Question

Consider an airplane trip from Chicago, Illinois, to Denver, Colorado. List some path-dependent functions and some state functions for the plane trip.

Short answer

Path-dependent functions for the airplane trip include total fuel consumption, total flight time, and the amount of turbulence encountered, as these depend on the specific route taken. State functions, which depend only on the initial and final states, include net change in altitude, net displacement, and net change in airspeed.

Step-by-step solution

Path-dependent functions examples:

1. Total fuel consumption: The amount of fuel consumed by an airplane during the trip depends on several factors, including the route taken. Different routes can have varying flight distances, altitudes, and atmospheric conditions, which affect the airplane's fuel consumption rate. 2. Total flight time: The time required to go from Chicago to Denver varies depending on the route, as well as the airplane's speed and the presence of any layovers. 3. Amount of turbulence encountered: Different routes will have different weather conditions and atmospheric factors, leading to varying levels of turbulence experienced throughout the flight.

State function examples:

1. Net change in altitude: After the trip from Chicago to Denver, the airplane will be at a higher altitude due to the different geographical elevation levels. The net change in altitude is a state function because it only depends on the starting and final altitudes. 2. Net displacement: The distance between Chicago and Denver remains constant, regardless of the route taken. Therefore, the net displacement is a state function. 3. Net change in airspeed: If the airplane starts from rest and ends the trip at rest, the net change in airspeed will be zero, no matter the specific path undertaken during the flight. This makes the net change in airspeed a state function. In summary, path-dependent functions are variables that depend on the specific route taken during the plane trip (e.g., total fuel consumption, total flight time, and the amount of turbulence encountered), while state functions are dependent only on the initial and final states of the system (e.g., net change in altitude, net displacement, and net change in airspeed).