Ch.5 - Thermochemistry

Problem 5a

Chapter 5, Problem 5a

Imagine that you are climbing a mountain. (a) Is the distance you travel to the top a state function?

Verified step by step guidance

Understand the concept of a state function: A state function is a property whose value does not depend on the path taken to reach that specific value. Common examples include internal energy, enthalpy, and entropy.

Consider the nature of distance: Distance is a measure of the total path traveled between two points.

Analyze if the distance depends on the path: Since the distance you travel can vary depending on the route you take up the mountain, it is dependent on the path taken.

Compare distance with state functions: Contrast this with state functions where the change in value is the same regardless of the path taken between two states.

Conclude whether distance is a state function: Based on the dependency on the path, determine if distance qualifies as a state function or not.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

State Functions

State functions are properties that depend only on the current state of a system, not on the path taken to reach that state. Examples include temperature, pressure, and enthalpy. In the context of climbing a mountain, a state function would be the elevation at the top, which does not change regardless of the route taken.

Path Functions

Path functions are properties that depend on the specific path taken to reach a particular state. Work and heat are classic examples of path functions, as they vary based on the process used. In the mountain climbing scenario, the distance traveled to the top is a path function because it can differ based on the route chosen.

Thermodynamic Principles

Thermodynamic principles govern the relationships between energy, work, and heat in physical systems. Understanding these principles helps differentiate between state and path functions. In the mountain analogy, recognizing that the elevation (a state function) is independent of the distance traveled (a path function) illustrates how these principles apply to real-world scenarios.

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Related Practice

Textbook Question

The accompanying photo shows a pipevine swallowtail caterpillar climbing up a twig. (a) As the caterpillar climbs, its potential energy is increasing. What source of energy has been used to effect this change in potential energy?

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Textbook Question

Consider the accompanying energy diagram. (a) Does this diagram represent an increase or decrease in the internal energy of the system?

The contents of the closed box in each of the following illustrations represent a system, and the arrows show the changes to the system during some process. The lengths of the arrows represent the relative magnitudes of q and w. (a) Which of these processes is endothermic?

Imagine that you are climbing a mountain. (b) Is the change in elevation between your base camp and the peak a state function?

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Open Question

Under constant-volume conditions, the heat of combustion of naphthalene (C10H8) is 40.18 kJ/g. A 2.50-g sample of naphthalene is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.50 to 28.83 °C. (b) A 1.50-g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from 21.14 to 25.08 °C. What is the heat of combustion per gram of the new substance?

Textbook Question

The diagram shows four states of a system, each with different internal energy, E. (a) Which of the states of the system has the greatest internal energy?

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