Too Cool To Expand

...blowing hot and cold!

Published: 19th April 2015 06:00 AM  |   Last Updated: 17th April 2015 01:01 AM   |  A+A-

Trust some people to be nitpicky. A V Ramana Rao at -- he of the test match hat-trick hall of fame problem -- has an iconic observation regarding why the hole in a metallic donut configurationexpands on heating. As he argues, this is because it inevitably assumes the material of the donut has a positive coefficient of thermal expansion. But, not to put too fine a point on it, apparently there are materials such as zirconium tungstate and scandium trifluoride if you please, to mention only two such dastardly deviants, which have a negative coefficient of thermal expansion -- meaning they contract when heated. Can you believe it?

However my question therefore is simple: what happens if such materials are cooled instead? Like, do they keep expanding continuously? (After all the above mentioned zirconium tungstate is almost world famous for contracting all the way from 0.3 to 1050 Kelvin and would probably have merrily continued to do so even beyond if it wasn’t for the fact that it begins to degrade by then.) And if so -- to maintain my line of thought -- what happens if the troublesome tungstate is cooled to as close to absolute zero as possible? Does it begin to exhibit near infinite volume/mass? Cool thought, no? Or do you want to rush into the Google section now to solve the questions before they’re written?


(The question was: “A hen and a half can lay an egg and a half in a day and a half. How many hens are needed to produce 12 eggs in six days?”)

Three hens are needed to produce 12 eggs in six days. (This is a problem in compound proportion so that H*D/E is always a constant where H stands for number of hens, D for number of days and E for number of eggs.) -- G

Srinivasa Rao,

A hen and a half can lay an egg and a half in a day and a half. So three hens can lay three eggs in a day and a half (not in three days). At this rate, three hens are needed to lay 12 eggs in 6 days. -- Ramakrishna Bhogadi,

(Among the first five who also got it right and a half are: Abhishek Narayan,; Rajamani,; R Viswanathan,; Hemalatha T,; V C


(Regarding the outcome of the undermentioned race between A, B, C, D and E, people have had some surprisingly similar views, as witness.)

It is easy to see that D cannot be first; C second and B third. This narrows down the first to B and second D or A. Further elimination will lead to the correct order  being BAEDC. This will ensure the predictions 1,

3 and 5 are completely  incorrect. Prediction #2 is correct with respect to positions 2 and 3 (AE) and prediction #4 is right on positions 1 and 5 (BC). The key is to recognise that the two correct predictions need not be so in respect of the same positions between them. -- Saikrishna S,

The order in which the five participants touched the finishing line is BAEDC. The person who predicted DAECB got A and E right. The person who predicted BDAEC got B and C right. The others (ECBAD, DCBAE and DCBEA) did not get even one right. -- Rajagopalan K T,

(And the third problem was: “Why are mountain-tops cold, considering the solar heat per unit area on a mountain is about the same as at sea level?”)

Mountain tops -- and hill stations too for that matter -- are generally colder by comparison to the plains areas because of air currents. Air ascending the side of mountains expands and therefore cools as it moves into less atmospheric pressure at higher altitudes. -- Dhruv Narayan,

When a parcel of air warms up near the surface of the earth, it rises because of reduction in density. But as it rises, it moves into regions of lower pressure and expands. As it expands, it cools. Thus mountain tops are always colder. -- Dr K N Murty,


1. You’re given a fixed-span compass and asked to draw a circle on a sphere and then on a flat sheet of paper. If the compass is big, the circle on the sphere will be smaller than the one on the paper because its diameter slices through the sphere. But which circle has more area?

2. Why does it take longer to raise a flag to half-mast than to full mast?

— Sharma is a scriptwriter and former editor of Science Today magazine.(


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