Problem 31 - Chemistry: The Central Science in SI Units, Global Edition

Question

Would each of the following changes increase, decrease, or have no effect on the number of microstates available to a system: (a) increase in temperature, (b) decrease in volume, (c) change of state from liquid to gas?

Step-by-Step Solution

Answer

(a) Increase in temperature leads to an increase in the number of microstates due to more energy levels and positions being available for particles. (b) Decrease in volume leads to a decrease in the number of microstates due to less available positions and energy levels in confined spaces. (c) A change of state from liquid to gas leads to an increase in the number of microstates as particles have more freedom to move around and occupy various positions and energy levels.

Step 1: (a) Increase in Temperature

: When the temperature of a system increases, the energy of its individual particles also increases. With more energy, the particles can occupy more energy levels and positions. This increase in available energy levels and positions results in an increase in the number of possible microstates. Therefore, an increase in temperature leads to an increase in the number of microstates.

Step 2: (b) Decrease in Volume

: When the volume of a system decreases, the particles are confined to a smaller space. As a result, there are fewer positions and energy levels that these particles can occupy within this limited space. This decrease in available positions and energy levels leads to a decrease in the number of possible microstates. Therefore, a decrease in volume leads to a decrease in the number of microstates.

Step 3: (c) Change of state from liquid to gas

: As a substance changes from a liquid phase to a gaseous phase, the particles of the substance have more freedom to move around and occupy various energy levels and positions. In a gaseous state, the movement of particles is less constrained compared to their movement in a liquid state. This increase in the availability of positions and energy levels results in an increase in the number of possible microstates. Therefore, a change of state from liquid to gas leads to an increase in the number of microstates.

Key Concepts

Temperature Effect on Microstates

The effect of temperature on microstates is an intriguing aspect of thermodynamics. When temperature increases, it results in an increase in the energy of individual particles within a system. Higher energy means that particles will have the ability to access more energy levels. They can move to different positions within these levels, which significantly broadens the range of microstates available.

• Higher temperatures give particles more kinetic energy.
• More energy levels become accessible to particles.
• The result is an upsurge in the number of microstates.

Thus, when you increase the temperature of a system, the number of possible microstates increases due to the increased degree of freedom for particles.

Volume Effect on Microstates

Volume also plays a crucial role in the number of microstates a system can possess. When the volume is reduced, particles are confined to a smaller space. This reduction means fewer positions and energy levels are accessible because of the limited room.

• Decreased volume confines particles to a smaller area.
• This confines their possible positions and energy levels.
• Consequently, the number of possible microstates decreases.

In essence, a decrease in volume restricts particles’ movement and leads to a decline in microstates available within the system.

Phase Transition and Microstates

When a substance transitions from one phase to another, like from liquid to gas, the number of microstates is significantly affected. In a gas phase, particles have far more mobility than in a liquid phase.

• Gas phase allows particles to freely move in more directions.
• This means more energy levels and positions are accessible.
• The transition leads to an increased number of microstates.

Therefore, a phase change from liquid to gas increases the microstates due to the significant rise in movement and energy level options for particles.

Entropy and Microstates

Entropy is a fundamental concept directly related to microstates. It is essentially a measure of the disorder or randomness within a system. The more microstates available, the higher the entropy.

• Entropy is linked to the number of ways particles can be arranged.
• More microstates imply a higher degree of disorder.
• The system will have a higher entropy if it can occupy more microstates.

Entropy thus reflects the number of microstates, embodying the idea that systems tend to move towards greater disorder, allowing particles to maximize their possible arrangements.