Final answer:
The volume of air in a passenger's stomach will increase when an airplane reaches cruising altitude due to the decrease in cabin pressure. By applying Boyle's Law, we can calculate the new volume by considering the initial volume and pressure at sea level, and the decreased pressure at cruising altitude. Cabin pressure, Boyle's Law, and cruising altitude are key to understanding this change in volume.
Step-by-step explanation:
The volume of air in an airplane passenger's stomach will change as the plane ascends to cruising altitude due to changes in pressure. At sea level, the atmospheric pressure is approximately 101,325 N/m² (1 atm). According to Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature remains constant (P1V1=P2V2), as the cabin pressure drops when the plane ascends, the volume of the gas will increase because the gas expands as the external pressure decreases.
So, if the air in the stomach is initially 100 cm³ at sea level pressure and the cabin pressure at cruising altitude drops to 7.50×10⁴ N/m², we can calculate the new volume (V2) using the equation V2 = (P1×V1)/P2. Plugging in the values: V2 = (101325 N/m² × 100 cm³) / 75000 N/m², we can find the new volume at cruising altitude.
Cabin pressure, Boyle's Law, and cruising altitude are important factors affecting volume of the air inside the stomach at different altitudes.