Imagine that you are climbing a mountain. (a) Is the distance you travel to the top a state function?
Ch.5 - Thermochemistry
Chapter 5, Problem 6a
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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Identify the internal energy values for each state from the diagram.
Compare the internal energy values of all the states.
Determine which state has the highest internal energy value.
Conclude that the state with the highest internal energy value has the greatest internal energy.
Verify your conclusion by rechecking the values from the diagram.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Internal Energy
Internal energy is the total energy contained within a system, encompassing both kinetic and potential energy of the particles. It is a state function, meaning it depends only on the current state of the system, not on how it reached that state. Understanding internal energy is crucial for analyzing thermodynamic processes and predicting how energy will transfer in a system.
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Internal Energy
Thermodynamic States
A thermodynamic state refers to the condition of a system as defined by its properties, such as temperature, pressure, and volume. Each state can have a distinct internal energy value, which can be represented in diagrams. Recognizing the differences between these states is essential for determining which state has the highest internal energy.
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First Law of Thermodynamics
Energy Comparisons
Comparing internal energy across different states involves analyzing the factors that contribute to energy changes, such as temperature and phase changes. Higher temperatures generally correlate with higher internal energy due to increased molecular motion. This concept is vital for identifying which state in the diagram possesses the greatest internal energy.
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Related Practice
Textbook Question
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Textbook Question
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. (c) Write an expression for the difference in energy between State C and State D.
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Open Question
You may have noticed that when you compress the air in a bicycle pump, the body of the pump gets warmer. (c) Based on your answers to parts (a) and (b), can you determine the sign of _x001F_E for compressing the air in the pump? If not, what would you expect for the sign of _x001F_E? What is your reasoning?
Textbook Question
Imagine a container placed in a tub of water, as depicted in the accompanying diagram. (a) If the contents of the container are the system and heat is able to flow through the container walls, what qualitative changes will occur in the temperatures of the system and in its surroundings? From the system's perspective, is the process exothermic or endothermic?
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