Monday, November 2, 2015

Microwave Heating Experiment (Fall 2015)

There are quite a few questions about the Microwave Heating experiment (procedure here), so let me try to address them all in one place.

The most common and persistent questions are related to the data analysis. The hands-on procedure and collection of the data seems to be going well, so let's not dwell on that part of the experiment. Once you have collected your data, you'll have a sea of numbers that you, as a scientific investigator, will have to process and interpret so you can get some useful information out of your experiment. The data you are collecting will look something like this:
The procedure tells you to prepare a graph of this data. Whenever you are collecting data (or just observing something interesting in your daily life) where one variable is under your control (in the case of this specific example, time), and another variable is simply a quantity you are measuring (in this case, temperature), it is ALWAYS interesting to consider what the graph of that information looks like. In this case, the graph of the above data looks like:
Hmm, interesting, although in this case not too surprising: as more time in the microwave passes, the sample gets hotter. But how much hotter? And how fast does it get hotter? If I want to heat a cup of water to make tea, should I put it in the microwave for 30 seconds or 5 minutes? The rate of heating is an interesting and important piece of information we can extract from this data!

How do we calculate a rate? Rate is the change in some observable quantity divided by the change in time. If you can eat a cheeseburger in 5 minutes, your rate of eating cheeseburgers is:
Change in the number of cheeseburgers / Change in time
1 cheeseburger / 5 minutes = 0.2 cheeseburgers per minute
In this experiment, you weren't eating cheeseburgers (well, OK, I guess you might have been eating cheeseburgers while you were watching water heat up…), but you were observing the change in temperature as time passed, so we should be able to calculate a rate in a similar way. Looking back at the data above, we can pick any two points and look at the change in temperature divided by the change in time. For example, from 90 seconds to 135 seconds the temperature changed from 116.04°C to 184.70°C, so the rate over that time period was:
(184.70°C - 116.04°C) / (135 seconds - 90 seconds)
(68.66°C) / (45 seconds)
1.5°C per second
We could pick any two points out of our data and calculate a rate, and they would all be pretty similar, but because there is some variability in our experiment they would not all be identical. But wait, if that's all we are going to do, then why did we make a graph? Graphs are pretty, but making a graph for the sake of making a graph doesn't seem like a great use of your time. Can we use the graph to determine the rate of heating? Hmm, change in temperature… the vertical axis (y-axis) is temperature, so that one should track changes in temperature… and the horizontal axis (x-axis) is time… WAIT! The data points in the graph look pretty close to linear, and the slope of a line is "rise over run"… if "rise" is the change in the y-axis variable and "run" is the change in the x-axis variable, then we should be able to get the slope from the graph, and the slope should be the rate of heating! If we draw a line that looks like it fits the data pretty well, we get:
From the line (we're not looking at specific points now), it looks like over the time period from 0 seconds to 300 seconds the temperature rises from about 5°C to about 390°C. So the rate based on the fit line is:
(390°C) / (300 seconds)
1.3°C per second
By using a fit line, we can even out some of the variability associated with any two points we might choose and we should get a more reliable answer. If we look at the rate for any two adjacent points (any 15 second period in our experiment) and calculate the rate using only those two points, we would get answers as low as 0.75°C per second and as high as 1.9°C per second, so using the fit line seems like a pretty good way to get a reliable single answer for the experiment.

Good luck on your data collection and analysis.

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