IGCSE Chemistry 0620: Kinetic Theory of Gas Volume, Temperature and Pressure

A meteorologist fills the rubber envelope of a weather balloon with a fixed mass of helium gas at ground level, then seals the neck of the envelope so that no gas can escape or enter afterwards. The envelope is flexible: it stretches to a larger size whenever the trapped gas pushes outward harder than the surrounding air pushes inward, and it stops stretching as soon as the two pressures are equal again. So, once sealed, the pressure of the trapped helium always adjusts until it matches the pressure of the atmosphere immediately around the balloon.

(a) Before release, the sealed balloon is left standing in direct sunlight at ground level for several minutes, which warms the trapped helium. The atmospheric pressure at ground level stays constant throughout. State and explain, using the kinetic particle model, what happens to the volume of the helium gas as it warms in the sunlight. [3]

(b) The balloon is then released and rises into the atmosphere, where the atmospheric pressure is considerably lower than at ground level. Assume the temperature of the trapped helium stays approximately the same as the balloon climbs. State and explain, using the kinetic particle model, what happens to the volume of this fixed mass of trapped gas as the surrounding pressure falls. [3]

(c) As the balloon continues to rise, the surrounding pressure keeps falling, and at the same time sunlight continues to warm the trapped helium, raising its temperature further. State, with a reason, what happens to the volume of the trapped helium when both of these changes happen at the same time. [2]

Setting up the gas system

The balloon’s envelope is sealed, so the same fixed mass of helium particles is trapped inside throughout. None can escape or enter. But the envelope is also flexible, so it is free to stretch or shrink. This means the trapped gas is not stuck at one fixed volume: instead, its volume keeps adjusting so that the pressure it exerts outward always matches the pressure the atmosphere exerts inward on the envelope.

Part (a): Warming the trapped gas at constant (ground-level) pressure

Warming the helium inside the envelope increases the average kinetic energy of its particles, so the particles move faster on average. Faster-moving particles collide with the inside surface of the envelope more often and with greater force.

Because the envelope is flexible and the surrounding atmospheric pressure at ground level stays constant, the particles push the envelope outward. This continues until the same fixed number of particles is spread through a large enough volume that the pressure they exert on the inside of the envelope again matches the constant pressure of the atmosphere outside.

Result: the volume of the trapped helium increases as it warms at constant pressure.

Part (b): Rising to lower atmospheric pressure

As the balloon climbs, the outside atmospheric pressure falls, while the temperature of the trapped helium stays approximately the same. Since temperature is unchanged, the particles’ average speed does not change.

However, a lower outside pressure means the atmosphere is now pressing inward on the envelope with less force per unit area than before. Less force is therefore needed from the particles inside to balance this smaller outside pressure, so the same fixed mass of trapped particles spreads out into a larger volume, reducing how often and how hard they need to collide with the envelope, until the pressure they exert matches the new, lower outside pressure.

Result: the volume of the trapped helium increases further as the balloon rises into lower pressure, even though the temperature has not changed.

Part (c): Pressure and temperature changing together

From part (a): raising the temperature (at constant pressure) increases the gas’s volume. From part (b): lowering the pressure (at constant temperature) also increases the gas’s volume.

If the pressure falls and the temperature rises at the same time, both effects act in the same direction. Each one alone would increase the volume, so together they increase the volume by more than either change would on its own.

Final answers

(a) Volume increases: warming speeds up the particles, so they need more space (at constant outside pressure) for their collisions with the envelope to balance the atmosphere.
(b) Volume increases further: at constant temperature, a lower outside pressure means the particles need less force to balance it, so the fixed mass of trapped gas spreads into a larger volume.
(c) Volume increases by more than either change alone, since falling pressure and rising temperature both act to increase the trapped gas’s volume.