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J. Perelman
"Entertaining physics". Book 2.
Chapter 6. Properties of liquids and gases

UP WITH STRATOSPHERIC

In previous articles we mentally traveled in the bowels of the earth, and helped us a formula for the dependence of air pressure from depth. Dare now to rise up and, using the same formula, let's see how changing the air pressure at high altitudes. The formula for this case takes the form:

R = 0,999h/8,

where p is the pressure in atmospheres, h is height in meters. The fraction 0,999 replaced here a number 1,001, because when you move up to 8 m, the pressure does not increase by 0.001, and decreases by 0.001.

Decide to start the task: how high you have to climb up to the air pressure was reduced to half?

This will equate in our formula for the pressure p = 0.5 and going to look for the height h. Get the equation 0,5 = 0,999h/8, to decide which will not be difficult for readers who are capable of dealing with logarithms. Answer h = 5.6 km determines the height at which the air pressure should be reduced by half.

Head is now even higher, after a brave Soviet aeronauts who have attained a height of 19 and 22 km. These high region of the atmosphere are already in the so-called "stratosphere". Therefore, the balls, which are similar rises, given the name not of balloons, and "stratospheric". I do not think that among the older generation there was at least one that is not heard if the names of the Soviet stratospheric "USSR" and "AAH-1", which in 1933 and 1934 world records elevation of the first 19 km, the second - 22 km

Try to calculate what the pressure of the atmosphere at these altitudes.

For a height of 19 km you will find that the air pressure should be

0,99919000/8 = 0,095 ATM = 72 mm

For a height of 22 km

0,99922000/8 = of 0.066 bar = 50 mm.

However, looking at the record of the stratosphere pilots, we find that at these heights were noted other pressure: at a height of 19 km of 50 mm, a height of 22 km - 45 mm

Why the calculation is not confirmed? What is our mistake?

The law of MARRIOTT for gases at such a low pressure is applied completely, but this time we did another omission: considered the temperature is the same throughout the 20-kilometre thicker, while it significantly decreases with height. On average take; that the temperature rise at each kilometer falls by 6.5°; it happens to the height of 11 km, where the temperature is equal to minus 56° and then at a considerable distance remains unchanged. If we take this fact into account (which is already insufficient funds elementary mathematics), you will get the results much more consonant with reality. For the same reason, the results of our previous calculations related to the pressure of the air in the depths, should also be viewed as approximate.

Entertaining physics J. Perelman

 




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