Brownian Motion and the Whitley Bay smoke cell

 Robert Brown first noticed the weird random agitation of particles by looking at pollen in a microscope. These days we look at smoke particles injected into a pot that can be illuminated from the side. This is called a Whitley Bay smoke cell.

 Einstein explained what was going on in 1905 by saying that the big visible smoke particles were being hit by tiny invisible air atoms. I modeled this by putting a table tennis ball into my kinetic model that creates a random motion of ball bearings. The ball bearings move randomly and that makes the table tennis ball move randomly as well. Einstein's analysis finally proved the long-postulated and assumed existence of atoms.

And special thanks to Di for her perseverance in getting the cell to work for us :)

Fractional distillation

I teach about the fractional distillation of crude oil. Crude oil is a mixture of liquids with different boiling points. The bigger the hydrocarbon chain the more energy that has to be supplied to overcome the forces holding the particles in the liquid. You heat them to vapourise all fractions except one and then send them up a column away from the heat source so that the temperature drops. One by one, each fraction falls below its boiling point and condenses back to a liquid. I demonstrate with a water and ethanol mixture. Both are boiled at the bottom and both vapours head up the column. It is fixed so that the temperature at the top is 78 degrees Celsius so that the ethanol condenses there and liquefies. The ethanol flows out down the side pipe. Much of the water vapour has already condensed as it fell below 100 degrees Celsius. It dribbles back down the inside of the fractionating column. There will still be some water vapour left at 78 degrees C but the ethanol solution is now strong enough to catch fire.

Spring constant in Dale Bottom

The gate across the footbridge below Low Nest Farm was very stiff. I can lift my whole body weight with one leg but an arm is weaker. Say I can push with a force of 200N. We can work out the force on the spring by equating moments measuring the distance from the hinge. Spring to hinge is about 3cm and hand to hinge is 30cm. This gives a force on the spring of 2000N. If the spring obeys Hooke's Law then force = spring constant x extension. Spring constant is how many Newtons of force  the spring needs per unit extension. It used to be called the stiffness of the spring and sometimes gets called the stiffness constant on exams. F=ke. So k=F/e. If the extension of the spring is 10cm or 0.1m so k=2000/0.1 = 20000 N/m.

Bunsen Burner and Bernoulli

It occurred to me yesterday that the Bunsen Burner works by way of the Bernoulli effect. That says that when a gas flows, it has lower pressure. Thus when the hole at the bottom is opened, the air outside will have higher pressure than the flowing gas inside. The pressure difference pushes the air into the flowing gas so you get a mixture of air and gas at flowing up the middle of the Bunsen Burner. A proper gas/air mixture burns at a higher temperature hence the blue flame. I suspect that with the air hole closed the gas reacts with the oxygen around the outside so combustion is not as complete.

Mistletoe in the Cotswolds: photosynthesis

We found amazing amounts of mistletoe in the Cotswolds. I've just been teaching the more detailed version of the photosynthesis reaction for the first time. The mistletoe must be using the light at this time of year when the leaves are off the host tree. The light dependent reaction uses the photon energy to split water. The hydrogen is taken to reduce NADP. The energy is also used to add a phosphate group to ADP to make ATP. NADPH and ATP are then the energy providers for the Calvin Cycle which turns carbon dioxide into sugar.

Cloud inversion at Stow-on-the-Wold

Having experienced the air getting colder as we reached the valley floor at Buttermere before Christmas and seen evidence of the denser cold air layer of a cloud inversion, we found this lovely example in the Cotswolds after Christmas. The clear skies meant that the Earth's surface was able to radiate a lot of thermal energy into space during the night; the humidity was right for fog to form; the Sun's energy heated the upper layers of the atmosphere first and the cloud vanished but the lack of sunlight reaching the surface delayed the warming of the surface of the Earth resulting in a cloud inversion. But because Stow is on a hill we were in the sunshine and were able to see the very rare Blue Rock Thrush, which is on the chimney in the picture below!

Wrap yourself in foil to keep warm

It has always seemed strange to me that you can keep yourself warm with just a thin piece of foil but that's exactly what a lot of runners do. It shows that we must lose a ot of our heat as infra-red. Suppose that I am 2 metres high by 0.5 metres wide. That might give a total area of 2 square metres front and back. By Stefan's Law where P = sigma x surface area x absolute temperature^4, and with 37 Celsius being 310K I get an output power of 1.1 kW. Googling suggests other people are getting 100W.

Relative motion and train travel

Trains are a classic example of relative motion. If you can see the train next to you and you notice motion, is it you or is it them? In theory you should be able to tell if it is you that has started moving because you feel the acceleration  as you are gently pushed back into your seat if you are facing forwards. But train acceleration is often very low so it is common to mistake the movement of the train next door as your train moving. The laws of Physics say that if a car is coming towards you at constant speed and you are driving towards it at constant speed, you add the speeds together and it would be as if you were stationary and it was coming towards you at that bigger speed.

The stoves at Tewkesbury Abbey

It occurred to me that the two heaters in Tewkesbury Abbey must mainly send out thermal energy by infra-red radiation like my log burner. They are, after all, painted black. So each heater is a black body radiator and as such can be modeled by Stefan's Law: output power = sigma x surface area x (absolute temperature)^4. Suppose a heater is 1 metre tall and has 30 fins on it and that each fin is 5 cm deep. Each fin has two sides so will have an area of 0.1 square metres exposed. Total area = 30 x 0.1 = 3 square metres. Add another square metre for the top and other exposed parts and we have a surface area of 4 square metres. Estimate a surface temperature of 60 degrees Celsius. It can't be too hot or it would have to be better caged. That is an absolute temperature of 333 Kelvin. Put into the equation and I get an output power of 2800 Watts. It doesn't seem unreasonable to think of each heater as 3 kW.

Charles Law experiment

 When you heat a gas, it expands. This experiment aims to quantify this. We trapped a volume of air in a capillary tube underneath a small plug of conc sulphuric acid. You get the acid in by heating the tube and up ending it into the conc acid whilst still hot. As the air cools and contracts, it pulls the acid up. I think it is conc sulphuric to keep the air dry. We recorded the length of the air column as the temperature increased. You can just make out the sulphuric acid plug in the picture below.

We investigated a range of temperatures between 20 and 100 degrees Celsius, dictated by the water. Then we plotted a graph, extrapolating backwards to find where the volume of the air column would be zero. This occurs when the temperature is absolute zero. It's not an accurate experiment because we extrapolate backwards over 3 times the range of the readings.

Density of air

We attached a round-bottomed flask to a vacuum pump and sucked the air out. We sealed the empty flask with a Hoffman clip and put it into a tub on the chemical balance. We zeroed the scales. Then we opened the Hoffman clip. We could hear a loud hiss as the air rushed in to fill the vacuum. 

400 cubic centimetres of air had rushed in and had a mass of 0.5 grams. That makes the density of air to be 0.00125 grams per cubic centimetre or 1.25 kg per cubic metre.

Sounding the alarm on Winchcombe camp site

A lot of camp sites have these metal triangles as fire alarms. On hitting the triangle, a stationary wave should with a node in the middle and an antinode at each end. Thus the length is equal to half a wavelength. Say the length of one side is 20cm, then one whole wavelength would be 1.2 metres. The wave equation says c = f x wavelength. If the speed of sound in air is 330 m/s then the frequency of sound would be 275 Hz. Middle C is 261 Hz so the note must be close to middle C.

Testing for carbon dioxide in combustion

 We burned natural gas. The products of full combustion are carbon dioxide and water. To show that carbon dioxide was produced we used the fact that hot gases are less dense than the surrounding air and float upwards into the boiling tube. We had a bung ready on the table. When the tube had cooled we added limewater.

 Limewater is normally clear but when you shake the tube, the carbon dioxide reacts with the soluble calcium hydroxide to produce calcium carbonate which is insoluble. Hence the limewater turns cloudy.

Stability experiment

I like this very simple experiment to investigate stability. You tilt a pop bottle sideways and record the angle it which it won't snap back to its upright position - the first angle at which it topples. The bigger the angle the more stable an object is. When you tilt an object, part of its weight creates a moment that tries to pull it back to its normal position and the other part of the weight creates an opposite moment trying to knock the bottle over. There is a resultant moment - the biggest moment pulls the bottle in its direction. Provided the line of action of the weight has not passed the edge of the base, the moment pulling back to the original position wins and the bottle remains upright. Objects with low centre of mass and wide base mean that the object can be tilted further before the line of action of weight passes the corner of the base and the bottle topples. The centre of mass of an empty bottle is in the middle. As you add water to the bottle, you lower the centre of mass of the bottle and it becomes harder to topple. When the bottle is full the centre of mass returns to the middle and the bottle is as unstable as it was at the start.

Weird shadow through a slatted blind

On this day, the slats of the blind were angled and facing the Sun. This weird spiky, almost digital shadow was projected onto the wall. I have been thinking about how this was made. There is a narrow gap between the slats through which sunlight seems to be coming directly. This would give a normal shadow. Some of the light would be hitting the angled slats, reflecting upwards and then reflecting in my direction from the underside of the slat above. Slats are slightly concave on the underside so this would likely have some kind of focusing effect. Even with these suggestions, I can't see fully how these shadows form.

Hairy ball theorem

We were listening to Roger Penrose being interviewed on The Life Scientific http://www.bbc.co.uk/programmes/b082ymnx and he mentioned the hairy ball theorem. I first came across it in the Sixth Form when we asked our maths teacher Dr Fernandez what he researched for his PhD. He told us that it was about combing hairy tennis balls and whether or not you could comb it all flat by combing in one dimension. We had a go at the weekend. You can on a hairy flat surface but in 3-dimensions on a ball you can't. You can on a torus - a donut shape, And he said he'd been working on it in any number of dimensions. We thought he was winding us up but here it is https://en.wikipedia.org/wiki/Hairy_ball_theorem And even better, watch this one minute long animation https://www.youtube.com/watch?v=B4UGZEjG02s If the winds on Earth correspond to the hairs on the sphere, you will get at least one spike. This will be a place with wind speed zero, so you have to get cyclonic behaviour. I'm working on how it relates to Penrose's work on space-time. In particular, I want to find out if the spikes are places where the vector function is actually discontinuous and therefore undifferentiable. When I was reading his book two years ago, there were points like this on Riemann surfaces that he then cut away to allow the surfaces to be patched. Are those places like the hairy spikes or have I misunderstood?

Dissipation experiment

The new way of teaching energy is keen to point out that in every energy transfer some energy follows the pathway of heating by particles or heating by radiation to increase the thermal energy store in the surroundings. It concerns me that classes will touch the walls and point out that they don't feel any warmer. So here's the experiment I use to open this can of worms. Two beakers with 150 ml of boiling water in each. One stands in a washing up bowl half full of cold water; the other stands in a smaller plastic tub half full of cold water. Temperatures of hot and cold water in each pair are recorded every minute and graphs are plotted. There is an energy transfer from the hot water to the cold water in each case. The cold water in the small tub gets warmer by a few degrees if correctly stirred and the cold water in the big tub stays almost exactly the same despite having clearly been in receipt of energy that should fill its thermal store. So why doesn't the temperature go up? It's because thermal energy makes atoms vibrate. Temperature is effectively a measure of atom vibration. It's called internal energy and is a little more complicated than this but you get the idea) In the big tub, far more atoms are in receipt of what should be the same amount of energy so each gets a much smaller share. The atoms wobble a tiny bit more but not enough to register on our thermometers. And that is what is going on when energy transfers use a heating pathway to transfer energy to the surroundings. We say that the energy has been wasted - a human value judgement - because we can't make any use of it. We call this loss of usefulness "dissipation".