastic baffle. When the baffle is removed, the balls fall down through the array, scattering as they go. By the time they reach the bottom, they have spread out into a curve, roughly approximating a proability graph. The columns at the bottom with more balls are the areas more probable for balls to scatter into, and those with few or no balls are less probable. As with I6-21, we can use different colors of balls to show how gases diffuse together over time.

 Now, you can try this in class or at home with this simulation from the PhET Collection at the University of Colorado. You can let a small or large number of particles of two different gases diffuse through each other, and watch their behaviour. How do the simulated particles here resemble the model “particles” of our demonstrations? What’s different? How can we explore the differences when talking about the behaviour or real gases?

 And explore more such experiments in our Directory of Simulations!

One of the most popular and visually stunning illustrations of buoyancy and relationship between temperature and pressure is the hot air balloon. Some of you may have had a chance to see one recently at our Maryland STEM Festival event, FLIGHT!

 A hot air balloon rises in the air as a result of its buoyancy. As the air is heated, the increased average kinetic energy of the particles in the gas mean its average density is less, and so it rises through the air. In the outdoors, a modern hot air balloon carries its heat source with it, and can keep the air at a constant higher temperature, so the balloon will rise until it reaches equilibrium at an elevation where the density of the outer atmosphere is no longer sufficiently higher than that of the air in the balloon.

 Our demonstration balloon, however, more closely resembles the earliest experimental crewed hot air balloons, which heated the air with a heat source located on the ground (a bonfire then, an electric heat gun for us). So these balloons rise only until they have gone too far from the fixed heat source and the air begins to cool down again, reducing buoyancy until they settle back to the ground – or return to the heat source!

 The earliest records of the development of uncrewed hot air balloons, like ours, go back over 1,000 years in China, and are recorded some other parts of East and Southeast Asia as well. The were used for entertainment purposes and for signaling between distant points. The earliest known crewed hot air balloon experiments currently known date to the eighteenth century in Europe, though others may have occurred earlier elsewhere.

 Simple hot air balloons are easy to make, and are a fun home experiment. Larger demonstration models can be valuable in class to spur discussion of buoyancy and the behaviour of gases, and studying the history of both the technology and the theoretical understanding of their thermodyanmics can be a useful and interesting student project.

Happy Labor Day to all in the US!

(and belated greetings to readers elsewhere for whom Labor Day was in May.)

This holiday celebrates all kinds of work, but in physics Work is a more specific and mathematically defined quantity Today we’re taking a look at a couple of recent articles in The Physics Teacher that related to the concept of work in the classroom.

In physics, work is the energy transferred to or from a body via the application of force over a distance. Positive work is work done in the direction of motion, negative work is done in the opposing direction (or has components in those directions, in a 3-dimensional system). We sometimes, conversely, refer to energy as the ability to do work.

A recent paper in The Physics Teacher by G. Planinšič & E. Etkina, “Boiling water by doing work” (https://doi.org/10.1119/5.0049411), shows some of this relationship between work and energy. As work is done on a system, moving a rope, some of the energy in the system is dispersed as heat. This heat is then seen to boil water. In their videos (linked in the article), you can see the relationship between work done on the system and temperature, and calculate for yourself the efficiency of energy conversion.

A paper in The Physics Teacher last year by P. Gash looks at potential energy and work in a more familiar mechanical system: a Slinky. In “A Slinky’s Elastic Potential Energy” (https://doi.org/10.1119/1.5145416), we can see a detailed breakdown of the forces acting on the coils of a Slinky. You can check out the experimental data for yourself and calculate the work done by gravity on the spring. It’s a handy reminder that work in the physics sense doesn’t always mean human labor!

We have many demonstrations in our collection relating to physical work. Section C8 of our demonstration index is all about the mechanics of energy, power, and work; all are useful in the classroom, and many can be tried at home as well with materials you have on hand! There are many other demonstrations that explore energy and work as well, from thermodynamics experiments like the one in the paper above, to the newly repaired J4-31: Energy Stored in a Capacitor, which shows a capacitor that holds enough energy to let a motor do the work of lifting the capacitor itself against gravity. Now that’s a nice bit of work!

  UMD Physics Outreach opens 2023 with a hot (and cold) time in the old town this month! 

• The evenings of February 3rd & 4th, we present Physics is Phun: A Show of Ice & Fire, a high school level program. Details and registration at https://umdphysics.umd.edu/events/aboutus-outreach/physics-is-phun.html
• The morning of February 25th, we present a Physics Discovery Day: Hot & Cold, an upper elementary & middle school level program. Details and registration at https://umdphysics.umd.edu/events/aboutus-outreach/discovery-days.html

Demonstrations include infrared radiaion, liquid nitrogen, combustion, convection, and therman expansion and contraction. A great way to warm up on a chilly weekend!

We talked before about the shape of the teapot; now, another question has come up online: Why does your tea water heat differently in the microwave than in an electric kettle?

 Several years ago, Nadia Arumgam mentioned this problem in an article for Slate on making tea. One thing that contributes to the taste of tea is how hot the water is when it is brewing. When you heat water with an electric kettle or on a stove, the heat source is at the bottom. The hot water at the bottom rises, forming convection currents, drawing the cold water downwards to be heated in turn. Over time, the entire pot of water reaches the same temperature. When you see the water boiling at the surface, you know that the entire container is boiling.

In a microwave oven, though, the molecules are heated by electromagnetic agitation at points throughout the container of water, with warm and cool spots. Some of these points may begin to boil while other areas of the water are still cool. When you take the water out and make tea, it may not be as hot as you intend.

 Let’s see what this looks like on a larger scale. We have a Dewar flask, an insulated glass container, filled with water. We lower a small heating element into the water so that it heats the top layer of water. We can lower a thermometer probe down to the bottom of the water.

As you can see in the picture, the bottom layer of water is still cold! 23°C, right about at room temperature, and not very appealing for a cup of tea.

The top is boiling; when we move the probe to the top, the temperature is much higher, 97°C. (Not quite 100°C, though, and here we’re only a few centimeters from the heating element.)

 This can be a surprising result. We are used to thinking of water as conducting heat well, and it certainly does conduct heat better than air or glass; but not nearly as well as metals or many other materials. In most circumstances, though, most of the heat transfer in water isn’t from conduction, but from convection. In a big container, if your heat source is near the top, there may not be enough convection to make up the difference.

So put on the kettle, curl up with a nice cup of tea, and enjoy the snow!

This week has seen some chilly weather on campus here, and with it a return to warm beverages and the physics behind them. So, for this week, we’re going to look at a bit of physics we heartily recommend you do NOT try at home: superheating water.

In this video, taken by our own Don Lynch, you will see a mug of water that has just been heated in the microwave. Note that the mug is freshly cleaned, smooth, and cylindrical. The water is quite still; but when a teabag is dropped in, suddenly the water bursts into boiling! After a few seconds, the boiling stops, and we are left with what appears to be a cup of tea. (Pity about the mess on the plate beneath.)

Normally, when water reaches its boiling point, it bursts into bubbles as the liquid water begins to turn into a gas. These bubbles usually first form around nucleation sites, tiny (or not so tiny) impurities in the water. The bubbles expand as the force of the vapor pressure of the steam inside the bubble exceeds the external forces of atmospheric pressure and the surface tension of the water. As the bubbles expand, their internal forces exceed the external forces more rapidly, and so once the boiling process has begun it accelerates and the entire liquid boils.

Occasionally, though, if there are no nucleation points and the water is not agitated, no single tiny bubble manages to overcome the atmospheric pressure and surface tension to start the liquid boiling, even though the temperature is at or even slightly above the usual boiling point. When the water is disturbed (in our case, by dropping the teabag in), suddenly there are lots of nucleation points, and the boiling begins in earnest.

We don’t know exactly how hot the water is here; if we put a temperature probe in the container, that itself would trigger the boiling effect before we could make a measurement! But we suspect that it is probably only very slightly above the boiling point. It is certainly not as hot as the more conventional “superheated” water one might find by heating water under pressure – but it is still more than hot enough to cause some very bad burns, so please don’t try to make your tea this way! Take a few more seconds and do things the old fashioned way, and enjoy a relaxing cup of tea and a pleasant winter break.

See you next year!

There's a lot happening overhead this week!

The Perseid Meteor Shower is at its peak this week. Meteor showers are a stunning sight in the night sky, and the Perseids are one of the brightest of the year. The sparks of light you see in the sky are the burning debris from past passages of Comet Swift-Tuttle, which passes through the solar system every 133 years... but we pass through its path in August every year! Read more about the Perseids at NASA's Solar System Exploration pages.

Ordinarily, this would not have been the best of years to see the Perseids anyway, since the moon is full, and its bright light would make them hard to see. But it has turned out to be a moot point in our region, as our skies are darkened by a phenomenon much closer to home: Tropical Storm Isaias. This storm has been making its way up the coast and is now dumping quite a lot of rain on us, so everyone please be cautious! These storms can be dramatic to watch, but also potentially dangerous.

Hurricanes and tropical storms are driven by converging winds and moist air over warm water. Climate change in recent years has warmed the waters of the ocean - by only a small amount, but in a large and complex system, a small change in initial conditions can have a dramatic effect on the outcome! You can see this modeled in the classroom with demonstrations like our chaotic pendulum, G1-60; be sure to check out the simulation linked there that lets you experiment with tiny changes in the initial conditions. 

 Keep your eyes on the sky - but be careful out there!

Read more:

National Hurricane Center

NOAA video: Fuel for the Storm

NASA: In Depth on the Perseid Meteor Shower

EarthSky.org: Perseid Meteors 2020

Double Pendulum Simulator by Erik Neumann

A question that came in via Twitter recently is one that comes up a lot this time of year, as we tend to want to spend more and more time curled up with a warm beverage. How does my little round teapot fill up so many cups? And why is the tea in the pot still warm when the tea in my cup has gone cold? The answer comes down to geometry!

Here’s a pretty ordinary sized teapot from the cabinet, and an official UMD Physics mug. We’ve tested it twice today and confirmed: This teapot can fill this mug six times. Sure, the pot is bigger than the mug, but it doesn’t look that much bigger, right?

The teapot can even fill this bigger UMD Physics travel mug four times! How?

The answer is related to what biologists call the Square-Cube Law. As an object grows in size, its volume increases faster than its surface area. If you take a cubical container and double its length, width, and height, multiplying by 2 in each direction, then its surface area is multiplied by 4, the square of 2. But its volume is multiplied by 8, the cube of 2. The exact numbers will change, though, depending on the shape of the container. Every shape has its own relationship among liner size, area, and volume. As it turns out, the most efficient shape, with the highest ratio of volume to surface, is a sphere.

This sounds like just abstruse math, but it actually explains a lot about things we deal with every day, from teapots and fuel tanks to giraffes and polar bears. (OK, maybe not all of us deal with polar bears every day, but it’s good to know about them anyway.)

Here’s an example from the demonstration collection. This round flask and this tall cylinder each hold the same volume of water, 500 milliliters. The cylinder is much longer and narrower than the sphere, so it looks bigger, but it has the same volume!

One thing that makes this interesting is that, having a larger surface area, the cylinder is also heavier. It takes more glass to make a 500mL cylinder than to make a 500mL sphere. That might not matter much for our purposes, when we just want one container to sit on the table, but it can make a big difference in large storage containers, or in places where weight is important, like spacecraft.

This is also why fluids in free fall, like raindrops, form into spheres. The surface tension of the liquid is pulling inwards, compressing the surface to the smallest area for that volume of water: a sphere. On a larger scale, this even happens to big accumulations of rock, pulled in by gravity over a long period of time. We call them planets – and luck for us, they do tend to end up round!

That’s all interesting, but isn’t my tea getting cold after all this?

No, and here’s why: The total amount of heat in the container is proportional to its volume. But the radiation of heat away from the container is proportional to its surface area. So my nearly spherical teapot loses heat a lot more slowly than that tall cylinder does. Plus, because there’s less surface area for the same volume, we can make the walls thicker for the same weight, giving it better insulation.

And that’s where the polar bears come in. (Not literally, polar bears should not drink tea.) Ever wonder why so many animals in warm climates evolved long, lanky builds, while arctic animals tend to be rounder? A lot of it comes down to heat. A round polar bear loses heat a lot more slowly, so they can burn fewer calories to stay warm. That can be important in the long winters when there’s not much to eat. In a hot climate where the bigger problem is staying cool, many animals tend to be thinner. Others find other ways to increase their surface area, like the big ears on an elephant, to radiate heat away faster. There are lots of other factors at play in evolution as well, of course, but heat is always an important one.

This relates to why animals only come in certain sizes, too. If you scale up an ant 100 times in each direction, its mass increases by one million - but the surface area of its legs doesn't, so it can't stand up!

So sit back, make a pot of tea, and curl up with a good book about somewhere warmer. And spring will be here before you know it!

(Note: No tea was harmed in the creation of this blog post. But quite a lot of it was consumed.)