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20 minutes on a train, 50 minutes on a bus, 6 hours in air terminals, 16 hours on an aeroplane, and 2 new passport stamps later I have made it to the Falkland Islands! So far it looks like the Welsh mountains or Scottish highlands with a few sheep and low level vegetation, but with far less evidence of humans. The roads are a mixture of solid and loose stones, no road markings, many cattle grids, occasional signs. The buildings generally have colourful, corrugated roofs; the vehicles are mostly 4×4’s. It’s cold. Ski jacket, gloves and hat cold – I hadn’t expected that so soon.

Whilst flying over the South Atlantic watching the layers of clouds between me and the ocean and trying to do some atmospheric physics revision, I started thinking about the air right outside the window. Television screens updated us on the flight conditions – including speed, height and local time. The air outside the window was a chilly -56°C.

What would happen if a parcel of air was brought inside? This high up (10972 m or 36000 feet according to the television screens) the pressure is much lower than at the Earth’s surface, so presuming the pressure inside the aircraft cabin is the Earth’s surface pressure, the pressure of the air parcel would increase.

When pressure is increased the temperature goes up – think what happens when you use a bike pump, the valve gets hot due to the pressure of the air being forced into the tyre.

So how much warmer would the air get? Potential temperature can be used to calculate this, it is the temperature a parcel would become if brought (at constant entropy, or energy state) to a reference pressure.

Potential temperature = T(Po/P)^(R/Cp)

Where T=temperature (in Kelvin), P0 = reference temperature, P=initial pressure, R= 287 Jkg-1K-1 (specific gas constant) and cp= 1004 Jkg-1K-1 (specific heat at constant pressure).

I knew T=-56 °C or 217 K, the aircraft height was 10972 m, which (from the US standard atmosphere look-up chart) corresponds to ~225 Pascals. The reference pressure inside the aircraft cabin is assumed to be surface pressure, ~1000 Pascals.

Substituting these values into the equation to calculate potential temperature:

Pot. T = 217 x (1000/225)^(R/Cp) = 332K or 59°C

So, rather oddly, the air outside the window would become uncomfortably hot if brought inside. Luckily this can only ever be a theoretical calculation, the cabin is pressurised, and so switching the air is not possible!

The same principles can be applied to the ocean, just in reverse. Water at depth is at a greater pressure than water at the surface due to the mass of water above it. If a water parcel could be brought to the surface at constant entropy it would lose temperature as its pressure would be decreased.

(Quick Disclaimer – these calculations have not been confirmed by a grown-up scientist… I think they are correct!)

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