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 a mountain is not a state function because it depends on the chosen path and is path-dependent. (b) The change in elevation between the base camp and the peak is a state function because it only depends on the initial and final points of the ascent and is path-independent.

Step-by-step solution

(a) Determine if the distance to the top is a state function

To find out if the distance a person travels to the top of a mountain is a state function, we have to determine if this quantity is path-independent. That is, does the distance depend only on the current state of the person's ascent? In general, the path a person takes to climb a mountain could be different each time they climb it. Therefore, the distance traveled to reach the top depends on the chosen path. Since it is path-dependent, the distance traveled is not a state function.

(b) Determine if the change in elevation is a state function

For the change in elevation between the base camp and the peak, we'll again determine if this quantity is path-independent. Let's analyze if the change in elevation depends only on the initial and final points of the ascent. Both the base camp and the peak have fixed elevations, and the difference between these elevations will be the same regardless of the path taken to climb the mountain. As a result, the change in elevation is path-independent, and thus, the change in elevation is a state function.