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Contextual Curriculum Connections
A9 Gas laws
in the context of weather balloons (and some other balloons)
The highest mountain peak on the planet is almost 9 km above sea level, and some flights may go to 11 km.
Weather balloons go three times as high. Then they burst.
Weather balloons carry sensing devices that then send their measurements of pressure, temperature and humidity back to the weather station. These devices are radiosondes.
Ascent, burst, and parachute descent of a weather balloon in the USA. (Also featured in topic A4.)
Atmospheric pressure at sea level is about 100 kPa.
Average global temperature at sea level is roughly 290 K.
Variation of temperature with altitude is more complex than variation of pressure.
Temperature decreases fairly linearly with altitude up to a little more than 10 km. Then there is a transition to increasing temperature.
At ground level
At altitude 33 kilometres
If the balloon has 1400 g and 2 g (approximately) makes up one mole, then a balloon is filled with about 700 mol of the gas.
It’s the same gas, hydrogen, and still the same amount – 700 mol.
At that altitude the latex material of the balloon is very stretched, so the balloon bursts.
The radiosonde can be returned to the ground by parachute.
Real gases behave, closely if not perfectly, according to some relationships that can be observed by experiment.
Boyle’s law: The volume of a fixed mass of gas at constant temperature is inversely proportional to pressure.
Taking a balloon up a mountain to demonstrate change in volume as pressure decreases.
(Pre-16 topic, but a worthy review.)
Charles’ law: The volume of a fixed mass of gas at constant pressure is proportional to temperature.
A fun … or at least enthusiastic … demonstration of volume change when balloons are submerged in liquid nitrogen, and then taken out again.
The pressure law: The pressure of a fixed mass of gas with constant volume is proportional to temperature.
In all of these three statements, the gas laws, the quantity of gas, whether measured in mass or in number of moles, stays the same. There are three variables, but simple experiments can only deal with two at a time.
The ultimate statement is that pV/T is constant.
For a fixed mass of gas, the starting values of pressure, volume, and temperature, p1, V1 and T1, such as at the Earth’s surface, and a set of later values, p2, V2, T2, such as high in the atmosphere, are related by:
p1V1/T1 = p2V2/T2
So, if at ground level,
p1 is 100 kPa, which is equal to 100 000 Pa
V1 is the volume of gas, typically 4 m3
and the temperature, if in the Antarctic, is 250 K (which is -23 °C)
and at an altitude of 33 km
p2 is 1 kPa, or 1000 Pa
T2 is again 250 K,
Then we can predict the new volume of gas, using
V2 = p1V1T2 / p2T1
= 100 000 x 4 x 250 / 1000 x 250
= 400 m3
The balloon’s volume is 100 times bigger than at ground level.
V2 / V1 = 400 / 4 =100
(C) David Brodie 2025 Note that all external videos and websites remain copyright of the creators