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May 2013 Archives

 Last week we had a new oven installed. Our old el-cheapo one that came with the house was never in Karen's good books. Small, dirty, incapable of getting to a high temperature and generally giving the impression that it was about to die at any moment. Indeed, it did a couple of Christmases ago - it refused to do anything. It turned out that the clock/timer chip had given up and was sending a permanent signal to the oven that it should turn off. The repair man took about a minute to diagnose it and another minute to bypass the clock chip - which meant we couldn't use automatic on/off settings or anything fancy but at least we could turn the oven on and off manually.

But the days of that oven are gone, and it's been replaced by something much more sensible. (I don't do product placement so I won't tell you make it is here) The thing that most strikes me about the new one, other than it does what you tell it, is how well thermally insulated it is. It's a cabinet-mounted oven, rather than part of a freestanding cooker. When we turned up the old one high, the oven door got very hot and the cupboards next door became rather warm too. With the new one, the cupboards next door hardly change in temperature, and the oven door itself, is only slightly warm. This has the unintended benefit of meaning the baby is rather safer in the kitchen - if he puts his hands against the oven door he will barely notice a temperature change. (Not that we encourage him to try - his latest kitchen trick is trying to climb into the dishwasher - something that even the cat though better of)

The thermal resistance of a material is defined in terms of the temperature differential between its front and back surfaces needed to drive a given amount of power (heat per unit time) through the material. Thermal resistance obviously depends on both how thick the material is (double the thickness, double the resistance) and also its area (double the area and you'll get twice the heat flow for the same temperature differential). We can take the area out of the equation by moving to a U-value - this describes the power loss for a degree kelvin (or celsius) difference between a unit area of the two surfaces. A low U-value means the material is a good insulator.  Still, U-value depends on how thick the material is. Taking this out of the picture and we get thermal conductivity, which is an intensive measure of how good a material is. Whatever is surrounding our new oven and is in our oven door surely has a pretty low thermal conductivity. The thought has occured that there is a vacuum somewhere - that has low thermal conductivity indeed!

 P.S. While putting in links for some of these terms I notice that there is some ambiguity in what people refer to as thermal resistance. I was taught it as being the temperature differential required per unit power (so SI units kelvin/watt - analogous to electrical resistance), but it also seems to be used as the reciprocal of the U-value. Not the same thing. 

 

 

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Somewhere in the Cambridge / Hamilton vicinity is a car with no oil in it. I know this because on the way in to work this morning there was a trail of oil on the road.  The damp road surface led to it being very prominent. A splash of oil, being less dense than water, will sit as a thin film on the water surface and show some colourful patterns due to interference of light reflected from the top and bottom surfaces.  

What was also clear was that these splashes of oil were not placed at equal intervals. They were closer together at intersections, and well spaced along the main road (to the point that I couldn't follow them at times). A reasonable conclusion is that the oil was dripping at a roughly constant rate (a roughly constant time between each drips). When the car was travelling fast, there was a long time between splashes. When the car was travelling slowly, they were close together (I could see that the car had clearly stopped at the roundabout in the centre of Cambridge, for example). On the assumption that the car was travelling at approximately the speed limit on most roads, I could have estimated the rate of dropping by measuring the distance between the drops. I might find physics fun, but I don't find it so fun as to stop on the side of SH1 and get out a long tape measure with heavy traffic roaring past, so I'm afraid I don't have an answer to this. Perhaps more worryingly for the car driver, the car was leaving behind evidence of whether it had really stopped at stop signs. 

The pattern of splashes reminded me a lot of our experimental introduction to kinematics at school. We used a ticker-tape machine. We had a cart that was placed on a ramp, and the cart pulled a stream of ticker-tape behind it. The tape went through a machine that stamped it with dots at a constant rate. If the dots were close together, it was because the cart was moving slowly; if they were far apart, it was because the cart was moving fast. By analyzing the dots afterwards we could work out the velocity of the cart at any point on its descent of the ramp and its acceleration. 

Nowadays you can do the same experiment with a camera and a bit of computer software to do all the calculations for you. It might be more efficient, but its probably not as constructive as ticker-tape in getting a student's head around what distance, velocity and acceleration are. And it's definitely not as fun as ticker-tape was.

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 One thing that's become really clear to me in teaching physics is that dimensions and units are not straightforward concepts for students. I might hazard the assertion that they are 'threshold concepts' - ones where grasping what they are about transforms you way of thinking. Most people at least half-understand the idea of units - if we measure a length, we can't say it's 26.5.  It's 26.5 what? nanometres? kilometres? light-years? There's big differences between them. 

There's also this mathematical conundrum to through out which illustrates the idea of dimensions: "I have a cube. What length does the side of the cube need to be in order for its surface area to equal its volume? "

The algebra-happy student will have no problem with this question. If the side of the cube is x, then the area of one face is x^2 (that is, x squared), so the total surface area is 6 x^2 since there are six faces. The volume is obviously x^3 (x cubed).  So we have 6 x^2 = x^3 and we can cancel a factor of x^2 from left and right to give 6 = x, and so there's our answer. Six. 

Six what?  Nanometres? kilometres? light-years? There's a big difference. The solution of the conundrum is straightforward. You can never have the surface area equal to the volume (unless you have no cube at all - i.e. x is zero). Surface area and volume are fundamentally different things (dimensions).  In S.I. units, the former would have units metres squared, the latter metres cubed. So the question is 'wrong'.

This afternoon I was talking with my students about the 'electron-volt' unit for energy. There's clearly some difficulty in grasping this. Literally, it is a volt (which is a measure of energy per unit charge) times the charge on the electron.  The context in which it came up is with contact potentials in solid state physics. If I put a material with work function A, in contact with one of work function  B, then the contact potential is just (A-B)/e, where e is the charge on the electron. Work in electron volt units, eV, and it's dead straightforward.  For example, if A is 7.0 eV, and B = 5.5 eV, then the contact potential is (7.0 eV - 5.5 eV) / e = 1.5 V.    On the numerator there's the charge on an electron times a voltage, on the denominator there's the charge on the electron, and so the charge on an electron cancels and we get a voltage. But many students felt that it couldn't be that simple - they felt they needed to put in a numerical value for e rather than just cancelling it. 

Units and dimensions are tricky things. 

 

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 I was at a local intermediate school this morning, talking to a group of students about energy. It's a pretty broad topic, and they were very enthusiastic, meaning I only got through about half of what I wanted, but that's OK. If it inspires them to go and find things out for themselves, then that's a positive result.

I talked a little bit about measuring energy, and the unit of the 'joule', 'kilojoule', 'kilowatt-hour' and so on, as well as what power is (the rate of change of energy). At the end I asked the students how much they thought that a 'unit' (a kilowatt-hour) of electricity cost. That's the cost of having a kilowatt of stuff running for one hour.  

Now, I didn't really think that the students would have much idea. I mean, they aren't the ones forking out every month for their power bills (ahem! that should be energy bill - remember a 100 W light bulb running for one hour will cost you the same as a 50 W light bulb for two hours - it's energy that you pay for, not power). Estimates ran from 2 cents a kWh to ten dollars, mostly weighted to the several dollars end of the spectrum. I'm rather glad they're not in charge of the power companies if they wish to charge that price!  I suggested that they ask their parents to look at an electricity bill (and compare a summer bill with a winter one). 

But I was a little surprised that the two teachers in the room had no idea either (or, if they did, they weren't going to air it in front of their students). They knew what they paid roughly a month, but not what it cost, for (say) a light bulb for eight hours. One of them said that her parents told her that leaving a light bulb on for a few hours was equivalent to her week's pocket-money (probably a good way of getting her to turn it off). I think they were being rather harsh on this one...

An incandescent light bulb, at 100 W (a bright one), will go through 800 watt-hours in eight hours (e.g. if you go out for the day). That's 0.8 kWh, or 0.8 units. At current prices, of around 30 cents a unit (depends on what sort of contract you have of course) that gives about 24 cents cost. Withdrawing a week's pocket money for this offence is a bit unreasonable! Leaving all the lights of the house on, while you go on holiday for a week, however, is a slightly different story. 

21/6/13 The observant ones among you will notice that I mucked up the units in my light-bulb calculation in my original attempt. Units really are slippery things.

 

 

 

 

 

 

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 After doing the washing up a few days ago, I returned to the sink to find a raft of bubbles had formed on the surface of the water. All the bubbles were roughly equal size, and they had aligned themselves into a close-packed lattice, as the photo shows. (Sorry about the quality of the photo - the bubbles were small and the light was poor - and I didn't have a tripod - but I did my best. )

bubble_raft.jpg

 

Look closely, however, and you'll see some defects on this lattice. If you follow a row of bubbles, you'll see in places that a row ends abruptly or another one is inserted. This is a 'dislocation'. Also, you'll see single point defects (a bubble missing) and grain boundaries - where parts of the raft with different directions of the bubble rows meet.

All these defects are found in real materials - though of course in a real crystal there is a third dimension which complicates things a bit more. For example, there is a 'screw dislocation' that can occur in a 3d lattice which has no analogue in 2d. 

Making a bubble raft is a good way of teaching about crystal structure and crystal defects - the tricky bit is getting all the bubbles about the same size. I'm not sure how it happened in this case, but it was worth grabbing the camera and having a closer look. 

 

 

 

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This morning I turned up to give my solid state physics lecture and I realised I was in the wrong place. I'd gone to the lecture room where the Friday lecture is held, not the Thursday one. The trouble is, I had absolutely no recollection of where the Thursday lecture was. 

Not being a smart-phone owner, I couldn't go to the online timetable easily and check. After some racking of my brain, I vaguely recalled giving a lecture somewhere in the I,J,K complex on campus. Couldn't remember exactly where though. I had to walk along the main I,J,K corridor looking in more-or-less every lecture room till I found my students.  

What was impressive was that I still beat half my students to the lecture! 

I've turned up at a lecture with the wrong course notes before, and I've turned up at the wrong time before (fortunately at 9am when the lecture was 10am, not the other way around), but this was the first time I'd had a complete location failure. 

Am I tired or am I just getting old?

 

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Friday is the last opportunity to view a solar eclipse in New Zealand for a long time (till 2021 - or 2025 if you don't count anything of a few percent or lower). I say 'view', but the reality is that such a smidgen of sun is going to be covered that you're going to have to look carefully at the right time. And that's only for us northerners - most  in the South Island are going to miss out. (Details for this eclipse are here). 

For Hamilton, the eclipse hits its maximum coverage (a mere 5%) at 11:49 am. 

But it's not all bad news - an eclipse famine is followed by an eclipse bonanza - three total and three annular eclipses visible from New Zealand between 2028 and 2045. Worth looking forward to. I'll be into my seventies for the last one of these. Ouch. 

 

11:51am, Friday 10th May. Just caught a glimpse of the sun in a clear patch between the clouds. Can I detect any 'nibble' out of it. Nope. I thought 5% was a bit of an unlikely viewing situation.

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I came across this paper while doing a bit of reading about the applications of transcranial magnetic stimulation (TMS). A TMS machine applies pulses of magnetic field to the brain. The rapidly-varying magnetic field induces an electric field (Faraday's law) and this in turn influences neural activity (but just how and where is an open question).  A team of leading sleep researchers (Marcello Massimin, Guilio Tononi and Reto Huber)  has probed the state of the brain using TMS for various states of consciousness. What they found was very interesting. When in deep sleep, a pulse from the TMS machine generates a single slow wave of activity, which has the same form as the naturally occuring slow waves that are a hallmark of deep sleep.

Now, these slow waves are important - they have been linked with memory consolidation. The more slow waves you have when sleeping, the better you are committing things into memory. And artificially-generated slow waves do the job too. 

In other words, the TMS can be viewed as generating artificially enhanced sleep and therefore artificially improved memory. 

But wait, there's more (as they say). When someone is awake, a TMS pulse doesn't do anything. But for someone teetering on the edge of sleep, but still not quite in it, a pulse from the machine can be enough to send them over the edge. So here we have a way of pushing someone into sleep more quickly than they'd otherwise get there. A cure for insomnia? Perhaps not - I mean, TMS machines are hardly unobtrusive, but interesting nonetheless. The remaining question is, do we get one for us or the baby?

 

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 Here's a great interactive website by Cary Huang to give you an idea of how big and small things are. Thanks to Greta Dromgool for pointing me towards it.

It covers a whopping 60 orders of magntiude in length - from ten to the power of minus thirty five (the Planck Length) through to 10 to the power of twenty six metres - the size of the universe. Admittedly, there's a great lot of nothing in the ten orders of magnitude between the neutrino 'size' and the Planck length, so one might more reasonably say there's only 50 orders of magnitude covered.

This shows a couple of interesting (but not necessary greatly meaningful) points.

1. That we 'live' in the middle of this range, at about ten to the power zero metres.  (10^0 = 1). Things we experience are broadly on the metre scale. We see things that are millimetres in size, and experience kilometre distances as we travel, which is a range of merely six orders of magnitude, right in the middle of what exists. 

2. That most of what we have in the universe is physics. Yay!   Anything you 'see' about ten to the power six metres or larger can broadly be called astronomy / astrophysics. And anything you 'see' about ten to the minus ten metres or smaller is also physics. Physics covers the extremes. But it also features in the middle ground - don't get the idea that this is exclusively the realm of chemistry and biology. 

So, enjoy. Don't confine yourself just to scrolling, you can click on each object (and there are a lot) for further information.  I warn you, though,  the music gets a bit bugging after a while.

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