The (almost) Perfect Teacup

It’s a glass really. Double walled, liquid suspended in air, beautiful to look at. But it really becomes a wondrous artifact of engineering when its combined with the heavy, rubber and stainless steel lid. The beauty and thermal efficacy of this tea-making system is … elegant. It’s certainly a worthy starting point for our discussion of heat, temperature and thermodynamics in general, and generates interesting questions about heat transport (convective, evaporative, conductive and radiative) and the greenhouse effect, that can be tested with relatively simple experiments.

The first, and most obvious thing my students observed was the fact that the lid prevented heat escaping. The weight of the lid confines the head space, which reduces convective heat loss above the cup and increases the vapor pressure, which reduces the amount of tea that evaporates. Evaporation is the primary way heat is lost from hot liquids, since each gram that evaporates takes 540 calories of heat with it. A simple evaporative heat loss experiment showed that about 70% of the cooling of a cup of water came from evaporation.

The second thing the students pointed out is that the double walled glass insulates, because it reduces conductive heat loss. Solid glass has a thermal conductivity of about 0.24 cal/(s.m.K) (Engineering Toolbox.com; 1 J = 0.24 calories). The conductivity of the air in the space between the walls is two orders of magnitude less at 0.0057 cal/(s.m.K). Of course, having a vacuum in the space would be even better, but it would test the strength of the glass.

Thermally, the glass falls short when it comes to radiative heat loss. A silvery coating would reflect radiated heat back into the cup much better than transparent glass. However, silica glass is relatively opaque to infra-red, which should reduce radiated heat emission. A simple experiment, comparing the cooling rates of water a glass flask wrapped in aluminum foil to one without the foil should give some indication if radiative heat loss is significant.

Finally, the glass does have a thermal advantage though, via the greenhouse effect. Because it is transparent to short, high-energy wavelengths of light, like that of sunlight, but blocks the longer wavelengths of heat energy, the glass should be able to capture some heat from sunlight. This can also be experimentally tested with a couple flasks in the sun. It would be interesting to find out how any greenhouse warming compares to the radiative heat loss through the glass walls.

Last week my students did some basic observations and came up with their own experiments. Then they learned a little about thermodyamics from reading the textbook. This week, we’ll try to get a little more quantitative with the experiments and applications of what they know, and it should be interesting to see if what they’ve learned has changed the way they observe the common objects around them.

Evaporative Heat Loss from a Cup Experiment

This simple experiment was devised to estimate just how much heat is lost from a teacup due to evaporation as compared to the other types of heat loss (conduction and convection).

evaporative-heat-loss-exp-0038a — Experimental setup for measuring evaporative heat loss.

The idea is that if we can measure the mass of water that evaporates over a short period of time, we can calculate the evaporative heat loss because we know that the amount of heat it takes to evaporate one gram of water (its latent heat of evaporation) is 540 cal/g. So we’ll take some hot, almost boiling, water and weigh and take its temperature as it cools down.

Materials

evaporative-heat-loss-exp-0041 — Apparatus.

It requires:

A thermometer (Celcius up to 100 degrees)
A styrofoam cup (because it’s light)
A digital scale (to take quick measurements to tenths of a gram)
A 100 ml graduated cylinder (optional)
A beaker (100 ml) or cup that can go in the microwave
water

Procedure

Our scale has a capacity of about 120 g so we need to make sure that the combined weight of our apparatus that will go on the scale is less. The plan is to have the styrofoam cup, with a thermometer and some water on the scale. Since we can be somewhat flexible with how much water is in the cup we’ll first weigh the cup and thermometer.

(my measurement, not necessarily yours)
Mass of styrofoam cup and thermometer = 29.6 g

So it should be safe to use 70 g of water, which is approximately equal to 70 ml since the density of water is 1 g/ml.

1. Measure the 70 ml of water in the graduated cylinder and put it into the beaker (or microwavable cup). The exact volume is not crucial here since we’ll be using the scale to measure the mass of water more precisely.

2. Microwave the water for about 40 seconds. Again you do not have to be too precise here, you just want the water to be close to boiling. The length of time you need to microwave the water will depend on the strength of your microwave. 40 seconds raised the temperature of my 70 ml of water from 22˚C to 82˚C. If you like you can calculate the heat absorbed by the water, and the effective power of the microwave from these numbers, but it is not necessary for this experiment.

3. Quickly place the hot water into the styrofoam cup with the thermometer on the scale and measure the mass and the temperature of the water.

4. Measure the mass and temperature of the water every 2 minutes for the next 10 minutes.

Calculations

1. Every time you took a measurement, the temperature and the mass should have dropped. The change in mass is due to evaporation. Every time one gram evaporated, 540 calories are lost. Calculate the amount of heat lost due to evaporation at every time measurement.

Hint: Evaporative Heat Loss = mass evaporated × latent heat of evaporation
Q_E = m_E L_E

2. Now that you know how much heat was lost, you can figure out how much of the temperature drop was caused by evaporation. Since the specific heat capacity of water is 1 cal/g/˚C, each calorie lost due to evaporation should have reduced the temperature of one gram of the water by one degree Celsius.

Hint: Evaporative Temperature Change = Evaporative Heat Loss × mass of water in container × specific heat capacity of water
∆T_E = Q_E / (m C_w)

You should also the temperature drop caused by evaporation as a percentage of the total temperature drop. Hopefully, your result is less than 100%.

For comparison, here is my data: Evaporative Heat Loss Results and Calcualtions

Discussion and Conclusion

There are quite a number of things that might come up in discussion here, for example: just how large are the potential for measurement errors; and are the results comparable to an actual teacup.

My trial of this experiment indicated that about 69% of the heat loss was due to evaporation. It should be possible to also calculate the amount of heat loss from conduction through the walls of the cup; the thermal conductivity of styrofoam is 0.033 W/mK (via the Engineering Toolbox). The radiative heat loss can be estimated using Stefan’s Law, which can be used to account for all the different methods of heat loss.

Finally, there is no control described in this experiment. A useful thing to try would be to use a styrofoam cup with a lid.

Additional Notes

When my students tried this experiment they use a small (50ml) beaker and 25g of water. Their evaporative heat loss was only 44% of the total, probably due to the smaller volume of water, which as a larger surface-area to volume ratio, and the thinner, more conductive glass walls of the beaker.

Seismic Waves Across the U.S.

Excellent video from the EarthScope project, showing the seismic waves from the August 23rd earthquake zipping across the United States. Note that the height of the wave was only 20 micrometers (20 millionths of a meter or 0.02 mm) as it passed through the midwest.

One question that might occur is, why are there so many seismic stations in the middle of the continent? My guess is that it has to do with monitoring of the New Madrid fault zone, which produced

More details about the earthquake can be found on its IRIS page.

(via Bad Astronomy)

Live from 1500 Meters Deep

cable-inspection — Link to live video feed from the ROV ROPOS surveying a cable on the ocean floor at the Juan de Fuca midocean ridge.

Live science. The remotly operated submersible ROV ROPOS is surveying an undersea cable recently laid across the the Juan de Fuca midocean ridge.

This scientific expedition will be going on until the end of August, and there’ll be live feeds every time the rover is deployed (which depends a bit on the weather at the surface).

If you have questions, they’re also answering your tweets.

Right now, the rover’s heading toward the caldera of the axial seamount volcano. It should get there some time tonight (if they don’t have to stop for anything). So far, we’ve seen dumbo octopuses, crabs, weird fish, brainless worms, sponges, deep sea corals, starfish and lots of pillow basalt. The basalts are unsurprising because these are the rocks produced when volcanos erupt under water.

r1465_2011-08-22_042927 — Dumbo octopus (from the ROV ROPOS seafloor gallery at Interactive Oceans).

Guide to Using a Microscope

Sitting innocuously on the clearance table at a Barnes & Noble (in Cedar Rapid, Iowa actually) was a copy of Georg Stehli’s The Microscope and How to Use It.

At 75% off it was less than $3, which is quite a steal for a guide to what I found to be the most fascinating piece of scientific equipment for my middle schoolers. One of their first natural world lessons was on how to use the microscope. In the classroom there was always one sitting on the shelf, protected by its translucent plastic cover, but easily accessible.

I also took one everywhere, including to the cabins on our immersion trips, which is where they discovered the crystalline structure of salt and sugar grains, and the microfossils at Coon Creek.

And, interestingly enough, my microscopy posts are some of the most popular posts on this blog (the onion cell is regularly in the top ten).

The Microscope and how to use it by Georg Stehli.

Apart from the basics of how to use a microscope, Stehli’s book goes into simple sample preparations and preservation for almost everything you’re likely to encounter in the curriculum, in the classroom, and in the back yard. Though neither crystal structure nor microfossils are covered, the techniques for looking a the hard parts of biological specimens are applicable.

I would have loved to have had a copy of this last year when I was trying to figure out which were the best dyes to use for some of the odder samples my students came up with, and how to make them into permanent slides. It’s not easy to find this kind of broad reference online.

Build Your Own Solar System: An Interactive Model

National Geographic has a cute little game that lets you create a two-dimensional solar system, with a sun and some planets, and then simulates the gravitational forces that make them orbit and collide with each other. The pictures are pretty, but I prefer the VPython model of the solar system forming from the nebula.

The models starts off with a cloud of interstellar bodies which are drawn together by gravitational attraction. Every time they collide they merge creating bigger and bigger bodies: the largest of which becomes the sun near the center of the simulation, while the smaller bodies orbit like the planets.

This model also comes out of Sherwood and Chabay’s Physics text, but I’ve adapted it to make it a little more interactives. You can tag along for a ride with one of the orbiting planets, which, since this is 3d, makes for an excellent perspective (see the video). You can also switch the trails on and off so you can see the paths of the planetary bodies, note their orbits and see the deviations from their ideal ellipses that result from the gravitational pull of the other planets.

I’ve found this model to be a great way to introduce topics like the formation of the solar system, gravity, and even climate history (the ice ages over the last 2 million years were largely impelled by changes in the ellipticity of the Earth’s orbit).

National Geographic’s Solar System Builder is here.