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Chapter 19: Problem 112

When most elastomeric polymers (e.g., a rubber band) are stretched, the molecules become more ordered, as illustrated here: Suppose you stretch a rubber band. (a) Do you expect the entropy of the system to increase or decrease? (b) If the rubber band were stretched isothermally, would heat need to be absorbed or emitted to maintain constant temperature? (c) Try this experiment: Stretch a rubber band and wait a moment. Then place the stretched rubber band on your upper lip, and let it return suddenly to its unstretched state (remember to keep holding on!). What do you observe? Are your observations consistent with your answer to part (b)?

Short Answer

Expert verified
In summary, when a rubber band is stretched, the entropy of the system decreases as the molecules become more ordered. During isothermal stretching, heat is emitted to maintain a constant temperature. In the experiment, the rubber band absorbs heat from its surroundings when returning to its unstretched state, resulting in a cooling sensation, which is consistent with the heat emission during isothermal stretching.

Step by step solution

01

1. Entropy change in the system

When a rubber band is stretched, its molecules become more ordered. Since entropy (S) is a measure of disorder, as the rubber band's molecules become more ordered, the entropy of the system decreases. So, the answer to part (a) is that the entropy of the system decreases when the rubber band is stretched.
02

2. Heat transfer during isothermal stretching

According to the second law of thermodynamics, the entropy change in an isothermal process is related to the heat transferred (Q) and the temperature (T) by the formula: \[ΔS = \frac{Q}{T}\] Since the entropy decreases when the rubber band is stretched, it means that during an isothermal process, heat must be emitted from the rubber band to maintain a constant temperature.
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3. Experiment

After stretching the rubber band and waiting a moment, place the stretched rubber band on your upper lip and, while still holding on, let it return to its unstretched state. When the rubber band contracts, you will observe a cooling sensation on your upper lip. This means that the rubber band absorbed some heat from its surroundings to regain the thermal energy it lost while contracting. This observation is consistent with the answer to part (b), in which we determined that heat would be emitted when the rubber band was stretched isothermally. Therefore, when the rubber band contracts, it absorbs heat.

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Most popular questions from this chapter

(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system? (b) For a certain process that occurs at constant \(T\) and \(P\) , the value of \(\Delta G\) is positive. Is the process spontaneous? (c) If \(\Delta G\) for a process is large, is the rate at which it occurs fast?

(a) In a chemical reaction, two gases combine to form a solid. What do you expect for the sign of \(\Delta S ?\) (b) How does the entropy of the system change in the processes described in Exercise 19.12\(?\)

(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which 2 mol of gaseous reactants are converted to 3 mol of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

Indicate whether \(\Delta G\) increases, decreases, or stays the same for each of the following reactions as the partial pressure of \(\mathrm{O}_{2}\) is increased: $$ \begin{array}{l}{\text { (a) } 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)} \\ {\text { (b) } 2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)} \\ {\text { (c) } 2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)}\end{array} $$

Indicate whether \(\Delta G\) increases, decreases, or does not change when the partial pressure of \(\mathrm{H}_{2}\) is increased in each of the following reactions: $$ \begin{array}{l}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)} \\ {\text { (b) } 2 \mathrm{HBr}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)} \\ {\text { (c) } 2 \mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)}\end{array} $$
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