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Chapter 5: Problem 29

(a) What is meant by the term state function? (b) Give an example of a quantity that is a state function and one that is not. (c) Is the volume of a system a state function? Why or why not?

Short Answer

Expert verified
(a) A state function is a property of a system that depends only on its current state, determined by factors such as temperature, pressure, and composition, and is independent of the path taken to reach that state. (b) An example of a state function is internal energy (U), while an example of a non-state function is heat (q) or work (w). (c) Yes, the volume of a system is a state function, as it depends only on the current state of the system and is independent of the path taken to reach that state.

Step by step solution

01

Define state function

A state function is a property of a system that depends only on its current state, which is determined by its temperature, pressure, and composition. The value of a state function is independent of the path taken to reach that particular state. In other words, it only depends on the initial and final states of the system, not on the process between those states.
02

Provide an example of a state function and a non-state function

An example of a state function is internal energy (U). The internal energy of a system depends only on its current state, so it is independent of the path taken to reach that state. A quantity that is not a state function is heat (q) or work (w). Both heat and work depend on the path taken during the process, so they are not state functions.
03

Determine if volume is a state function and explain why or why not

The volume of a system is a state function. The volume depends only on the current state of the system, which is determined by factors such as temperature, pressure, and composition, and is independent of the path taken to reach that particular state. This is because the volume of a system is an extensive property that could be calculated by adding up the volumes of any subsystems based on their states, without the need to consider the history or path of how the system reached the given state.

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Most popular questions from this chapter

Consider a system consisting of the following apparatus, in which gas is confined in one flask and there is a vacuum in the other flask. The flasks are separated by a valve. Assume that the flasks are perfectly insulated and will not allow the flow of heat into or out of the flasks to the surroundings. When the valve is opened, gas flows from the filled flask to the evacuated one. (a) Is work performed during the expansion of the gas? (b) Why or why not? (c) Can you determine the value of \(\Delta E\) for the process?

Indicate which of the following is independent of the path by which a change occurs: (a) the change in potential energy when a book is transferred from table to shelf, (b) the heat evolved when a cube of sugar is oxidized to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\), (c) the work accomplished in burning a gallon of gasoline.

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is heated by adding 850 J of heat. It expands, doing $382 \mathrm{~J}\( of work on the atmosphere. (b) A \)50-g$ sample of water is cooled from \(30^{\circ} \mathrm{C}\) to \(15^{\circ} \mathrm{C}\), thereby losing approximately \(3140 \mathrm{~J}\) of heat. (c) A chemical reaction releases \(6.47 \mathrm{~kJ}\) of heat and does no work on the surroundings.

From the enthalpies of reaction $$ \begin{gathered} 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) \quad \Delta H=-221.0 \mathrm{~kJ} \\ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g)+4 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{CH}_{3} \mathrm{OH}(g) \quad \Delta H=-402.4 \mathrm{~kJ} \\ \text { calculate } \Delta H \text { for the reaction } \\ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g) \end{gathered} $$

You may have noticed that when you compress the air in a bicycle pump, the body of the pump gets warmer. (a) Assuming the pump and the air in it comprise the system, what is the sign of \(w\) when you compress the air? (b) What is the sign of \(q\) for this process? (c) Based on your answers to parts (a) and (b), can you determine the sign of \(\Delta E\) for compressing the air in the pump? If not, what would you expect for the sign of \(\Delta E\) ? What is your reasoning? [Section 5.2]
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