What if a balloon floated very high?

Whoosh! A balloon floats up, up, up into the sky.

It gets smaller and smaller until you cannot see it. But is it really getting smaller? What happens to it way up high?

Every day, weather scientists let go of big balloons that carry small instruments high into the sky. As a balloon floats away it looks smaller and smaller, but that is only because it is getting farther away.

What really happens to its size? The air gets thinner and colder the higher you go. In this lab you can send a perfectly stretchy balloon from the seaside up to 20 kilometers, more than twice as high as Mount Everest, and watch its size as it rises.

The U.S. National Weather Service has measured the upper air with balloon-borne instruments called radiosondes since the late 1930s. A sealed balloon is a simple gas experiment: a fixed amount of gas whose volume responds to the pressure and temperature around it.

This lab follows a perfectly elastic balloon through the International Standard Atmosphere from 0 to 20 km. How much does it grow, how much do falling pressure and falling temperature each contribute, and where does the model part company with a real weather balloon?

At the seaside, there is lots of air all around the balloon.

The air pushes on the balloon from every side. The gas inside pushes back. So the balloon stays the same size.

At sea level, the air around a balloon presses on it from every side with a pressure of 101.3 kilopascals in the model. The gas inside presses outward just as hard, so the balloon stays the same size. In the lab, this is the balloon's launch size: 1.0 times.

The gas inside a balloon is like a spring that has been squashed a little. If the push from outside gets weaker, the gas can spread out.

At launch the model's balloon is at 101.325 kPa and 288.15 K, and its volume is the reference V₀ (1.0×). The model assumes the balloon is perfectly stretchy, so the gas inside is always at the outside pressure and temperature.

OpenStax describes the two gas laws at work. Boyle's law: at constant temperature, a fixed amount of gas has a volume inversely proportional to its pressure. Charles's law: at constant pressure, its volume is directly proportional to its kelvin temperature. A rising balloon experiences both changes at once.

Now Olly lets the balloon go. Up it floats!

The higher it goes, the bigger it gets. Way up high, it is many times bigger than when it started!

Set the height to 20 kilometers and press play. In the model the balloon rises at 5 meters per second and swells all the way up. By about 6.7 kilometers it is twice its launch size. Near where airliners fly, 11 kilometers up, it is 3.4 times as big. At 20 kilometers it is about 14 times as big.

Up there the air pressure is only 5.5 kilopascals, about one eighteenth of sea level, and the air is about −56 °C.

Ascending at 5 m/s, the model's balloon passes 2.0× at 6.7 km, 3.4× at 11 km, 10× at 18 km and reaches 13.9× at 20 km, where p = 5.47 kPa and T = 216.65 K (−56.5 °C).

Pressure alone would give p₀/p = 18.5. The cold, by Charles's law, shrinks that by T/T₀ = 0.75, giving 13.9. Because volume grows with the cube of size, a balloon 13.9 times bigger in volume is only about 2.4 times wider.

High up, there is less air. So the air pushes on the balloon less.

The gas inside can spread out. The balloon gets bigger!

Air has weight. UCAR explains that gravity pulls the air down toward Earth, so the air pressure is highest near the ground and gets lower the higher you go. NASA explains why: the higher you are, the less air there is above you.

As the balloon rises, the outside push gets weaker, so the gas inside spreads out until it pushes as hard as the air outside. Cold air works the other way: OpenStax explains that cooling a gas makes it shrink. But the pressure drops so much that the balloon still grows.

Pressure at any height is the weight of the air column above, so it falls with altitude (NASA Glenn). For a gas in a perfectly elastic balloon, pV = nRT with n fixed gives V/V₀ = (T/T₀)(p₀/p). In the troposphere both p and T fall; pressure falls far faster, so volume rises. Above 11 km the model's temperature is constant and the growth is pure Boyle's law.

The model's limits: it uses an average atmosphere; its balloon is perfectly stretchy, never bursts, and its gas always matches the outside temperature; and it stops at 20 km. Real balloons burst, and the NWS hangs its instruments 25 to 35 m below the balloon so that heat shed from the balloon's skin does not spoil the temperature readings: a reminder that a real balloon is not always at the temperature of the air around it.

Every day, scientists send up weather balloons. Each one carries a tiny box that measures the air.

The balloon grows and grows until it pops! Then a little parachute brings the box gently down.

The National Weather Service sends up weather balloons filled with hydrogen or helium. Each carries a radiosonde, a small box of instruments weighing 60 to 80 grams, that radios back the pressure, temperature, humidity and its position every second.

The NWS says the balloon is about 1.5 meters wide at launch and grows as the air pressure drops. When it is 6 to 8 meters wide, it bursts, and a small orange parachute slows the radiosonde's fall. By then it can be more than 35 kilometers up, far above our model's top.

According to the NWS, a radiosonde rises at about 300 meters per minute (5 m/s, the rate the model uses) and a typical sounding lasts more than two hours, reaching beyond 35 km and drifting more than 300 km. The instruments meet temperatures as low as −90 °C and pressures below 1 percent of the surface value.

The balloon grows from about 1.5 m across at release to 6 to 8 m when it bursts: four to more than five times wider. If it stayed round, the cube law gives roughly 64 to 150 times its launch volume (our arithmetic: 4³ = 64, 5.3³ ≈ 150), far more than the model's 13.9 at 20 km. More than 800 upper-air stations worldwide share these soundings.