Question

commercial planes routinely fly at altitudes of 10 km , where the atmospheric pressure is less than 0.3 atm , but the pressure inside the cabin is maintained at 0.75 atm . suppose you have an inflatable travel pillow that, once you reach cruising altitude, you inflate to a volume of 1.7 l and use to take a nap. you manage to sleep through the rest of the flight and awaken when the plane is about to land.What is the volume of the pillow after landing? Ignore any effect of the elasticity of the pillow’s material.

Answer 1

Main answer:

The volume of the pillow after landing will be approximately 4.08 liters.

Explanation:

When the plane reaches cruising altitude, the pressure inside the cabin is maintained at 0.75 atm, while the atmospheric pressure outside is less than 0.3 atm. The initial volume of the pillow at cruising altitude is 1.7 liters.

As the plane descends for landing, the external pressure increases, causing the volume of the inflated pillow to expand. Using Boyle's Law, which states that pressure and volume are inversely proportional at constant temperature, we can calculate the final volume of the pillow.

Given the change in external pressure from 0.3 atm to approximately 1 atm upon landing, the volume of the pillow can be calculated as Vf = Vi × (Pi / Pf), where Vi is the initial volume, Pi is the initial pressure, and Pf is the final pressure. Therefore, Vf = 1.7 L × (0.3 atm / 1 atm) ≈ 4.08 liters. This increase in volume occurs due to the higher external pressure upon landing, causing the inflated pillow to expand accordingly.

Answer 2

Using Boyle's Law, the volume of the pillow after landing can be calculated by comparing the initial and final pressures. The volume of the pillow after landing is 4.25 L.

Step-by-step explanation:

To find the volume of the pillow after landing, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume, as long as the temperature remains constant. In this case, the pressure inside the cabin is maintained at 0.75 atm and the atmospheric pressure at cruising altitude is 0.3 atm. Since the pressure is lower at cruising altitude, the volume of the pillow will increase.

To calculate the volume of the pillow after landing, we can use the equation:

P1*V1 = P2*V2

Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Substituting the known values, we have:

(0.75 atm)*(1.7 L) = (0.3 atm)*(V2)

Solving for V2, we get:

V2 = (0.75 atm)*(1.7 L) / (0.3 atm)

V2 = 4.25 L

Therefore, the volume of the pillow after landing is 4.25 L.