Question

It is January, and you take off from New York City for a well deserved vacation in the Caribbean. After YOU REACH A CONSTANT CRUISING ALTITUDE of 30,000 ft, would you expect the pressure outside of the plane to...

Answer 1

The variation of atmospheric pressure with the altitude can be expressed by the following equation:

Where P is the pressure at a given height,

P_{​​​​​​0} is the atmospheric pressure at sea level=1013.25 mbar,

g is the acceleration due to gravity=9.8m/s^{​​​​​​2} ,

m is the molar mass of air=0.02896 kg/mol,

T is the average temperature of the Earth's atmosphere=288K,

And R is the universal gas constant=8.3143 N.m/mol.K

We are supposed to calculate the atmospheric pressure at the given height h=30000 ft=9144 m.

According to the expression given above, the atmospheric pressure decreases exponentially with height. So let us just plug in the values:

So the atmospheric pressure at a height of 30000 ft is about 344.09 mbar. In units of atm, this translates to about 0.33 atm.

In units of Pascal, this translates to about 34409 Pascal.