Final answer:
There is no general limit on the volume of liquids in checked baggage, but airline policies and safety regulations apply. For the physics problem, Boyle's law is used to calculate how air volume changes from sea level to cruising altitude when pressure decreases.
Step-by-step explanation:
When considering the volume of liquid you can take on a plane in checked baggage, there is generally no limit to the quantity. However, this is subject to airline policies and potential safety regulations regarding specific substances. As a physics problem, this question relates to how gas volumes change under different pressures, which can be explained by the Ideal Gas Law. For example, a passenger has 100 cm³ (cubic centimeters) of air in their stomach at sea level, and we want to determine what volume this air would occupy at cruising altitude where cabin pressure drops to 7.50×10⁴ N/m².
To solve this, we can use Boyle's Law which states that pressure and volume are inversely proportional for a given amount of gas at constant temperature. If we know the sea-level pressure (approximately 1.013×10⁵ N/m²), we can set up the equation P1V1 = P2V2 where P1 is the sea-level pressure, V1 is the original volume of air (100 cm³), P2 is the cabin pressure at cruising altitude, and V2 is the volume we want to find.
So, if we solve for V2, we get V2 = (P1V1) / P2. Plugging in the known values, sea-level pressure (P1) as 1.013×10⁵ N/m², original volume (V1) as 100 cm³, and cabin pressure (P2) as 7.50×10⁴ N/m², we can calculate the new volume (V2) of the air at cruising altitude.