Question

An airplane passenger has 100 cm³ of air in his stomach just before the plane takes off from a sea-level airport. What volume will the air have at cruising altitude if cabin pressure drops to 7.50 × 10⁴ N/m²?

a) 50.0 cm³
b) 75.0 cm³
c) 125 cm³
d) 150 cm³

Answer 1

The volume of air in the passenger's stomach at cruising altitude will be approximately 140 cm³.

Step-by-step explanation:

When the plane takes off and ascends to cruising altitude, the cabin pressure drops, causing the air in the passenger's stomach to expand. We can use Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure, to calculate the new volume of air. Using the formula V1P1 = V2P2, where V1 is the initial volume, P1 is the initial pressure, V2 is the final volume, and P2 is the final pressure, we can solve for V2:

V2 = (V1 * P1) / P2

Plugging in the values V1 = 100 cm³, P1 = 105 N/m² (sea level pressure), and P2 = 7.50 x 10⁴ N/m² (cruising altitude pressure), we get:

V2 = (100 cm³ * 105 N/m²) / (7.50 x 10⁴ N/m²)

V2 ≈ 140 cm³

Therefore, the volume of air in the passenger's stomach at cruising altitude will be approximately 140 cm³.