The inner core of the Earth is made of solid metal, mostly iron. The outer core is also made of metal, but it’s liquid. Since it formed from the solar nebula, our planet has been cooling down, and the outer core has been freezing onto the inner core. Somewhat counter-intuitively, the freezing process is a phase change that releases energy – after all, if you think about it, it takes energy to melt ice.
The energy released from the freezing core is transported upward through the Earth’s mantle by convection currents, much like the way water (or jam) circulates in a boiling pot. These circulating currents are powerful enough to move the tectonic plates that make up the crust of the earth, making them responsible for the shape and locations of the mountain ranges and ocean basins on the Earth’s surface, as well as the earthquakes and volcanics that occur at plate boundaries.
Conceptual drawing of assumed convection cells in the mantle. (via The Dynamic Earth from the USGS).
Eventually, the entire inside of the earth will solidify, the latent heat of fusion will stop being released, and tectonics at the surface will slow to a stop.
The topic came up when we were talking about the what heats the Earth. Although most of the energy at the surface comes from solar radiation, students often think first of the heat from volcanoes.
Note: An interesting study recently published showed that although the core outer core is mostly melting, in some places it’s freezing at the same time. Unsurprising given the convective circulation in the mantle.
Model of convection in the Earth's mantle. Notice that some areas on the mantle are hotter, creating hot plumes, and some are cooler (image from Wikipedia).
Note 2: Convection in the liquid outer core is what’s responsible for the Earth’s magnetic field, and explains why the magnetic polarity (north-south) switches occasionally. We’ll revisit this when we talk about electricity and dynamos.
Morning Edition has an excellent piece that points out that there is little or no actual experimental data supporting the idea that teaching should be individually tailored for different learning styles.
So presenting primarily visual information for visual learners has no proven benefit.
This is something we’ve seen before, however, this article points out that providing each student with the same information in different ways makes it much more interesting for them, increasing their motivation to learn and their retention of what was taught.
Which is fortunate because it means that if you were trying to teach in multiple ways, hoping that the more vocal stuff benefits the auditory learners and the pretty diagrams resonate more with the visual learners, even if this principle is all wrong, all of your students would still have gotten the benefits of variety.
So the educational psychologist, Doug Rohrer, recommends giving less math problems at a time but spreading the work out over a longer time. Our block schedule, with three weeks on and three weeks off, ought to work well for this, since students will be studying math intensely on the on-blocks and doing revision assignments on the off-blocks.
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.
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).
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
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
QE = mE LE
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
∆TE = QE / (m Cw)
You should also the temperature drop caused by evaporation as a percentage of the total temperature drop. Hopefully, your result is less than 100%.
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.
When girls talk, they spend so much time dwelling on problems that:
it probably makes them feel sad and more hopeless about the problems because those problems are in the forefront of their minds [and]…makes them feel more worried about the problems, including about their consequences.
…In general, talking about problems and getting social support is linked with being healthy. [But it can be] too much of a good thing.
Rose recommends that they, “engage in other activities, like sports, which can help them take their minds off their problems, especially problems that they can’t control.”
The furniture is starting to move. So far it has just been the couch, which also happens to be the heaviest piece of furniture. Yesterday I helped a couple students rotate it 180 degrees to face the wall, to make quieter, less distracting space. Today we rotated it toward the whiteboard and about half a dozen kids piled onto it for a lesson. I’ve always favored giving students as much control of their environment, and allowing the flexibility of movement, so I’m glad to see that they’re starting to take advantage of that freedom.
Rotating couch.
While I’m not quite sure why the couch has been the first thing to move there are probably a couple of reasons. One is that, compared to the rest of the furniture, the couch is relatively informal. This, in and of itself might have lead the students to consider it a good candidate for rearrangement, but I think it’s also that the couch’s informality meant that no one sat on it on the first day of class; everyone was at one of the desks (bright eyed, bushy tailed and eager to learn). As a result, no one specifically “owned” that space, and negotiating its movement did not involve a large group of people.
The couch also has the space around it so it’s easy to move without having to rearrange a lot of other furniture. It’s not the only piece like that though.
Now, with everyone piling on for today’s lesson, the couch-space has a much more communal feel. Students are becoming more attracted to it when they feel the need for a break, but they tend to go back to the desks when they need to work. Its population shifts over the course of the class.
It’s nice to see that, so far, the students are using the space responsibly. We’ll see how it develops.
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.
While it’s nice to have the math concepts arranged nicely based on their presentation in the textbook. Since my plan is to give just a few overview lessons and let students discover the details I’ll be presenting things a little differently based on my own conceptual organization. So I’ve created a second graphic map, which looks a bit disorganized, but gives links things by concept, at least in the way I see it.
Concept map for an introduction to pre-Algebra based on the first chapter of the textbook, Pre-Algebra an Accelerated Course, by Dolciani et al., (1996).
This morning I presented just the first branch, about equations, expressions and variables. The general discussion covered enough to give the students a good overview of the introduction to Algebra. Tomorrow the pre-Algebra and Algebra topics will start to diverge, but I think today went pretty well.
We’ll see how it goes as we fill in the rest of the map.
