Author: Lensyl Urbano

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).

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%.

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.

Talking Themselves into Depression

When it comes to approaches to solving problems, boys tend to think that talking isn’t particularly useful, while girls, who do prefer to talk things out, run the risk of talking themselves into depression.

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.

— Amanda Rose (2007) from the University of Missouri, Columbia, in Girls Who Complain About Their Problems At Greater Risk Of Developing Anxiety And Depression

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.”

Mobile Classroom

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.

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)

Concept Maps of Math

Introduction to algebra.

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.

Live from 1500 Meters Deep

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.

Dumbo octopus (from the ROV ROPOS seafloor gallery at Interactive Oceans).

Mindmapping Online with Mind42

Excerpt from my pre-Algebra/Algebra mindmap created on Mind42.com

I was trying to figure out how I could create a graphic organizer/mindmap to outline my math class that my students could access online. Even better would be if they could also edit the map online. That way I could set up the outline of my lesson notes and they could fill in definitions for vocabulary words. Mind42 (pronounced mind for two) allows just that. It’s free to use and allows you to link to or embed your mindmaps (e.g. pre-Algebra/Algebra) into other websites:

It’s almost perfect, all it needs is for you to be able to save the state of the map, with certain branches collapsed for example, or with a set zoom level. Right now the best way to explore the above map is to collapse all the nodes (use the second button on the lower left) and gradually expand them out as you go through.

I do think the style of the nodes and lines on the maps are elegant and make it easy to read. It’s also really easy to create the maps.

Apart from putting your maps to other websites, you can also print them out as pdf’s or images (png), or you can save the map itself in a format that other mindmapping software, like Freemind, can use.

I really like this website, and as soon as they add the ability to save zoom levels and collapsed nodes I’m going to try using it for my classes.

Searching for Answers: Earlier Puberty Over the Last 200 Years

Puberty starts somewhere in the age range of 8 to 13 years for girls and 9 to 14 years for boys. However, in Norway, in 1850, girls hit puberty at around seventeen. Over the next 100 years that age decreased to thirteen and a half, where it has stabilized, but a similar trend has been seen in pretty much all the industrialized countries, including the U.S.. No one knows quite why, but there are a number of theories, including:

  • Better nutrition,
  • increased stress, and
  • artificial chemicals in the environment or in the diet.
The trend in the timing of puberty in girls (menarche) for four western countries, from 1850 to 1950. Figure via NIH via INSERM.

It seems clear that this trend has something to do with improving living conditions. Rapidly developing countries like China are experiencing the same trend in earlier puberty right now. Wealthier areas in developing countries have girls starting puberty at the same age as girls in “privileged” countries, while their compatriots in the poorer areas do not. Also, Overweight kids tend to start puberty earlier.

However, explaining the earlier puberty is difficult because no one knows for sure what exactly triggers puberty to begin with. The genetic switch that tells the hypothalamus to start the process probably involves multiple genes that are affected in complicated ways by how and where a person grows up (when the environment affects how genes are expressed it’s called epigenetics; NOVA has a nice little program that explains how epigenetics results in differences in identical twins.).

Increased stress might be another explanation. Girls in Bosnia and Croatia started having puberty later and later during the war in the 1990’s. However, it appears that other types of stress, such as from insecure relationships with parents and adoption, can do the opposite and trigger even earlier puberty (note: really early puberty in kids as young as 9 is called precocious puberty and is a growing problem).

Certain artificial chemicals that disrupt the endocrine system, which is responsible for hormone production, have also come under suspicion, but their effects have been hard to prove.

Whatever the reason, the earlier onset of puberty has lead to an increase in the length of adolescence (which tends to start with puberty and ends somewhere in the mid-twenties). It’s hard to say though, if all the extra time is beneficial, since it does give the developing brain extra time to adjust to a more complex society, or if it just makes for a longer period of trying times.