Textbook Question
(a) What is the difference between a state and a microstate of a system?
Ch.19 - Chemical Thermodynamics
Chapter 19, Problem 31b
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
Verified step by step guidance1
Understand the concept of microstates: Microstates refer to the different ways in which the energy of a system can be distributed among its particles at a given energy level. The number of microstates ( ext{W}) is related to the entropy ( ext{S}) of the system, where higher microstates mean higher entropy.
Consider the effect of volume on microstates: When the volume of a system decreases, the particles are confined to a smaller space. This confinement limits the number of positions and orientations each particle can assume.
Relate volume decrease to particle movement: In a smaller volume, particles have less space to move around, which reduces the number of possible energy distributions among the particles.
Conclude the effect on microstates: Since the number of available positions and orientations for particles decreases with a decrease in volume, the number of microstates ( ext{W}) available to the system also decreases.
Link to entropy: A decrease in the number of microstates leads to a decrease in the entropy ( ext{S}) of the system, according to the formula ext{S} = k ext{ln} ext{W}, where ext{k} is the Boltzmann constant.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Microstates
Microstates refer to the specific configurations or arrangements of particles in a system that correspond to a particular macroscopic state. The number of microstates is crucial in statistical mechanics, as it relates to the entropy of the system. A higher number of microstates indicates greater disorder and higher entropy, while fewer microstates suggest more order and lower entropy.
Recommended video:
Guided course
01:23
The Boltzmann Equation
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 while maintaining the same energy level. According to the second law of thermodynamics, the entropy of an isolated system tends to increase over time, reflecting a natural tendency towards greater disorder.
Recommended video:
Guided course
02:46Entropy in Thermodynamics
Volume and Microstates
The volume of a system directly influences the number of available microstates. When the volume decreases, the space available for particles to occupy is reduced, which typically leads to a decrease in the number of possible arrangements of those particles. Consequently, this reduction in volume generally results in a decrease in entropy, as there are fewer microstates available for the system.
Recommended video:
Guided course
02:35Constant-Volume Calorimetry
Related Practice
Textbook Question
(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?
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
(a) In a chemical reaction, two gases combine to form a solid. What do you expect for the sign of ΔS?
Textbook Question
(b) How does the entropy of the system change in the processes described in Exercise 19.12?