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 is not a state function, as it depends on the path taken and not just the initial (base camp) and final (peak) states. (b) The change in elevation between base camp and peak is a state function, as it depends only on the initial and final states and is independent of the path taken.

Step-by-step solution

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

To determine if the distance traveled to the top is a state function, we need to consider if the distance depends only on the initial and final states (base camp and peak) or if it also depends on the path taken. Different routes can be taken to reach the peak, with varying distances. Therefore, the distance traveled depends on the path taken, not just the initial and final states. Hence, the distance traveled to the top is not a state function.

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

To determine if the change in elevation is a state function, we need to consider if the elevation difference depends only on the initial and final states (base camp and peak) or if it also depends on the path taken. Regardless of the route taken, the initial elevation (base camp) and the final elevation (peak) remain the same. The elevation difference is only dependent on these initial and final states, and not on the path taken. Hence, the change in elevation between base camp and peak is a state function.