Problem 49 - Chemistry Matter and Change

Question

Describe how a system's entropy changes if the system becomes more disordered during a process.

Step-by-Step Solution

Answer

Entropy increases when a system becomes more disordered.

Step 1: Define Entropy

Entropy is a measure of the disorder or randomness in a system. It quantifies the amount of information needed to describe the microscopic configurations of the system.

Step 2: Understand System Changes

When a system undergoes a process that leads to increased disorder, the possible configurations of its particles become more numerous and more random.

Step 3: Relate Disorder to Entropy

As the disorder increases, the entropy of the system increases. This is because more disorderly systems have a greater number of possible microstates, which means more information is needed to describe them.

Step 4: Use the Second Law of Thermodynamics

According to the second law of thermodynamics, in an isolated system, the entropy tends to increase or remain constant. Thus, when a system becomes more disordered during a process, the entropy increases.

Key Concepts

Second Law of Thermodynamics

The Second Law of Thermodynamics is a fundamental principle that describes how energy evolves in isolated systems. It states that the total entropy of an isolated system will tend to increase over time, reaching a state of maximum entropy. This essentially means that processes in such systems naturally evolve towards more disorder rather than order.

• Entropy is a measure of disorder: In isolated systems, the entropy will never decrease. It's the universe's way of ensuring energy is spread evenly.
• Natural processes favor increased entropy: For example, when ice melts into water, the molecules move from a structured lattice to a more random liquid state—thus increasing entropy.

The Second Law explains why certain processes happen spontaneously. If you mix two substances, they will naturally blend rather than separate. This is because the mixed state exhibits more disorder than the separate state, hence higher entropy.

System Disorder

System disorder refers to the complexity and unpredictability within a system. When we say a system is disordered, it means there is a higher level of randomness in the arrangement of its components. This is closely linked to the concept of entropy.

• Greater disorder means greater entropy: If a system's components are arranged randomly, it typically has more entropy.
• Order vs. Disorder: In a perfectly ordered system, all particles are arranged in a predictable pattern. As disorder increases, so do the combinations and randomness.

Let's imagine a neat stack of bricks. This is a low-disorder state. Knock them over into a pile, and the disorder — and thus the entropy — increases. This principle is what dictates that time flows in one direction, from order to disorder.

Microscopic Configurations

Microscopic configurations refer to the specific arrangements of particles in a system at a microscopic level. When we consider entropy, these configurations are crucial because they determine the level of disorder.

• Microstates and Macrostates: Each specific configuration of a system's components is a microstate. A macrostate describes a set of microstates that share the same macroscopic properties like pressure and temperature.
• More microstates mean higher entropy: As the number of possible microstates increases, the entropy of the system increases because there are more ways to achieve a given macrostate.

Consider a container with gas: Each gas molecule can occupy numerous positions, making countless microstates possible. As temperature increases, the molecules move faster and occupy positions more randomly, increasing the number of microstates and thus the entropy.