Final answer:
To determine the pressure altitude at cruising altitude, we use the initial pressure at sea level and the percentage decrease at cruising altitude, accounting for standard atmospheric pressure. The problem can be solved using Boyle's Law, by relating the drop in pressure to the increase in volume of a gas, given the initial volume and pressure conditions.
Step-by-step explanation:
To find the pressure altitude at cruising altitude, we utilize the relationships between pressure, volume, and altitude. The student's question involves the concept of how air pressure (Patm) changes with altitude and affects the volume of gas, according to Boyle's Law for a constant temperature.
Given that the standard atmospheric pressure at sea level is 760 mm Hg, which is equivalent to 101.325 kPa, and that the pressure at cruising altitude is approximately 80% of this value, we can estimate the pressure altitude. At cruising altitude, the cabin pressure typically drops, as in the example given where it drops to 7.50×104 N/m². To find the new volume of the air in the passenger's stomach at this reduced pressure, assuming constant temperature and number of moles of gas, we can use Boyle's Law:
V1 × P1 = V2 × P2
Where V1 is the initial volume (100 cm³), P1 is the initial pressure (760 mm Hg), V2 is the final volume, and P2 is the final pressure given in N/m² (which can be converted to mm Hg or atm for consistency).