Question

Decide Does the entropy of a system increase or decrease when you dissolve a cube of sugar in a cup of tea? Define the system, and explain your answer.

Short answer

The entropy of the system, defined as the cup of tea and the sugar cube, increases when a cube of sugar is dissolved in a cup of tea. This is because the dissolving process is irreversible, and the sugar particles become dispersed and mixed with the tea particles, resulting in a more disordered state. According to the second law of thermodynamics, when an irreversible process occurs, the entropy of the system will increase.

Step-by-step solution

Defining the system

We will define our system as the cup of tea and the sugar cube. The system includes the tea particles and the sugar particles.

Understanding entropy

Entropy is a thermodynamic property of a system that is a measure of the disorder or randomness of the particles within the system. In general, the higher the entropy, the greater the disorder. The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. When the process is irreversible, the entropy of the system will increase.

Analyzing the dissolving process

The dissolving process is irreversible, where the sugar cube dissolves into the tea, dispersing the sugar particles throughout the cup of tea. Initially, the sugar particles were ordered in a structured arrangement in the sugar cube, while the tea particles were randomly dispersed in the rest of the cup. Now, the sugar particles become mixed with the tea, creating a more disordered state.

Explaining the change in entropy

When the sugar cube dissolves, the sugar particles become dispersed and mixed with the tea particles, making the system more disordered. Since the dissolving process is irreversible and our system goes from a more ordered state to a more disordered state, the entropy will increase. Therefore, the entropy of the system increases when a cube of sugar is dissolved in a cup of tea.

Key concepts

Second Law of Thermodynamics

The Second Law of Thermodynamics is a fundamental principle in physics that explains the direction of various processes and phenomena. It states that the total entropy, or disorder, of an isolated system always tends to increase over time. This can be easily understood by imagining a process where energy becomes more spread out and less ordered. The second law is crucial in predicting whether a process will be spontaneous or require energy.

Imagine pouring milk into a cup of coffee. The milk will naturally mix with the coffee over time, creating a uniform color and taste. This spontaneous mixing increases the disorder, or entropy, of the system. According to the second law, natural processes like these increase entropy, reflecting the tendency towards more chaos or disorder in isolated systems.

Irreversible Process

An irreversible process is one that happens in one direction and cannot easily be reversed to restore the system and its surroundings to the original state. These processes often involve an increase in entropy. Take, for example, the act of smashing an egg. You can't easily put the egg back together again, and the system becomes more disordered after the smashing.

Real-world processes are mostly irreversible. They tend to produce more chaos. When a sugar cube dissolves in tea, the sugar particles spread out and do not neatly return to their original state. The increased randomness is characteristic of an irreversible process, and thus, the entropy of the system rises significantly.

Dissolving Process

The dissolving process is a great example of an irreversible process, commonly observed in everyday life. When you drop a sugar cube into a cup of tea, you initiate a dissolving process. Here, the sugar molecules disperse among the tea molecules.

Initially, the sugar molecules are orderly and compact in the cube, while the tea molecules are more disorganized. When they mix, the sugar breaks away from the structure and spreads throughout the tea, increasing disorder. This rise in disorder leads to an increase in entropy. The process is irreversible because once dissolved, the sugar does not separate from the tea without an external influence.

Thermodynamic Property

Entropy is a thermodynamic property that plays a pivotal role in thermodynamic systems. Properties in thermodynamics describe the condition or state of a system. Entropy is particularly important as it measures the degree of randomness or disorder across the system.

Thermodynamic properties like pressure, temperature, and volume are used to describe systems and predict changes. Unlike the potentially intuitive properties like temperature, entropy measures are often less visible. To visualize, consider a clean, organized room. As items are used and leave their place, the room becomes more untidy or disordered, akin to an increase in entropy. In thermodynamics, observing these changes in properties helps us understand and predict energy distribution and system behavior.