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Ch.19 - Chemical Thermodynamics
All textbooksBrown 14th EditionCh.19 - Chemical ThermodynamicsProblem 30b
Chapter 19, Problem 30b

(b) As a system goes from state A to state B, its entropy decreases. What can you say about the number of microstates corresponding to each state?

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Understand the concept of entropy in thermodynamics, which is a measure of the disorder or randomness in a system. It is related to the number of microstates (W), which are the different ways in which the system's particles can be arranged while still having the same total energy.
Recognize that entropy (S) is related to the number of microstates by the Boltzmann's equation, S = k \ln(W), where k is the Boltzmann constant and W is the number of microstates.
Identify that a decrease in entropy, as the system goes from state A to state B, implies that the number of microstates in state B is less than in state A. This is because a decrease in entropy suggests a decrease in disorder or randomness, meaning fewer possible arrangements of particles.
Conclude that since the entropy decreases from state A to state B, state A has more microstates compared to state B. This means that state A is more disordered or has more configurations at the microscopic level compared to state B.
Apply this understanding to predict the behavior of systems in different scenarios, considering how changes in entropy reflect changes in the number of microstates and thus the disorder of the system.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of ways a system can be arranged at the microscopic level, with higher entropy indicating more disorder. When a system transitions from a state of higher entropy to lower entropy, it suggests a decrease in the number of accessible microstates.
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Microstates

Microstates refer to the specific configurations of a system at the molecular or atomic level that correspond to a particular macroscopic state. Each microstate represents a unique arrangement of particles, and the total number of microstates determines the entropy of the system. A decrease in entropy implies that the number of microstates available to the system has also decreased.
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Second Law of Thermodynamics

The Second Law of Thermodynamics states that in an isolated system, the total entropy can never decrease over time. This law implies that processes tend to move towards a state of greater disorder. However, in specific scenarios, such as the transition from state A to state B, if the entropy decreases, it may indicate that the system is interacting with its surroundings, leading to a net increase in the entropy of the universe.
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Related Practice
Textbook Question

For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = 0, and w = 0. (b) Explain why no work is done by the system during this process.

Textbook Question

(a) What is the difference between a state and a microstate of a system?

Textbook Question

(c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of ΔSsurr?

Textbook Question

Would each of the following changes increase, decrease, or have no effect on the number of microstates available to a system: (b) decrease in volume