Airplanes typically fly at an altitude of about 10,000 meters. At this altitude the atmospheric pressure is significantly less than it is at sea-level. Because of this, airplane cabins must be pressurized so that the people on board can continue to get enough oxygen. If a typical 747 has a volume of 28,000 m3 and is filled with air at 101.3 kPa on the ground, what is the new volume of air inside when the cabin is pressurized to 75 kPa once it is in flight?

37,818.67 m3

Explanation:

The pressure a gas will exert on a container is inversely proportional to the volume of the gas. According to Boyle's law, at a constant temperature, the pressure of a gas is inversely proportional to its volume. The law can be mathematically represented thus:

   P1V1 = P2V2

In this case, P1 = 101.3 kPa, V1 = 28,000 m3, P2 = 75 kPa, V2 = ?

V2 = P1V1/P2

         =    101.3 x 28,000/75

                = 37,818.67 m3

Hence, the new volume of the air inside the cabin after pressurizing would be 37,818.67 m3.