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

Some path-dependent functions for an airplane trip from Chicago to Denver include total distance traveled, fuel consumption, and total flight time. These quantities depend on the specific flight route and other factors such as wind conditions and delays. Some state functions for the trip include altitude difference, latitude and longitude, and temperature difference between the departure and arrival cities. These properties depend only on the initial and final states of the system, regardless of the path taken during the process.

Step-by-step solution

Understanding path-dependent functions

Path-dependent functions are properties or quantities that depend on the specific path taken during a process. In other words, the value of a path-dependent function depends on the detailed history of the system, such as the route of the trip. For the airplane trip, examples of path-dependent functions can include distance traveled, fuel consumption, and flight time.

List some path-dependent functions

Here are some examples of path-dependent functions for an airplane trip from Chicago to Denver: 1. Total distance traveled (in miles or kilometers): The exact distance traveled will depend on the specific flight route. 2. Fuel consumption (in gallons or liters): The fuel consumption of the airplane will depend on factors such as flight path, altitude, wind conditions, and any detours or stopovers. 3. Total flight time (in hours or minutes): The duration of the trip will depend on the route taken and factors like air traffic and other delays.

Understanding state functions

State functions are properties that depend only on the initial and final states of a system, regardless of the path taken during a process. In contrast to path-dependent functions, state functions do not depend on the detailed history of the system. For the airplane trip, examples of state functions can include altitude, latitude and longitude, and temperature difference between the departure and arrival cities.

List some state functions

Here are some examples of state functions for an airplane trip from Chicago to Denver: 1. Altitude difference (in feet or meters): This would be the difference in elevation between the airports in Chicago and Denver. This is a state function because it depends only on the initial and final elevations, not on the detailed flight path. 2. Latitude and longitude: These coordinates define the locations of the departure and arrival airports, and are independent of the flight route taken. 3. Temperature difference (in degrees Celsius or Fahrenheit): The temperature difference between the departure city (Chicago) and the arrival city (Denver) is independent of the flight path and depends only on the ambient temperatures of the two cities.