Problem 112 - Chemistry The Central Science

Question

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)?

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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.

Key Concepts

Elastomeric Polymers

Elastomeric polymers, like those found in rubber bands, are a fascinating type of material. They consist of long chains of molecules that are connected by flexible bonds. This structure allows them to stretch and return to their original shape. When you pull on a rubber band, the long polymer chains within it become aligned and more ordered.

This increased order leads to a decrease in entropy, which is a measure of disorder in the system. Initially, the elastomers are in a more disordered state, but as you stretch them, they lose some of that disorder.

These polymers are incredibly useful in everyday life. Their ability to stretch and recover without permanent deformation makes them ideal for use in products like elastic bands, tires, and various sealing applications.

In essence, elastomeric polymers are remarkable because of their capacity to balance flexibility and strength, offering useful applications across a wide range of industries.

Second Law of Thermodynamics

The second law of thermodynamics plays a crucial role in understanding how energy is transferred in a system. It states that the total entropy of an isolated system can never decrease over time. In simpler terms, processes tend to move towards greater disorder or maximum entropy.

When we apply this to an elastomeric polymer like a rubber band being stretched isothermally (at constant temperature), interesting things happen. Since stretching the band makes its molecular structure more ordered, its entropy decreases. To abide by the second law, heat must flow out of the system to compensate for this decrease in entropy.

In a practical context, this means when you stretch a rubber band and keep the temperature constant, it needs to release heat. The loss of heat is necessary because less entropy translates to less thermal energy stored within, aligning with the second law's regulation that entropy in a system doesn't spontaneously decrease.

Heat Transfer During Isothermal Process

Heat transfer during an isothermal process involves maintaining a constant temperature while allowing heat to flow in or out of a system as needed. This concept is essential when dealing with substances like elastomeric polymers.

Consider the rubber band exercise: when stretched isothermally, the rubber band becomes more ordered. According to the thermodynamic equation \[ΔS = \frac{Q}{T}\]where \(ΔS\) is the change in entropy, \(Q\) is the heat exchanged, and \(T\) is the temperature, the decreased entropy indicates a need for heat release to maintain constant temperature.

If you conduct the experiment, you notice a cooling effect on your lip when the band returns to its original state. This is because, upon contraction, the band absorbs heat from the environment to regain the thermal energy it emitted earlier.

Understanding this phenomenon gives insight into how thermodynamic principles govern everyday interactions, showing the importance of heat transfer in maintaining equilibrium in processes and systems.