Question

Imagine that you are climbing a mountain. (a) Is the distance you travel to the top a state function? Why or why not? (b) Is the change in elevation between your base camp and the peak a state function? Why or why not? [Section 5.2]

Short answer

(a) The distance traveled to the top of the mountain is not a state function because it can vary based on the path taken. (b) The change in elevation between the base camp and the peak is a state function because it remains the same regardless of the route taken.

Step-by-step solution

(a) Distance traveled as a state function

In order to determine if the distance traveled to the top of the mountain is a state function, we need to analyze whether the distance depends on the path taken or not. It is crucial to realize that a person could take several different paths up the mountain (direct path, zigzagging, etc.), which could result in different lengths of distance traveled. Since the distance traveled to the top of the mountain can vary based on the path taken, it is not a state function.

(b) Change in elevation as a state function

Now we will assess if the change in elevation between the base camp and the peak is a state function. Unlike the distance traveled, the change in elevation is not concerned with the path taken; it is solely concerned with the difference in height between the starting point and the ending point. The change in elevation between the base camp and the peak remains the same regardless of the route taken. Therefore, the change in elevation between the base camp and the peak is a state function.