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Chapter 5: Problem 5

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

Expert verified
(a) The distance traveled to the top is not a state function because it depends on the specific path taken to climb the mountain and can change based on the chosen path. (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 states and remains the same regardless of the path taken to reach the peak.

Step by step solution

01

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

To decide if the distance traveled to the top is a state function or not, let's consider what would happen if we took different paths to climb the mountain. If the distance traveled depends on the specific path taken, then it is not a state function because its value depends on the process rather than just the initial and final states. Imagine climbing the mountain using a straight path from the base camp to the peak. The total distance traveled in this case would be different from when you take a more winding path up the mountain. Since the distance traveled changes depending on the chosen path, it is not a state function.
02

(Part b: Determine if the change in elevation between the base camp and the peak is a state function)

Now let's analyze the change in elevation between the base camp and the peak. In this case, we are looking at the difference in elevation between the two points, regardless of the path we take to reach the peak. Unlike the distance traveled in part (a), the change in elevation does not depend on the path taken. When you start at the base camp and eventually reach the peak, the difference in elevation would remain the same, regardless of the specific path taken. This property depends only on the initial and final states and does not rely on the process. Therefore, the change in elevation between the base camp and the peak is a state function.

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