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!

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.)