So, earlier in my career a student came to me to complain that, at the end of the
lesson when I asked them to label up the tubes that they've been using, she'd
written her name on a sticker, placed it onto her test tube, and her name had
disappeared again. And then I asked her to show me the pen
that she'd been using and it turned out as one of these new-at-the-time style of
friction pens. And I worked out pretty quickly it must be a thermochromic ink
that they've got here. When I investigated a little bit further it
turned out that this this ink disappears at around 65 °C but you can
actually reverse that process and make the ink come back again at about -5 °C
by putting in the freezer. So then I thought there are all kinds of
applications that we could have for this kind of thermochromic technology. In the
past we've actually looked at using this as a temperature indicator when we were
microwaving some solvents to determine whether or not they had got hot. And
today we're going to look at two other examples that we can use this kind of
ink for: 1 – an alternative to the classic marshmallow in a microwave
demonstration to determine the speed of light; and 2nd – a bit of a teaching
life hack that I've developed to help me with my marking. So let's jump on in.
So, most people are probably going to be familiar with the old 'determining the
speed of light using marshmallows or chocolates in a microwave'. But just
in case you aren't, the general idea is that you have an array of microwaveable
foodstuff, so marshmallows, chocolate, something that can melt. And
you're gonna put it into the microwave specifically having turned the plate
that's inside the microwave upside down. So inside every microwave we have a
plate like this and that rotates. The idea being that inside the microwave
there ... in the cavity there ... there's going to be a standing wave setup of microwave
radiation. And that some parts of the food, if it's not rotated, will get hot because
they're going to be lined up alternatively either with a node or antinode okay.
So, some parts are gonna get hot, some parts are gonna stay cool.
So, you want to rotate the food to make sure that it's evenly being heated. If we
flip the plate upside down so that the plate does not rotate any more, we can
then actually heat up some of our marshmallows not some others and
actually measure the distance from one hot spot to another, and from that
determine the speed of light. So we'll have a look at what that looks like and
I'm going to show you how potentially might improve on this methodology using
one of these pens.
So you take your marshmallows, you put them in.
I'm just gonna be heating here until ... and checking every sort of five to ten
seconds to see whether the marshmallows are heating up in one spot or another.
Okay, so let's take a look at what we have here. I've got my array of marshmallows
and it might be tricky to see that's here there's some melting taking place on
this edge over here. We've got some melting that's taken place just in this
sort of spot here. This marshmallow over here has got a little bit warmer
and expanded a bit but it's not that sort of convincing. And we realize first
of all we have a problem with sort of determining are we looking from one
antinode to the next, which would be half a wavelength, or are we looking at a
complete wave? Now, I know from experience that if I'm looking at this kind of
distance in the microwave that that's going to be one complete wave.
But will that be obvious to a student? Perhaps not, okay.
Really we ought to be seeing perhaps that there should be sort of a hotspot
in this sort of central point here. I've got about 13 cm, give or take.
There's quite a broad range of values that I could take from my wavelength
coming through here. And it's not easy for me to justify that I'm actually
looking at a complete wave rather than half a wave. I can perhaps if I'm lucky
take a measurement over to this point again because I know that this I should
be looking for a hotspot somewhere around here. This kind of also agrees
with my sort of 13 cm. So I've got sort of two measurements of 13 cm
roughly. But it's quite difficult for me to be much more precise
than that. So we have an issue with resolution. We have an issue with the
fact that actually this is quite a small plate compared to the size of the cavity
of the microwave. And we also have an issue with the fact that the more
material we actually put into the microwave, the more we're going to
distort the wave form that can potentially form within the
cavity. So, one way around this is to get yourself a piece of paper. And what I've
done here is just scribbled on this piece of paper but with some of this
thermochromic ink. And it may not be true for every single microwave but certainly
for the microwaves that I have here, the actual width of the cavities is actually
the exact or almost exactly the same as the length of a sheet of A4 paper.
So I've taken in a sheet of A3 paper here and just made a mark for the depth of
the oven, marked it off trimmed to size and scribbled over it with my
thermochromic ink. And I'll see what kind of a difference we can get in terms of
the measurements that we can pull out from our experiments. So I've got all my
marshmallow mess cleaned up now. We'll pop the piece of paper into the
microwave, and again sort of still be getting the full benefit of the edge to
edge cavity from within the microwave, and a very small amount of mass, and see
what kind of results we can get, and how quickly we can get them. So I'm just going to pop this in.
This is a 1200 W oven. I find that sort of five-second bursts, I can
sort of stick my nose in and see what kind of patterns are forming and keep an
eye on it that way. So let's have a look.
I wouldn't necessarily do this in front of a class just yet, but just to
show you what's happening, immediately five seconds we have our first spot
that's appearing as our hot spot. So at this point I might actually mark this
one off just to get an idea of where the center of that spot was, I've just got a pencil.
... five seconds ... and so I've got one spot here, let's develop this a little bit further.
Are we getting ... there's no indications of any other spots appearing just yet.
Okay, now this turns out to be quite lovely so I'm going to mark off here,
mark off here, here and we've got another spot here.
And perhaps a spot there but it's not that clear to me.
And so already it's sort of a couple of seconds we've
got some very fine resolution spots that are appearing, from which we
can take some measurements. So I'm gonna mark these up in a slightly fatter
pen so they can appear on camera a little bit better and then we'll see
what kind of outcome we get from those. Okay, so hopefully you can see the
resolution with which we're able to actually sort of get some measurements
coming off from our thermochromic ink. Now we're going to actually go for some
center-to-center measurements. And the other nice thing about this
of course is that you can photocopy this and pass it around so that students can
take their own measurements and make some maximum / minimum values so
they can actually come up with some confidence intervals within which
they would expect their speed of light to be. So, I'll measure these up and get back
to you in a couple of seconds.
Okay, so I've taken my measurements and I've gone
for 7.5 cm here, 7 cm and 8 cm here,
measuring to the nearest half centimetre using the ruler. I've also noted that
we've got this reading here about 11.5 cm. But this is a
point where we can say well, these values here sort of seem to agree with each
other within a centimetre, this one seems to be a little bit further out. And if we
look at the the maximum-minimum range of values that we could measure from this
point on the spot here, so over here, we find that actually we're up into the
14 cm + range as our maximum value for the distance between
these two spots. That's an ideal point to bring in, well,
are we actually measuring the same thing here between these further spots as we
were between these nearest spot? And from there we can perhaps bring in this
idea that we've got half wavelengths and full wavelengths that we could perhaps
be measuring. So, I've taken these three values, averaged them out, that gives me
7.5 cm. And by taking the reading from the frequency on
the back of the microwave oven we can see that this oven is operating at 2450 MHz,
so that's 2450 times ten to the six Hz.
And from speed being equal to frequency times wavelength, that would give us a speed of light for the
microwaves in this oven as being 3.7 times ten to the eight m/s
Now, from there we could perhaps even say well is it
possible that we could include this 11.5 figure and maybe even take
some more measurements to improve our value?
Because we know that the real value, true value of course we want to compare to is 3.0 times ten to the eight m/s.
So, when we factor this one in, actually that would bring our
value down to sort of 3.5 times ten to the eight m/s
second and then of course you know you've got a larger class you can
actually start handing out some other patterns. So here's some ones I made
earlier. And it turns out actually at least with this oven as you repeat more and
more we tend to converge on 3.5 times ten to the eight m/s as being
the speed that we're getting up from here. So although we have sort of zoomed
in and reduced our random errors, we seem to have locked in on that 3.5 figure,
suggesting that we have some kind of a systematic error, be that to do with
the shape the waveform that we're looking at in this particular wave cavity,
the two-dimensional nature of the wave versus this sort of one-dimensional
that we were sort of imagining when we're explaining to students.
And of course, at this point you now have your maximum and minimum values between which
your true speed could lie. And you have the ability to know to actually talk
about systematic error versus random error, as well as confidence intervals in
your appreciation of the true value. So in the case that I've used with this
oven I find that actually the the true speed of the light 3.0 times ten to the eight m/s
actually lies within the confidence intervals that
I've actually been able to map out based on the maximum and minimum values
associated with my half wavelength figures. So that's one thing you can do
with this kind of ink. The final thing that actually that I've sort of
started using in the last year or two has been to do with marking so I'm going
to push this stuff aside and just show you what you might get for like a
typical exam script. Now we know that students tend to look, perhaps when you
give them back exam scripts, they just tend to look for
marks and maybe ignore any comments that you might make on those.
In fact, Dylan William often says that you know the best person to actually mark a test
is the person who just actually wrote the test, but sometimes you may be
required by post by school to actually do a formal marking exercise on an exam
script, a mock for example. But you still want students to actually learn from the
experience. So this is where I worked out how useful these pens can be, because
actually what I want my students to be able to do is actually get together,
again as recommended by Dylan William, get together and agree a best possible
answer to any one of the particular questions that they've been asked,
benefiting from the peer teaching effect.
And then have a look at the mark scheme, compare their best possible answers
against that one, benefiting from the sort of 'hyper-correction effect', before
they can then actually go back and perhaps sort of see my comments which we
know from evidence suggests they don't actually look at unless you've actually
made them engage with the work beforehand, make them go hunting for their feedback.
Now, in the past let's say for example I was marking something I wanted
to actually sort of tick things off as I was going through because I wanted to
actually help myself keep count. But the problem was that then I needed a kind of
erase all of my marking to stop students from just lazily looking at where I
had already given the marks. This is where these pens are such a valuable
addition to my toolkit. Because now I can actually go through, mark an entire set
of scripts, pop them into the oven, set to about 80 °C to make sure that
they're well above that 65 °C transition temperature, and all of my
marking disappears. Then I can hand the students back their scripts, they can in
pencil make their own comments, improvements to their answers, and
compare with the mark scheme, and only then when they've sort of provided me
with evidence that have really engaged with the level of feedback that I'm
expecting from them, then they earn the rights to get back from me what I
thought you know my marks were, and they can compare for that final sort of
comparison and improvement point by just taking
my scripts and sticking them back into the freezer to have all of my marking
come back of course when they're doing their
marketing they need to be using pencil or something that's going to be
different from what they've written in. And it's really important of course when
they're doing their writing in the first place that they're not using
thermochromic pens themselves, which of course can make this whole exercise a
real pain in the neck. So give it a try, it's something that works really well for me
and my students enjoy it too. So, worthwhile giving a try.