Why does a fountain pen often leak inside an aeroplane flying at high altitude?

Introduction / Context:
Many everyday observations can be explained using basic physics of pressure and fluids. One classic example is that a fountain pen, which works normally on the ground, may start leaking ink when carried in an aeroplane flying at high altitude. Understanding why this happens connects concepts of atmospheric pressure, pressure inside a container and the behaviour of liquids and trapped air when the surrounding pressure changes.

Given Data / Assumptions:
• The pen is a fountain type or ink pen with ink and trapped air inside its reservoir.
• The pen was filled and sealed at normal atmospheric pressure on the ground.
• The aeroplane is flying at high altitude where cabin pressure is lower than sea level pressure, even though it is partially regulated.
• Temperature changes are not large enough to be the main effect in this basic explanation.

Concept / Approach:
The key idea is the relation between pressure inside the pen and pressure outside in the cabin. When the pen is filled at ground level, the air above the ink is at roughly one atmosphere of pressure. As the aeroplane climbs, even in a pressurised cabin, the air pressure outside the pen decreases. The air trapped inside the reservoir now has a pressure greater than the surrounding air. Gases expand when external pressure drops. The expanding air inside the pen pushes on the ink, forcing it out through the nib and feed. This extra push overcomes the normal balance that keeps the ink in place and causes leakage.

Step-by-Step Solution:
Step 1: Consider the pen when it is filled and closed at ground level where outside atmospheric pressure is high. Step 2: Some air remains trapped above the ink and this enclosed air has the same pressure as the outside air at that moment. Step 3: When the aeroplane climbs to cruising altitude, the cabin pressure is reduced compared with ground pressure. Step 4: The trapped air inside the pen now has higher pressure than the air outside in the cabin. Step 5: This higher internal pressure makes the trapped air expand, which in turn pushes the ink out through the nib, leading to leakage.

Verification / Alternative check:
A similar effect is observed in other closed containers taken to lower external pressure, such as loosely sealed plastic bottles that bulge out slightly when taken to high mountains. In all these cases, the pressure inside was set at a higher external pressure at the time of sealing. As external pressure falls, the imbalance leads to expansion or leakage. For pens, manufacturers often advise travellers either to carry them empty or to keep them in a nib up position during flights, which is a practical confirmation that pressure differences are the main cause.

Why Other Options Are Wrong:
Reduced viscosity of the ink: A moderate change in temperature does not reduce viscosity enough to suddenly cause leakage in this way, and viscosity changes do not explain directional flow outwards.
Increased viscosity of the ink: Higher viscosity would actually make the ink flow more slowly, so it would help to prevent leakage, not cause it.
Higher atmospheric pressure outside the pen: In an aeroplane at altitude, cabin pressure is lower than ground level, so this statement is opposite to reality.
Very high temperature inside the cabin: Cabin temperature is controlled for passenger comfort and does not become high enough to directly cause such leaking behaviour on its own.

Common Pitfalls:
Learners sometimes blame temperature alone or think the ink boils, but modern aircraft cabins are temperature controlled and the main physical change is in pressure. Another confusion comes from mixing up cabin pressure with conditions outside the aircraft; although cabins are pressurised, they still operate at a lower pressure than sea level. The safest way to reason through such problems is to compare pressure inside a container with pressure outside and then apply the simple rule that gas expands when external pressure decreases, pushing on any liquid in contact with it.

Final Answer:
A fountain pen leaks in an aeroplane mainly because the atmospheric pressure outside the pen is lower at altitude, so the higher pressure air trapped inside expands and pushes the ink out.