Nature Fables 2: the four dogs

The Four Balloonists

One day four dogs of normal mass wished to ascend into the sky by means of a helium. They came to Confucius to confer with him about their plans and to learn, if possible, how large a balloon they would need.

Dogs! said the Sage, consider that under standard conditions a gallon of ideal gas contains 10²³ molecules, a number of entities which the Ancients called a mole. The twelfthmass upon which the scale of molecular weight is based is 1/131 × 10^-23 ounce and therefore a mole of the twefthmass amounts to 1/131 ounce.

Consider further the molecular weights of helium and air, continued the Sage. They are 4 and 29, the latter being an average of 28 for nitrogen and 32 for oxygen in their observed proportions. Accordingly the mass of a mole of helium is 4/131 ounce while that of a mole of air is 29/131 ounce. A mole of helium, which occupies a gallon under standard conditions of temperature and pressure, is therefore able, explained Confucius, to lift 25/131 ounce.

Most honored sage, the dogs ventured, what are these standard conditions whereof we hear you speaking? In the Wei Chun mountains, replied Confucius, on an afternoon in early autumn, the temperature is 2 grade and the pressure is 2 oc per square bone. We say these conditions are standard because the temperature equals the pressure when both are expressed in this manner. Foreigners have different ideas of what is normal. They say that normal pressure at sealevel is 2.19 oc per square bone, and as to temperature they have many norms including 2.19 grade for human body temperature. If the air in your lungs were at body temperature and the pressure deemed normal by foreigners then indeed the air's conditions would also be standard.

Sage, exclaimed the dogs, your wisdom extends beyond the stars and is even greater than that of a parrot! Let us always go ballooning when conditions are standard. But how then shall we determine the number of gallons of gas needed to lift us?

To understand that, Confucius answered, you must realize that your mass as normal dogs is 1000 ounces each. You must divide 4000 ounces (since there are four of you) by the 25/131 ounce which one gallon can lift—and make allowance as well for the bag and the basket.