Tag Archives: pressure

Phase diagrams

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Everybody knows that water freezes at 0°C and melts at 100°C, right?

Except that’s not always true. The melting point and boiling point of water depends on the pressure of the water: water only freezes at 0°C and melts at 100°C when it’s at standard atmospheric pressure: 101325 pascals. For example, you cannot make a good cup of tea at the peak of Mount Everest because the pressure is lower there and therefore water boils at a lower temperature (around 71°C), lower than the temperature required to properly release the flavour from the tea.

Information about a substance’s melting and boiling points at different pressures can be represented on a phase diagram. The phase diagram for water is shown below:

Phase_diagram_of_water.svg

From the diagram, we can see that at pressures below around 600 Pa, water transforms from a solid to a gas without passing through a liquid phase. This is a process known as sublimation, and is most well-known from the carbon dioxide “fog” created when dry ice is placed into hot water. We can also see the triple point, a combination of temperature and pressure (0.01°C and 611.73 Pa) at which ice can exist in all three states simultaneously.

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Cyclohexane at its triple point boiling and freezing simultaneously.

At higher pressures, the melting point of water changes. Water can remain as solid ice up to temperatures of more than 300°C when the pressure is above ten gigapascals. What is also interesting is the different types of solid water that are formed at different pressures and temperatures.

Why you can’t open aeroplane doors in flight

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There have been many stories of people trying to open aeroplane doors whilst the aeroplane is in flight. Below is an explanation of why you shouldn’t worry if this happens during your flight.

The cruising altitude of most transport aeroplanes is about 38 000 feet (11 600 metres). At this altitude there is less air above the aeroplane pushing down upon it and thus the air pressure is lower. At 38 000 feet the air pressure is about 21 kilopascals (21 000 newtons per square metre) compared with 100 kilopascals (100 kPa) at ground level.

At this altitude there wouldn’t be enough oxygen present in the cabin air for people to breathe (this is why aeroplanes carry oxygen masks, in case the cabin depressurises for some reason). Therefore the cabin has to be kept pressurised to a greater level, usually to the equivalent of about 8000 feet (2440 metres). At 8000 feet the air pressure inside the cabin is about 75 kPa, more than three times the exterior pressure at cruising altitude. There is therefore a difference in pressure between the interior and exterior of the aeroplane of 54 kPa, or 54 000 newtons per square metre.

The passenger doors on a 747 (for example) are 1.19 metres wide by 1.93 metres tall, giving the door an area of 2.3 square metres. This means that there is a force of 124 000 newtons (54000 N/m2 × 2.3 m2) pushing the door closed. To put this in perspective, a force of 124 000 newtons is equivalent to the weight of 12.6 tonnes; so unless a passenger is some sort of Superman, capable of exerting a force bigger than this, the door will remain closed.

Aeroplane doors are wedge-shaped so that the fuselage bears this force, relying on the pressure differential rather than on some sort of internal locking mechanism to keep the door closed and maintain a good seal. The same is also true for spacecraft doors.

Thanks to JU for asking the question that prompted this post.

Biosphere lungs

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Some people refer to the rainforests as “Earth’s lungs”. In reality this is quite far from the truth, as rainforests actually contribute little (net) oxygen to Earth’s atmosphere; 70% of oxygen production is done by water-bourne green algae and the cyanobacteria present in every habitat on Earth.

Biosphere 2, a sealed ecological system built in Arizona to study the interaction between different forms of life and as a test of the possibility of using closed systems in space colonisation, also had lungs.

Biosphere 2’s oxygen came from the facility’s six biomes: a 1900 square meter rainforest, an 850 square meter “ocean”, a 450 square meter mangrove wetland, a 1300 square meter savannah grassland, a 1400 square meter fog desert and a 2500 square meter agricultural system.

During the day the heat of the Arizona sun would cause the air inside the facility to expand. In order to avoid the large pressure difference that this would create (5000 Pa, or 5% of standard atmospheric pressure), Biosphere 2’s creators included two giant hemispherical “lungs”.

As the air inside the facility expanded it would flow through underground tunnels into the lungs. Each lung contained a large weight hanging from a rubber sheet; as the air expanded during the day the increased pressure would raise the weight into the air. In the evening, as the air cooled, the weight would pull the rubber sheet back down and push air back into the facility, thereby equalising any pressure difference as it appeared.

Source: lumierefl

William Dempster, “Biosphere 2 engineering design”, Ecological Engineering 13 (1999): 31-42 doi:10.1016/S0925-8574(98)00090-1 (.PDF).

Boiling point and pressure

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A vapour is created when a substance forms a gas at a temperature below its boiling point; the vapour pressure of a liquid is the pressure of this vapour. A liquid boils when the vapour pressure of the liquid is equal to the atmospheric pressure of the air above it.

You can therefore boil a liquid in two ways: by heating it so that the vapour pressure increases to match the atmospheric pressure; or by decreasing the atmospheric pressure until it matches the vapour pressure at whatever the ambient temperature is.

In this video you can see me boiling water at room temperature: a beaker full of water at room temperature is placed in a vacuum chamber and the pressure lowered until it boils – the pressure gauge is on the right of the picture.

Notice how I can put my finger in the water both before and after boiling without scalding myself. It’s said that it’s impossible to make a good cup of tea at the summit of Mount Everest because water boils at only 70.4°C and this isn’t hot enough to properly brew tea.