Boyle’s law

Boyle’s law is the principle that, at constant temperature, the volume occupied by a gas is inversely proportional to pressure (at least until the pressure gets extremely high). In symbolic terms, PV = k, where k is a constant. The pioneering scientist and amateur theologian Robert Boyle published this law in 1662, in his New Experiments Physico-Mechanical, Touching the Air (2nd edition): Whereunto is added a defence of the authors explication of the experiments against the objections of Franciscus Linus and Thomas Hobbes. The chart above shows the data he collected, together with a diagram of his apparatus and a scan of his original data table (cleaned up from an image in the Wellcome Collection).

Boyle’s apparatus involved an uneven U-shaped tube, sealed at the short end, and with mercury in the “U.” Further mercury was added to the long end, in order to compress the air in the short end to a specified volume. The pressure in each case (in inches of mercury) was the measured amount in the long end of the tube, plus 29.125 inches for atmospheric pressure.

Boyle’s experimental work was excellent, with all errors less than 1% (on my calculation). This is shown visually by the close fit of his experimental datapoints to the line PV = 351.9. His arithmetic was not quite so good – column “E” in his original table showed his predicted pressure, calculated laboriously using fractions. Seven of the 25 entries are incorrect. For example, using his approach, the 7th entry should be 1398 / 36 = 38 5/6, but Boyle has 38 7/8.

Home replications of Boyle’s work generally involve weights, a large syringe, some precarious balancing, and the fact that the air column sitting on a square centimetre weighs about 1.03 kg. Like so:


Powers of 10: the Australian version

In the footsteps of the classic short film, we explore the powers of 10 (click to zoom).

We begin with a classic NASA photograph of the Earth seen from Saturn, with a field of view (in the distance) about 100,000,000 km across. We zoom in by a factor of 10 to see the Earth and the Moon beside it. After three more such jumps (to 10,000 km), the Earth fills the frame. Three further jumps (to 10 km) zooms in on Melbourne, Australia. Two more jumps show us the city centre (1 km) and St Paul’s Cathedral (100 m). Another two jumps (to 1 m) give us a small boy on the grass beside the Cathedral. Two more give us the iris and pupil of his eye (1 cm) and a small patch of his retina (1 mm). Finally (at 100 µm or 0.1 mm), we see red blood cells inside a blood vessel in his retina. Fifteen jumps in all, zooming in by 1015.


Energy!

Science has a concept called energy, which includes electrical energy, chemical energy, kinetic energy, and other (interconvertible) forms. Energy can be measured, and obeys laws like E =  and E = ½mv2.

Then you have the “energy” involved in “energy medicine.” It does not correspond to energy in the scientific sense, cannot be measured or detected, and obeys no scientific laws. It is obviously not the same as the energy that scientists talk about. Why, one might even think it does not exist


Thermodynamic visualisation

This plaster model was made by the great James Clerk Maxwell in 1874 (the photograph was by taken by James Pickands II, 1942). This historic artefact is one of three copies, held in museums around the world, including the Cavendish and the Sloane Physics Laboratory at Yale.

The model shows the relationship between volume, energy, and entropy for a fictitious water-like substance, based on theoretical work by Josiah Willard Gibbs. The lines connect points of equal pressure and of equal temperature. Maxwell found the model a useful aid in his research. The model prefigured modern visualisation techniques – today we would use computer software to visualise such surfaces, like this:

400px-AiryAi_Abs_Surface

Ground-penetrating radar and archaeology

Ground-penetrating radar (shown in action above) is a useful application of science to archaeology. Exploring the underground with microwaves saves a lot of digging!

The image below (click for details) is of a “slice” though an historic cemetery. The vertical axis shows depth. Yellow arrows mark probable human burials, while dashed blue lines mark probable lines of bedrock. The upper half-metre is a tangle of tree-roots, which it would have been difficult to dig through (had that been permitted, which it was not).

You can imagine how useful this technique would be in searching for a lost and buried city!

Rainbows!

Rainbows are one of the most frequently observed atmospheric phenomena, although double rainbows can still get a strong reaction.

Rainbows form when light is refracted and reflected in droplets of water from rain (or some other source) as shown below. The light emerges at angles of up to 42°, so that the primary rainbow forms a circular halo around the antisolar point, at an angle of 42° from it. For the secondary rainbow, light enters the droplet from below and is internally reflected twice, emerging at angles of 51° or more, thus forming a larger halo (with reversed colours) around the antisolar point.

No light is refracted into the region between the primary and secondary rainbow, and this dark region (shown below in a photo by L.T. Hunter) is called Alexander’s band, after Alexander of Aphrodisias, who first discussed it in around 200 AD, in his commentary on Aristotle’s Meteorology.

Blue LEDS nobly rewarded


A blue LED (photo by “Hoenny”)

The Nobel Prize in Physics for 2014 goes to Isamu Akasaki, Hiroshi Amano, and Shuji Nakamura “for the invention of efficient blue light-emitting diodes which has enabled bright and energy-saving white light sources.” Congratulations!

Gallium nitride and indium gallium nitride were the key materials in making blue LEDs, while cerium(III)-doped yttrium aluminium garnet phosphors convert blue LEDs into white ones.

Blogroll: Carnot Cycle

Carnot Cycle is a thermodynamics blog (yes, it’s great that such a thing exists!). The image above is from a post on the ideal gas equation. Other interesting posts include converting relative to absolute humidity and lessons from science history. Definitely a blog worth reading!

Noctilucent clouds!

The beautiful Noctilucent clouds (photo above by Kevin Cho) are slightly misnamed. The name means “night-shining clouds,” but in fact they are only visible between the end of civil twilight and the end of astronomical twilight (and at latitudes north of 45°N or south of 45°S).

Noctilucent clouds are the visible form of polar mesospheric clouds, made up out of ice crystals in the normally very dry almost-vacuum at extremely high altitudes, around 80–90 km up (see NASA image of a polar mesospheric cloud above).

Noctilucent clouds were first identified as a distinct atmospheric phenomenon in 1885 (see the Google ngram below for uses of the phrase). The ice crystals from which noctilucent clouds are formed require both water vapour and dust for crystal growth nuclei. The sources of these ingredients is still mysterious, although at least some of the dust may come from meteors.

Yet another atmospheric phenomenon for the bucket list!

The green flash!

The green flash (photo above by TheBrockenInaGlory) has been seen at sunset by a few lucky people. Under the right conditions, the atmosphere behaves like a prism, separating the last solar light via refraction, so that the final trace of the Sun is green (blue light is scattered too much to be visible). This rare atmospheric phenomenon forms the backdrop to Jules Verne’s 1882 novel The Green Ray:

All eyes were again turned towards the west. The sun seemed to sink with greater rapidity as it approached the sea; it threw a long trail of dazzling light over the trembling surface of the water; its disk soon changed from a shade of old gold, to fiery red, and, through their half-closed eyes, seemed to glitter with all the varying shades of a kaleidoscope. Faint, waving lines streaked the quivering trail of light cast on the surface of the water, like a spangled mass of glittering gems.

Not the faintest sign of cloud, haze, or mist was visible along the whole of the horizon, which was as clearly defined as a black line traced on white paper.

Motionless, and with intense excitement, they watched the fiery globe as it sank nearer and nearer the horizon, and, for an instant, hung suspended over the abyss. Then, through the refraction of the rays, its disk seemed to change till it looked like an Etruscan vase, with bulging sides, standing on the water. There was no longer any doubt as to the appearance of the phenomenon. Nothing could now interfere with this glorious sunset! Nothing could prevent its last ray from being seen!

The sun was just half way below the horizon, and its powerful rays were shot across the sky like golden arrows; in the distance the cliffs of Mull and the summit of Ben More were bathed in brilliant, purple light.

At last only a faint rim of gold skimmed the surface of the sea.

‘The Green Ray! The Green Ray!’ cried in one breath the brothers, Dame Bess, and Partridge, whose eyes for one second had revelled in the incomparable tint of liquid jade.