Final answer:
If cabin pressure drops to 7.50×10⁴ N/m², the 100 cm³ of air in a passenger's stomach at sea level expands to approximately 1351 cm³ at cruising altitude, in accordance with Boyle's Law.
Step-by-step explanation:
When an airplane passenger experiences a loss of cabin pressure at high altitudes, the volume of gases in the body will expand due to the decrease in external pressure. This can be explained by Boyle's Law, which states that at constant temperature, the volume of a gas is inversely proportional to its pressure (P1V1=P2V2).
For example, if a passenger has 100 cm³ of air in his stomach at sea level where the pressure is approximately 101325 N/m², and then experiences a drop in cabin pressure to 7.50×10⁴ N/m² at cruising altitude, we can calculate the new volume (V2) using Boyle's Law:
(V1 * P1) / P2 = V2
(100 cm³ * 101325 N/m²) / 75000 N/m² = V2
V2 = 1351 cm³
The air in the passenger's stomach will expand to approximately 1351 cm³. This is a significant increase from the original 100 cm³ and showcases how changes in pressure affect gas volumes.