physikanten & co // News // Dead Sea Science // Part 1: The Air Pressure

Part 1: The Air Pressure

The Dead Sea lies 428 metres below sea level, assuming that is the level of the world’s oceans. Water from Jordan flows into it but cannot flow out, instead it can only evaporate. The salt is left behind, giving the Dead Sea extraordinary properties.

The Dead Sea puts pressure on your ears…

I had the privilege of being accompanied by Hamse and Samir, two employees from the Jordan Children’s Museum. The journey began in the capital of Jordan, Amman, and took barely an hour. The experiments themselves however began before departure, in my hotel room on the sixth floor, approximately 970 metres above sea level. I wanted in particular to measure how big the difference in air pressure is between Amman (more specifically the hotel room) and the Dead Sea (on the beach). At any rate the height difference of around 1,400m should be clearly noticeable. In the same way that water pushes harder on your ears deep underwater compared to on the surface, a bigger air column likewise exerts more pressure.
Unfortunately in Amman I couldn’t get hold of a barometer. I really wanted to measure the difference in air pressure, and in the end I was encouraged through the internet chat of the British Interactive Group, an organisation of science communicators, who I had asked for ideas for experiments at the Dead Sea. The solution: a completely normal plastic drinking bottle. In my hotel room I emptied the bottle and sealed the cap on tightly, and simply took it with me to the Dead Sea. The increase in air pressure subsequently resulted in the bottle being squashed a decent amount during the journey.

At the Dead Sea I turned the bottle upside down, put it in a glass of tap water and opened it under the water. The bottle then immediately sucked in the water until it took on its normal shape. As I had no scales with me, I took the bottle home with me and weighed it there. Using the weight of this amount of water and a few calculations, I was able to determine the difference in air pressure between Amman and the Dead Sea.

For the sake of simplicity I assumed that the temperature in my hotel room and at the Dead Sea was the same, which is not really correct as it was April, and night time in the hotel, so it was rather cold. To be more precise, because of the broken air conditioning I was freezing…

The calculation

p0 = Air pressure in Amman
p1 = Air pressure at the Dead Sea
V0 = Volume in the bottle in Amman
V1 = Volume in the bottle at the Dead Sea
VW = Volume of water sucked in

For an ideal gas (at the same temperature) we can use Boyle-Mariotte’s law:
V0 • p0 = V1 • p1     (1)
The greater the pressure, the smaller the volume
For V1 therefore:
V1 = V0 - VW
For the difference in pressure Δp:
Δp = p1 - p0
p1 = Δp + p0
Which when inserted into (1) gives:
V0 • p0 = (V0 - VW) • (Δp + p0)
V0 • p0 = V0 • Δp + V0 • p0 - VW • Δp - VW • p0
0 = Δp • (V0 – VW) - VW • p0
Δp = (VW • p0) / (V0 – VW)
Δp = p0   / (V0 / VW - 1)
My values were:  
p0 (from the internet, as I had no barometer...) = 1017 hPa
V0 = 1,5 l
VW = 0,190 l
Therefore it follows:
Δp = 148 hPa
That is indeed a lot! To put this in comparison: the excess of pressure required to pop a balloon is 40 hPa. The pressure difference at the Dead Sea is more than three times as big!

According to Wikipedia the air pressure at the Dead Sea is 1060 hPa, which does not agree with my calculations. It is possible the stated value from Amman is too high. The temperature difference would also falsify the result in the other direction, meaning the bottle would not have been so strongly squashed together in a higher temperature.
Maybe next time someone goes to the sixth story of the Dana Plaza Hotel in Amman, they can take a barometer with them…

--->Click here to go to part two.

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