12 Cups: Thermal Energy

December 10, 2013

Students study the twelve different containers, using reason to deduce their thermal properties.

Students study the twelve different containers, using reason to deduce their thermal properties.

I gave the middle-schoolers twelve containers — cups, bottles, mugs, etc. — that I found around the classroom and asked them to figure out which one would keep in heat the best. In fact, I actually asked them to rank the containers because we’d just talked and read about thermal energy. This project is intended to have them learn about thermal energy and heat transfer, while discovering the advantages of the scientific method through practice.

Day 1: Observation and Deduction: When I asked them to rank that containers based on what they knew, I’d hoped that they’d discuss the thermal properties of the cups and bottles. And they did this to a certain degree, however, part of their reasoning for the numbers one and two containers, were that these were the ones I used. Indeed, since I use the double walled glass mug with the lid (container number 7) almost every day, while I only use the steel thermos-mug (container number 6) on field trips (see here for example), they reasoned that the glass mug must have better thermal properties.

The twelve containers are labeled with sticky notes, while students' initial assessment of  thermal ranking is written on the paper pieces in front of the containers.

The twelve containers are labeled with sticky notes, while students’ initial assessment of thermal ranking is written on the paper pieces in front of the containers.

Day 2: Exploratory Science and Project Organization: On day 2, I asked the class to see how good their ranking of the containers was by actually testing them. Ever since the complex machines project where they had to choose their own objective, they’ve been wanting more independence, so I told them to pretend I was not in the room. I was not going to say or do anything to help, except provide them with a hot plate and a boiling kettle, and keep an eye out for safety.

They got to work quickly. Or at least some of them did while the other half of the class wondered around the room having their own, no-doubt important, conversations. I pulled them all back in after about half and hour to talk about what had happened. But before we discussed anything, I had them write down — pop quiz style — what their procedure was and how it could be improved. The vagueness of some of the answers made it obvious to both to me and the ones who had not been paying attention who’d actually been working on the project.

Experiments in progress.

Experiments in progress.

Of the ones who’d been working in the project, I brought to their attention that they’d not really spent any time planning and trying out a procedure, but they’d just jumped right in, with everyone following the instructions of the one student who they usually look to for leadership. Their procedure, while sound in theory would have benefited from a few small changes — which they did recognize themselves — and the involvement of more of the class. In particular, they were trying to check the temperature of the water every 10 seconds, but it would take a few seconds to unscrew lids, and about 5 additional seconds for the thermometer to equilibrate. They also were restricted because they were all sharing one stopwatch while trying to use multiple thermometers.

Day 3: First Iteration: Now that they’ve had a bit of trial by fire, tomorrow they’ll try their testing again. I’m optimistic that they’ve learned a lot from the second day’s experience, but we’ll see how it turns out.

Citing this post: Urbano, L., 2013. 12 Cups: Thermal Energy, Retrieved April 20th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

The Physics of How Microwaves Work

July 3, 2012

An excellent explanation of how microwaves work. It talks about waves (how to determine the frequency and wavelength of microwaves), electricity (magnetrons), heat and temperature.

Citing this post: Urbano, L., 2012. The Physics of How Microwaves Work, Retrieved April 20th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Curious Correlations

March 27, 2012

The Correlated website asks people different, apparently unrelated questions every day and mines the data for unexpected patterns.

In general, 72 percent of people are fans of the serial comma. But among those who prefer Tau as the circle constant over Pi, 90 percent are fans of the serial comma.

Correlated.org: March 23’s Correlation.

Two sets of data are said to be correlated when there is a relationship between them: the height of a fall is correlated to the number of bones broken; the temperature of the water is correlated to the amount of time the beaker sits on the hot plate (see here).

A positive correlation between the time (x-axis) and the temperature (y-axis).

In fact, if we can come up with a line that matches the trend, we can figure out how good the trend is.

The first thing to try is usually a straight line, using a linear regression, which is pretty easy to do with Excel. I put the data from the graph above into Excel (melting-snow-experiment.xls) and plotted a linear regression for only the highlighted data points that seem to follow a nice, linear trend.

Correlation between temperature (y) and time (x) for the highlighted (red) data points.

You’ll notice on the top right corner of the graph two things: the equation of the line and the R2, regression coefficient, that tells how good the correlation is.

The equation of the line is:

  • y = 4.4945 x – 23.65

which can be used to predict the temperature where the data-points are missing (y is the temperature and x is the time).

You’ll observe that the slope of the line is about 4.5 ºC/min. I had my students draw trendlines by hand, and they came up with slopes between 4.35 and 5, depending on the data points they used.

The regression coefficient tells how well your data line up. The better they line up the better the correlation. A perfect match, with all points on the line, will have a regression coefficient value of 1.0. Our regression coefficient is 0.9939, which is pretty good.

If we introduce a little random error to all the data points, we’d reduce the regression coefficient like this (where R2 is now 0.831):

Adding in some random error causes the data to scatter more, making for a worse correlation. The black dots are the original data, while the red dots include some random error.

The correlation trend lines don’t just have to go up. Some things are negatively correlated — when one goes up the other goes down — such as the relationship between the number of hours spent watching TV and students’ grades.

The negative correlation between grades and TV watching. Image: Lanthier (2002).

Correlation versus Causation

However, just because two things are correlated does not mean that one causes the other.

A jar of water on a hot-plate will see its temperature rise with time because heat is transferred (via conduction) from the hot-plate to the water.

On the other hand, while it might seem reasonable that more TV might take time away from studying, resulting in poorer grades, it might be that students who score poorly are demoralized and so spend more time watching TV; what causes what is unclear — these two things might not be related at all.

Which brings us back to the Correlated.org website. They’re collecting a lot of seemingly random data and just trying to see what things match up.

Curiously, many scientists do this all the time — typically using a technique called multiple regression. Understandably, others are more than a little skeptical. The key problem is that people too easily leap from seeing a correlation to assuming that one thing causes the other.

Citing this post: Urbano, L., 2012. Curious Correlations, Retrieved April 20th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Watching Snow Melt: Observing Phase Changes and Latent Heat

February 17, 2012

Waiting, observing, and recording as the snow melts on the hot plate.

Though it might not sound much more interesting than watching paint dry, the relationships between phase changes, heat, and temperature are nicely illustrated by melting a beaker of snow on a hot plate.

A light, overnight snowfall, lingers on the branches that cross the creek.

This week’s snowfall created an opportunity I was eager to take. We have access to an ice machine, but closely packed snow works much better for this experiment, I think; the small snowflakes have larger surface-area to volume ratio, so they melt much more evenly, and demonstrate the latent heat of melting much more effectively.


My instructions to the students are simple: collect some snow, and observe how it melts on the hot plate.

I also ask them to determine the mass and density of the snow before (and after) the melting, so I could show that throughout the phase changes and transformations the mass does not change (at least not a lot) and so they can practice calculating density1,2.


I broke up my middle school students into groups of 2 or 3 and had them come up with a procedure and list of materials before they started. As usual I had to restrain a few of the over-eager ones who wanted to just rush out and collect the snow.

A 600 ml beaker filled with (cold) snow. A thermometer is embedded in the ice.

I guided their decision-making a little, so they would use glass beakers for the collection and melting. Because I wasn’t sure what the density of the packed snow would be, I suggested the larger, 600 ml beakers, which turned out to work very well. They ended up with somewhere between 350 and 400 grams of snow, giving densities around 0.65 g/ml.

When they put the beakers on the hot-plate, I specifically asked the students to observe and record, every minute or so, the changes in:

  • temperature,
  • volume
  • appearance

I had them continue to record until the water was boiling. This produced the question, “How do we know when it’s boiling?” My answer was that they’d know when they saw the temperature stop changing.

They also needed to stir the water well, especially when the ice was melting, so they could get a “good”, uniform temperature reading.


We ended up with some very beautiful graphs.

Temperature Change

Changing temperature with time as the beaker of snow melted into water and then came to a boil. Graph by E.F.

The temperature graph clearly shows three distinct segments:

  1. In the first few minutes (about 8 min), the temperature remains relatively constant, near the freezing/melting point of water: 0 ºC.
  2. Then the temperature starts to rise, at an constant rate, for about 20 minutes.
  3. Finally, when the water reaches close to 100 ºC, its boiling point, the temperature stops changing.

Volume Change

The graph of volume versus time is a little rougher because the gradations on the 600 ml beaker were about 25 ml apart. However, it shows quite clearly that the volume of the container decreases for the first 10 minutes or so as the ice melts, then remains constant for the rest of the time.

The change in volume with time of the melting ice. Graph by E.F.


To highlight the significant changes I made copies of the temperature and volume graphs on transparencies so they could be overlain, and shown on the overhead projector.

Melting Ice: Latent Heat of Melting/Fusion

Comparison of temperature and volume change data shows that the temperature starts to rise when the volume stops changing.

The fact that the temperature only starts to rise when the volume stops changing is no coincidence. The density of the snow is only about 65% of the density of water (0.65 g/ml versus 1 g/ml), so as the snow melts into water (a phase change) the volume in the beaker reduces.

When the snow is melted the volume stops changing and then the temperature starts to rise.

The temperature does not rise until the snow has melted because during the melting the heat from the hot plate is being used to melt the snow. The transformation from solid ice to liquid water is called a phase change, and this particular phase change requires heat. The heat required to melt one gram of ice is called the latent heat of melting, which is about 80 calories (334 J/g) for water.

Conversely, the heat that needs to be taken away to freeze one gram of water into ice (called the latent heat of fusion) is also 80 calories.

So if we had 400 grams of snow then, to melt all the ice, it would take:

  • 400 g × 80 cal/g = 32,000 calories

Since the graph shows that it takes approximately 10 minutes (600 seconds) to melt all the snow the we can calculate that the rate at which heat was added to the beaker is:

  • 32,000 cal ÷ 10 min = 3,200 cal/min

Constantly Rising Temperature

The second section of the temperature graph, when the temperature rises at an almost constant rate, occurs after all the now has melted and the beaker is now full of water. I asked my students to use their observations from the experiment to annotate the graphs. I also asked a few of my students who have worked on the equation of a line in algebra to draw their best-fit straight lines and then determine the equation.

The rising temperatures in the middle of the graph can be modeled with a straight line. Graph by A.F.

All the equations were different because each small group started with different masses of snow, we used two different hot plates, and even students who used the same data would, naturally, draw slightly different best-fit lines. However, for an example, the equation determined from the data shown in the figure above is:

  • y = 4.375 x – 35

Since our graph is of Temperature (T) versus time (t) we should really write the equation as:

  • T = 4.375 t – 35

It is important to realize that the slope of the line (4.375) is the change in temperature with time, so it has units of ºC/min:

  • slope = 4.375 ºC/min

which means that the temperature of the water rises by 4.375 ºC every minute.

NOTE: It would be very nice to be able to have all the students compare all their data. Because of the different initial masses of water we’d only be able to compare the slopes of the lines (4.375 ºC/min in this case, but another student in the same group came up with 5 ºC/min).

Furthermore, we would also have to normalize with respect to the mass of the ice by dividing the slope by mass, which, for the case where the slope was 4.375 ºC/min and the mass was 400 g, would give:

  • 4.375 ºC/min ÷ 400 g = 0.011 ºC/min/g

Specific Heat Capacity of Water

A better alternative for comparison would be to figure out how much heat it takes to raise the temperature of one gram of water by one degree Celsius. This can be done because we earlier calculated how much heat is being added to the beaker when we were looking at the melting of the ice.

In this case, using the heating rate of 3,200 cal/min, a mass of 400 g, and a rising temperature rate (slope from the curve) of 4.375 ºC/min we can:

  • 3,200 cal/min ÷ 4.375 ºC/min ÷ 400 g = 1.8 cal/ºC/g

The amount of heat it takes to raise the temperature of one gram of a substance by one degree Celsius is called its specific heat capacity. We calculated a specific heat capacity of water here of 1.8 cal/ºC/g. The actual specific heat capacity of water is 1 cal/ºC/g, so our measurements are a wee bit off, but at least in the same ballpark (order of magnitude). Using the students actual mass measurements (instead of using the approximate 400g) might help.

Evaporating Water

Finally, in the last segment of the graph, the temperature levels off again at about 100 ºC when the water starts to boil. Just like the first part where the ice was melting into water, here the water is boiling off to create water vapor, which is also a phase change and also requires energy.

The energy required to boil one gram of water is 540 calories, which is called the latent heat of vaporization. The water will probably remain at 100 ºC until all the water boils off and then it will begin to rise again.


This project worked out very well, and there was so much to tie into it, including: physics, algebra, and graphing.


1 Liz LaRosa (2008) has a very nice density demonstration comparing a can of coke to one of diet coke.

2 You can find the density of most of the elements on the periodic table at periodictable.com.

Citing this post: Urbano, L., 2012. Watching Snow Melt: Observing Phase Changes and Latent Heat, Retrieved April 20th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Collapsing a Milk Jug: Atmopheric Pressure and the Ideal Gas Law

September 9, 2011

Collapsed milk jug.

Place a little hot water (400 ml at 94-100°C) into a plastic, gallon-sized, milk jug. Give it a moment to warm the air in the jug, then put the cap on and seal tightly (hopefully airtightly).

As the air in the jug cools the gas inside with shrink, reducing its pressure, and causing the atmospheric pressure to push in the sides of the jug.

Admittedly, this experiment is a little more dramatic if you use a metal tin, but it works well enough with the milk jug to surprise and impress.

Citing this post: Urbano, L., 2011. Collapsing a Milk Jug: Atmopheric Pressure and the Ideal Gas Law, Retrieved April 20th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Heat and Hurricanes

September 8, 2011

What could possibly go wrong?

— Kai Ryssdal (2011) in Freakonomics: Preventing a hurricane on Marketplace by American Public Radio.

In what one can only hope is an extremely tongue-in-cheek article, Marketplace discusses how we might geoengineer a solution to stop hurricanes forming.

Hurricanes get their energy from the warm surface waters in the tropics. The warm water evaporates, transferring heat from the oceans to the atmosphere as latent heat in the form of water vapor. As the air rises, the water vapor condenses to form water droplets (clouds) releasing the stored heat into the air, causing the air to rise faster, sucking up more moisture, and setting up a positive feedback loop that turns storms and hurricanes.

But they need a constant supply of warm water.

Between 100 and 200 m below the ocean's surface, the temperature drops rapidly. This is called the thermocline. You will notice that the deepest, coldest water is at 4 °C, the temperature at which water is most dense. (Image adapted from the Woods Hole Oceanographic Institute, via Wikipedia).

Unfortunately for the storms, the warm water in the tropics is only a thin layer, a couple of hundred meters deep, that sits above about 3,000 meters of colder deep-water. As the storms suck up the heat and moisture, they stir the oceans, cooling down the surface water, and leaving cooler water in their wakes. The cooler water means that subsequent storms have access to less energy.

The energy in the atmosphere and oceans “wants” to distribute itself evenly over the surface of the Earth. Hurricanes are just one violent means of moving heat from the tropics to the poles, and from the surface to the depths of the oceans.

Cool water from the deep Atlantic is stirred up to the surface by hurricanes. This image shows the cool wake of Hurricane Igor. (Image from

NOAA’s National Hurricane Center monitors sea-surface temperatures closely: it’s one of the key factors that go into their predictions of how bad the hurricane season is going to be, and what path a storm might take.

A Salter Sink for mixing the warm shallow water with the deeper cold water. Image from Intellectual Venture via NewScientist.

The suggestion in the Marketplace article is that we could build about 10,000 long tubes (called Salter Sinks) to connect the warm shallow surface water to the colder water below the thermocline. Wave energy at the surface would drive the warm water downward, causing mixing that would reduce the temperature of the surface water the storms feed off.

The devices might cost tens of millions of dollars per year, but that would be a lot less than the cost in property damage alone of a large storm like Irene, not to mention the loss of life it would prevent.

Apart from the “benign” environmental impact (according to Stephen Dubner) the only real question left is:

What could possibly go wrong?

Kai Ryssdal (2011)

Citing this post: Urbano, L., 2011. Heat and Hurricanes, Retrieved April 20th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Infrared Cloak

September 5, 2011

Image adapted from Wired.

In an interesting application of thermodynamics, BAE Systems has developed panels that can be placed on a tank to mask what it looks like to infra-red goggles, or help it fade into the background.

The panels measure the temperature around them and then warm up or cool so they’re the same temperature and therefore emitting the same wavelength of infrared light. So someone looking at the tank with infra-red goggles would have a harder time distinguishing the tank from the background.

The panels are thermoelectric, which means they use electricity to raise or lower their temperatures, probably using a Peltier device.

Peltier devices, also known as thermoelectric (TE) modules, are small solid-state devices that function as heat pumps. A “typical” unit is a few millimeters thick by a few millimeters to a few centimeters square. It is a sandwich formed by two ceramic plates with an array of small Bismuth Telluride cubes (“couples”) in between. When a DC current is applied heat is moved from one side of the device to the other – where it must be removed with a heatsink. The “cold” side is commonly used to cool an electronic device such as a microprocessor or a photodetector. If the current is reversed the device makes an excellent heater.

— Peltier-info.com: Peltier Device Information Directory

A Peltier element - it cools on one side and heats on the other. Image via Wikipedia.

Citing this post: Urbano, L., 2011. Infrared Cloak, Retrieved April 20th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Global Warming Art

September 1, 2011

Global temperatures (averaged from 1961-1990). Image created for Global Warming Art by Robert A. Rohde.

Talk about evoking conflicting emotions. The image is astoundingly beautiful – I particularly like the rich, intense colors – but the subject, global warming, always leaves me with sense of apprehension since it seems so unlikely that enough will be done to ameliorate it.

The source of the image, Global Warming Art has a number of excellent images, diagrams and figures. The National Oceanic and Atmospheric Administration also has lots of beautiful, weather-related diagrams. I particularly like the seasonal temperature change animation I made from their data.

Citing this post: Urbano, L., 2011. Global Warming Art, Retrieved April 20th, 2018, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

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