Problem 112 - Chemistry: The Central Science in SI Units, Global Edition

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

When a rubber band is stretched, its molecules become more ordered, leading to a decrease in entropy. If stretched isothermally, heat must be absorbed to maintain constant temperature. When a stretched rubber band returns to its unstressed state, it releases the absorbed heat, feeling cool to the touch. This observation is consistent with the requirement of heat absorption during isothermal stretching.

Step 1: (a) Entropy Change

When a rubber band is stretched, its molecules become more ordered as opposed to their relatively random alignment in the unstressed state. Entropy is a measure of the randomness or disorder of a system. So, when the rubber band is stretched and its molecules become more ordered, the entropy of the system decreases.

Step 2: (b) Heat Absorption/Emission

If the rubber band is stretched isothermally, it means the process takes place at a constant temperature. By stretching the rubber band, we are doing work on it, which requires energy. Since the entropy of the system decreases in this process (from part (a)), according to the second law of thermodynamics, the heat must flow into the system to maintain the total entropy constant. Therefore, heat needs to be absorbed by the rubber band to maintain a constant temperature during an isothermal stretch.

Step 3: (c) Observation after the Experiment

Stretch a rubber band and wait for a moment. Then, place the stretched rubber band on your upper lip and let it return suddenly to its unstressed state while still holding on to it. You will observe that the rubber band feels cool on your lip. This is because the rubber band absorbed heat from its surroundings while stretching (part (b)). When the rubber band returns to its unstressed state, the absorbed heat is released, making the rubber band feel cool to the touch. This observation is consistent with the answer given in part (b).

Key Concepts

Entropy

When discussing entropy, we are referring to a concept from thermodynamics that measures the disorder or randomness of a system. In an unstressed state, elastomeric polymers like rubber bands have molecules that are randomly aligned, creating a higher entropy level.
However, when the rubber band is stretched, the molecules become more orderly as they align along the direction of the stretch.

• This increased order leads to a decrease in entropy.
• Lower entropy indicates a state of less randomness.

As a general rule, when molecules in a material become more ordered, the system's entropy decreases. This understanding is crucial in predicting how systems behave under changes, such as stretching in elastomers. Remember, entropy is a way to gauge how "spread out" or "scattered" energy is within the system.

Isothermal Process

An isothermal process is one where the temperature remains constant throughout. Think about the gentle flow of heat in and out to keep that balance.
Now, apply this to a stretching rubber band. When you stretch it isothermally:

• The temperature needs to stay the same.
• You are doing work on the rubber band.

According to the laws of thermodynamics, particularly the second law, when you decrease the entropy by ordering the molecules more (as happens when stretching), some energy must compensate for this decrease. That means heat has to enter the system to maintain total entropy, leading to the absorption of heat from the surroundings.

Elastomeric Polymers

Elastomeric polymers, such as rubber bands, exhibit fascinating behaviors when subjected to forces like stretching. These polymers consist of large, flexible molecules that allow them to stretch and retract with relative ease.

• When these polymers are stretched, the molecular chains become elongated and align in a more ordered fashion.
• This alignment due to external stretching forces means reduced entropy, as discussed earlier.

Upon releasing a stretched rubber band, a kind of molecular "spring-back" occurs, where the chains return to their disordered state. During stretching, elastomeric polymers absorb heat from their surroundings to maintain thermal equilibrium; thus, when released, they cool, releasing the stored heat back, an effect you can feel on your skin during experiments.