Final answer:
The volume of air in the passenger's stomach at cruising altitude, when cabin pressure drops to 7.50 x 10⁴ N/m², would be approximately 134.67 cm³, having expanded from the original 100 cm³ at sea-level pressure.
Step-by-step explanation:
The student's question relates to the behavior of gases at different pressures, which is a topic in physics dealing with gas laws and their implications in real-world scenarios such as aviation.
Specifically, it combines concepts from Boyle's Law (or the more general Ideal Gas Law) and applications concerning oxygen requirements at high altitudes.
Volume of Air at Cruising Altitude
If an airplane passenger has 100 cm³ of air in their stomach at sea-level pressure (1.01 x 10⁵ N/m²), and the cabin pressure drops to 7.50 x 10⁴ N/m² at cruising altitude, assuming temperature remains constant (as per Boyle's Law:
P1V1 = P2V2), one can find the new volume (V2) using the initial conditions (P1 and V1). The calculation would be V2 = (P1V1)/P2. Plugging in the values from the question, V2 = (1.01 x 10⁵ N/m² * 100 cm³) / (7.50 x 10⁴ N/m²) = 134.67 cm³ (approximately).
Therefore, the volume of air at cruising altitude would be 134.67 cm³, indicating that the air has expanded due to the reduced pressure.