Question

Predict the sign of \(\Delta S_{\text {sys }}\) for each process: (a) Gasoline vapors mix with air in a car engine. (b) Hot air expands. (c) Humidity condenses in cold air.

Short answer

a) Positive \(\Delta S_{\text{sys}}\). b) Positive \(\Delta S_{\text{sys}}\). c) Negative \(\Delta S_{\text{sys}}\).

Step-by-step solution

Identify Entropy Change in Mixing Process

When gasoline vapors mix with air in a car engine, the randomness or disorder of the system increases because you are mixing two different types of molecules. This leads to a positive change in entropy (ΔS).

Determine Entropy Change in Expansion of Hot Air

When hot air expands, the particles move to occupy a larger volume. This increased space allows for more positional possibilities for the particles, increasing disorder. Hence, \(\Delta S_{\text{sys}}\) is positive.

Analyze Entropy Change in Condensation

When humidity condenses in cold air, water vapor turns into liquid, which is a more ordered state compared to vapor. Thus, the entropy (\(\Delta S_{\text{sys}}\)) decreases, leading to a negative change in entropy.

Key concepts

entropy

Entropy is a measure of the disorder or randomness in a system. The higher the entropy, the more disordered the system is. Think of it as the amount of 'spread out' within a system.
For example, a messy room has high entropy compared to a neatly organized room because there are more ways to arrange the mess than the neatness.
Entropy is an integral concept in thermodynamics and helps predict the direction of processes. Systems tend to move towards higher entropy to become more stable. Thus, understanding entropy is crucial in figuring out how and why certain processes occur.

entropy change

Entropy change, denoted as \(\Delta S \), refers to the difference in entropy between the initial and final states of a system. A positive \(\Delta S \) means that the entropy has increased, leading to a more disordered system. Conversely, a negative \(\Delta S \) signifies a decrease in entropy, indicating a more ordered state.
In chemical and physical processes, the sign of \(\Delta S_{\text{sys}} \) can tell us a lot:

• Mixing substances usually increases entropy due to the increase in randomness.
• Expansion of gases or liquids tends to increase entropy because the molecules spread out more.
• Phase transitions, like condensation from gas to liquid, generally decrease entropy as the system becomes more ordered.

thermodynamics

Thermodynamics is the branch of physics that studies the relationships and conversions between heat and other forms of energy. It encompasses principles that explain how energy moves within and between systems.
There are four laws of thermodynamics:

• The Zeroth Law, which deals with thermal equilibrium.
• The First Law, which states that energy cannot be created or destroyed, only transformed (Law of Energy Conservation).
• The Second Law, which declares the tendency of systems to move towards higher entropy (greater disorder).
• The Third Law, which implies that as temperature approaches absolute zero, the entropy of a perfect crystal approaches zero.

Understanding these laws helps explain why processes occur naturally, like why heat flows from hot objects to cold ones and why certain chemical reactions take place.

phase transition

A phase transition is the transformation of a substance from one state of matter (solid, liquid, gas) to another. Examples include melting, freezing, and condensation.
During a phase transition, the entropy of the system changes significantly. For instance:

• Melting ice (solid to liquid) increases entropy because the water molecules move more freely in the liquid state than when they are locked in a solid structure.
• Freezing water (liquid to solid) decreases entropy as the molecules align into a more ordered solid form.
• Condensation (gas to liquid) also reduces entropy because gas molecules are more spread out compared to when they are in a liquid state.

By predicting the entropy change during these transitions, one can understand the energy dynamics and stability of different phases.