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?

Short answer

(a) Increasing the temperature will increase the number of microstates. (b) Decreasing volume will decrease the number of microstates. (c) Changing the state from liquid to gas will increase the number of microstates.

Step-by-step solution

(a) Increase in Temperature

Increasing the temperature of a system typically adds energy to it. The increased energy allows particles to move more freely (higher kinetic energy) and occupy different levels. This increase in ways particles can arrange themselves leads to an increase in the number of microstates available. Therefore, increasing the temperature will increase the number of microstates.

(b) Decrease in Volume

Decreasing the volume of a system means the particles will be confined to a smaller space. When particles are confined to a smaller space, they have fewer possible positions, which results in a decrease in the number of microstates available. Therefore, decreasing volume will decrease the number of microstates.

(c) Change of State from Liquid to Gas

When a system changes its state from liquid to gas, the particles now have more freedom to move around (higher kinetic energy) and occupy different levels. This change leads to an increased number of ways that particles can arrange themselves, leading to an increase in the number of microstates available. Therefore, changing the state from liquid to gas will increase the number of microstates.

Key concepts

Increase in Temperature and Microstates

Understanding how an increase in temperature affects microstates in thermodynamics is crucial for students grappling with the concept of entropy and the statistical nature of thermodynamic systems.

Consider a group of atoms in a solid block of metal. At low temperatures, these atoms vibrate but don't move from their fixed positions. As the temperature increases, the atoms gain kinetic energy and vibrate more vigorously. In the context of thermodynamics, these different energy levels and positions the atoms can occupy are referred to as 'microstates'.

An increase in temperature provides the system’s particles with more energy, allowing them to access a greater number of these energy levels and positions. The result is a larger number of possible arrangements or microstates. This is why, as the step-by-step solution indicates, increasing the temperature will increase the number of microstates available to a system. For students, visualizing particles as having the freedom to 'explore' more positions with increased temperature can help solidify this concept.

One can further relate this to the concept of entropy, where an increase in microstates corresponds to an increase in entropy, signifying a more disordered system.

Decrease in Volume and Its Effect on Microstates

Picturing how the decrease in volume affects microstates can be a bit more intuitive. Imagine a gas contained in a syringe; as the plunger is pushed down, the space available for the gas particles decreases. These particles, which once roamed the larger volume of the syringe, are now forced into closer proximity to one another.

In thermodynamic terms, the reduction in volume limits the positions and energy levels that particles can occupy—effectively reducing the number of microstates. This constraint means that the system's particles have fewer arrangements available, and this leads to a decrease in the entropy of the system. It's an inverse relationship compared to the effect of temperature; where temperature increased the number of microstates, a decrease in volume does the opposite, as the solution guide clearly explains.

This concept is foundational in understanding phenomena such as pressure increase in compressed gases and why such a system exhibits more ordered behavior as volume decreases.

Change of State in Thermodynamics

The change of state from liquid to gas introduces an intriguing shift in the number of microstates in a system. When a liquid becomes a gas, the molecules that were once relatively close together and sliding past one another—as is characteristic of liquids—are now much farther apart and moving independently.

This conversion means that molecules in a gaseous state have a hugely increased volume to explore and can occupy many more positions and energy levels. The increase in space and movement freedom directly correlates with an increase in microstates, as the solution suggests. This is a key feature of the gas state and provides insight into why gases exhibit high entropy.

A Real-World Example

Consider water evaporating from a puddle on a warm day. In its liquid state, water molecules are confined to the puddle's area. But as they evaporate and become a gas, each molecule can spread out into the atmosphere, increasing the number of possible microstates significantly. The change of state is a powerful illustration of thermodynamic principles at work and helps students comprehend the profound effect that phase transitions have on the behavior of particles in a thermodynamic system.