杏吧原创

It flies like a bird

Last weekend I bought a helium-filled balloon. Sadly my friend let it go. How high could it climb and how far could it have travelled?

鈥� The balloon will rise until the mass of the air it displaces is no greater than its own.

Let鈥檚 assume the balloon material weighed 1 gram and when filled with helium was spherical with a diameter of 20 centimetres and a volume of about 4.2 litres. The ideal gas laws give a density of 0.164 grams per litre for helium at 25 掳C and at 1 atmosphere, so the mass of helium in the balloon is 0.69 grams, and the total mass of the balloon plus helium is 1.69 grams. This means the balloon will stop rising when the surrounding air has a density of 1.69 grams per 4.2 litres, which is equivalent to 0.4 grams per litre. Air has this density at a height of approximately 8 kilometres above sea level.

Obviously, this answer is very sensitive to all the assumptions I鈥檝e made about the balloon鈥檚 size and weight, and the initial pressure of the helium. I鈥檝e also assumed the balloon does not change shape and is impermeable. In reality, several other factors complicate the problem. First, the pressure and temperature at a height of 8 kilometres are about -40 掳C and 0.35 atmospheres respectively. In these conditions, the gas in the balloon will want to expand to about 2.3 times its original volume, assuming the material can stretch. This will make it less dense, and hence more buoyant, but the balloon may also burst as it expands. Secondly, the helium will tend to diffuse out, while the surrounding air will diffuse in. This process will be accelerated by the low external pressure at high altitude, so the balloon will lose its buoyancy more rapidly.

Simon Iveson

Department of Chemical Engineering University of Newcastle, New South Wales

鈥� Unfortunately, the most likely fate of your balloon is that it will burst. However, if the balloon is made of particularly strong latex it is possible it could reach buoyancy equilibrium with the thin air at high altitude. At 8 kilometres and above, strong jet stream winds could certainly push the balloon hundreds or even thousands of kilometres.

If the balloon survived the harsh high-altitude conditions for long enough, the helium leaking slowly through the micropores in the latex would cause it to start sinking. From my own unscientific observations, I reckon a latex helium balloon can deflate in less than seven days to a level where it no longer floats, so your balloon would eventually have landed somewhere.

To make the balloon less likely to burst, a good strategy would be to attach a small weight that would limit its altitude.

Evan Yates

Hamilton, New Zealand

鈥� During our celebrations for the Queen鈥檚 Golden Jubilee on 1 June here at Knowle Church of England Primary School, we released 467 helium-filled balloons to see which would be returned from farthest away. A month later, the results are in.

Of the balloons that were found, four arrived in Belgium, two in Germany and the farthest two were in Halmitz and Ein枚de in Austria, around 1300 kilometres away.

I suppose other balloons could have travelled farther, but I suspect they are caught high up in trees, and the squirrels can鈥檛 afford the postage.

Ruth Brown

Knowle, West Midlands

Solar flower

Sunflowers rotate to keep the flower facing the Sun during the day. Do they face sunset all night and then flip around when dawn comes up behind them?

鈥� When the sunflower plant, Helianthus annuus, is in the bud stage, the head and the leaves do indeed track the path of the Sun. The genus name Helianthus is from the Greek helios 鈥渟un鈥� and anthos 鈥渇lower鈥�.

Interestingly, however, and contrary to popular belief, once the massive topmost flower opens into the radiance of yellow petals, it slows and then stops moving, ending up permanently facing east.

This fixed orientation is thought to be an adaptive feature. Sunflower pollen gets damaged at temperatures greater than 30 掳C, so by facing east all the time, the flower reduces the net radiation falling on its face at noon, keeping itself cool and promoting fertilisation and seed development. In addition, the heads receive more sunlight early in the morning, which helps dry off any dew that has formed overnight and decreases the likelihood of fungal attack. It also increases the temperature of the flower head in the chilly early morning, attracting warmth-loving insect pollinators.

The heliotropic movements of the leaves and sunflower bud are the result of bending during rapid growth. This is caused by build-up of the plant growth hormone auxin on the side of the stem opposite the Sun. The direction of the head lags behind the Sun鈥檚 position by about 12 degrees, or a time of 48 minutes. When the Sun sets, the auxin is redistributed and the head swivels back, so that by around 3 am it is facing east again, waiting for the Sun to come up 鈥� Ed

With thanks to Loren Rieseberg, Professor of Plant Evolutionary Genetics, Department of Biology, Indiana University

This week鈥檚 question

Bog standards

At this time of the year the moors of Scotland are covered with cotton grass, or bog cotton (genus Eriophorum). As the picture shows, the grass produces large cotton-like balls of fibre. It is easy to pick substantial quantities of these cotton balls, and the fibres from them can be twisted into a thread. Have cotton grasses ever been harvested commercially anywhere in the world, or could they be?

Eleanor Blackpoint, Shetland Isles