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?

Short answer

(a) When a rubber band is stretched, the molecules become more ordered, which means the entropy of the system decreases. (b) During an isothermal process, heat needs to be absorbed to maintain a constant temperature while stretching the rubber band.

Step-by-step solution

Understanding entropy

Entropy is a thermodynamic quantity that measures the degree of randomness or disorder in a system. An increase in entropy means the system has become more disordered, while a decrease in entropy indicates an increase in orderliness. In the given scenario, when the rubber band is stretched, the molecules become more ordered. Therefore, we can infer that the entropy of the system changes.

Determine the change in entropy

Since the molecules become more ordered when the rubber band is stretched, we can conclude that the system becomes less disordered. Therefore, the entropy of the system decreases. Answer (a): The entropy of the system decreases.

Understanding isothermal processes

An isothermal process is a thermodynamic process that occurs at a constant temperature. In such a process, the heat absorbed by the system is used to do work on the system, without causing a change in temperature. In the given situation, we need to determine whether heat should be absorbed or emitted to maintain a constant temperature while the rubber band is stretched isothermally.

Determine the heat exchange for an isothermal process

In an isothermal process, the change in internal energy (∆U) is zero, since the temperature remains constant. So, the heat absorbed by the system (Q) is equal to the work done by the system (W): \[ Q = W \] Since the entropy of the system decreases when the rubber band is stretched, the process is non-spontaneous (i.e., it requires external work). Therefore, heat needs to be absorbed by the system to maintain a constant temperature during the isothermal process. Answer (b): Heat needs to be absorbed to maintain a constant temperature while the rubber band is stretched isothermally.

Key concepts

Understanding Entropy

Entropy is a fundamental concept in thermodynamics that helps us understand the level of disorder within a system. Imagine a messy room filled with toys and clothes scattered everywhere; that's high entropy. In contrast, a tidy room with everything in its place represents low entropy.

When the molecules of a substance, like those in a rubber band, get stretched, they often align more neatly—this looks more organized. Therefore, the entropy, or disorder, decreases. The concept of entropy is crucial because it signifies the energy within a system that isn’t available for doing useful work. Hence, when the rubber band becomes more ordered during stretching, it actually loses some of this disordered, unusable energy.

Exploring the Isothermal Process

The term 'isothermal' originates from Greek roots, where 'iso' means same and 'thermal' means heat. In an isothermal process, the temperature of the system remains consistently the same.

This is significant because, at constant temperature, all the heat added to the system goes into doing work instead of raising the internal energy. Mathematically, this is represented as \[ Q = W \] where \( Q \) is the heat exchanged and \( W \) is the work done. This means that for any work done during an isothermal expansion or compression, heat must enter or leave the system to maintain the constant temperature.

The Role of Heat Exchange

Heat exchange is the transfer of thermal energy from one system to another. When dealing with an isothermal process, the role of heat exchange becomes clear. Since the temperature does not change, any work done by or on the system requires a corresponding amount of heat to enter or exit the system, keeping everything balanced.

In the context of a stretched rubber band, imagine it as a spring. As you stretch it, it becomes more ordered, requiring energy input. So, even though it maintains constant temperature isothermally, it absorbs heat from the environment to perform this work. This external heat provides the necessary energy to order the molecules further.

Molecular Order and Thermodynamics

At the microscopic level, molecular order describes how molecules are arranged in a material. The more ordered the molecules, the lower the entropy, as demonstrated with the stretched rubber band—a more ordered state compared to when it's relaxed.

Molecular order has vital implications in thermodynamics. It dictates not just entropy changes but also how energy moves through systems. As molecules align more neatly, they often convey energy differently compared to when they're in a disorganized state. This concept ties directly into how entropy and heat exchange manifest in practical scenarios. Understanding the molecular order provides insight into the broader systems at play in thermodynamics.