Question

In experiment \(A\), a student mixes ink with water and notices that the two liquids mix evenly. In experiment \(\mathrm{B}\), the student mixes oil with water; in this case, the liquids separate into two different layers. The entropy change is: a. positive in experiment A and negative in experiment B. b. positive in experiment \(\mathrm{A}\) and zero in experiment \(\mathrm{B}\). c. negative in experiment \(A\) and positive in experiment \(B\). d. zero in experiment \(A\) and negative in experiment \(B\).

Short answer

a. positive in experiment A and negative in experiment B.

Step-by-step solution

Understanding Experiment A

In experiment A, ink is mixed with water, and the two liquids mix evenly. This uniform mixing results in an increase in disorder, or entropy, of the system.

Understanding Experiment B

In experiment B, oil is mixed with water, and the liquids separate into two distinct layers. This separation signifies a decrease in disorder, or entropy, because the substances become more ordered.

Determining Entropy Change for Experiment A

Since the ink and water mix evenly in experiment A, the entropy change is positive because the system becomes more disordered.

Determining Entropy Change for Experiment B

Because the oil and water separate into layers in experiment B, the entropy change is negative, as the system becomes more ordered.

Concluding the Correct Answer

Given the entropy changes identified in the previous steps, the correct choice is: a. positive in experiment A and negative in experiment B.

Key concepts

Entropy

Entropy is a measure of disorder or randomness in a system. In the context of thermodynamics, it signifies how energy is distributed among the particles of a system. The higher the entropy, the more disordered the system.
When two different liquids mix, as in experiment A where ink and water mix uniformly, the system’s entropy increases because the combined state is more random.
Conversely, when two liquids separate, like oil and water in experiment B, the system's entropy decreases because the molecules are more organized into distinct layers.
Understanding entropy helps in various fields such as predicting chemical reactions, energy distribution, and even the behavior of gases and solids.

Disorder in Systems

Disorder, or randomness, plays a crucial role in understanding entropy.
Imagine a well-organized bookshelf as a low-entropy system and a bookshelf with books randomly placed as a high-entropy system. In physics, disorder can be seen in how particles or molecules are arranged.
In experiment A, mixing ink with water results in a highly disordered system because the ink molecules spread evenly throughout the water.
This indicates high entropy. Conversely, in experiment B, oil and water don't mix uniformly but form separate layers. This separation signifies an orderly arrangement, resulting in lower entropy.
Recognizing the level of disorder in a system is essential for predicting how entropy will change.

Mixing Liquids

When two liquids are mixed, the change in entropy depends on how they interact.
Some liquids mix well, creating a homogeneous mixture with increased entropy due to enhanced disorder.
For example, ink and water in experiment A mix completely, increasing the system’s entropy.
On the other hand, some liquids don't mix well and instead separate into layers due to their molecular properties.
In experiment B, oil and water do not mix but form distinct layers, leading to a decrease in entropy as the system becomes more ordered.
The degree of mixing is a critical factor in determining whether the entropy change will be positive or negative.

Thermodynamics

Thermodynamics is the study of energy, heat, and work in systems. One of its essential principles is the Second Law, which states that the total entropy of an isolated system can never decrease over time.
This law helps explain why certain processes occur spontaneously.
For instance, in our example, ink mixes with water (experiment A) naturally because it leads to increased entropy.
Oil and water, however, naturally separate (experiment B) due to their molecular properties, resulting in a negative entropy change locally, even though the total entropy considering the surroundings may still increase.
Grasping the basics of thermodynamics, including entropy changes in mixing liquids, is crucial for fields like chemistry, physics, and engineering.